From ed4bf24eedc4d0044a1bdc6b12c0115bb793a269 Mon Sep 17 00:00:00 2001
From: GitHub Action <action@github.com>
Date: Fri, 1 Mar 2024 23:22:49 +0000
Subject: [PATCH] Update documentation

---
 _images/MN_geopartition_ensamble.gif          |  Bin 293742 -> 289091 bytes
 _images/example_box_pandas.svg                | 1347 ++++++++---------
 _images/gerrymandria_ensamble.gif             |  Bin 168480 -> 183039 bytes
 _images/gerrymandria_region_ensamble.gif      |  Bin 124008 -> 236274 bytes
 _images/gerrymandria_water_and_muni_aware.png |  Bin 51733 -> 51999 bytes
 _images/gerrymandria_water_muni_ensamble.gif  |  Bin 123875 -> 178538 bytes
 .../gerrychain/proposals/tree_proposals.html  |   22 +-
 _modules/gerrychain/tree.html                 |  342 ++++-
 _sources/user/data.rst.txt                    |   40 +-
 _sources/user/geometries.rst.txt              |    2 +-
 _sources/user/install.rst.txt                 |    3 +-
 _sources/user/partitions.rst.txt              |    4 +-
 _sources/user/quickstart.rst.txt              |    4 +-
 _sources/user/recom.rst.txt                   |  166 +-
 api.html                                      |   49 +-
 full_ref.html                                 |   59 +-
 genindex.html                                 |    2 +
 index.html                                    |    3 +-
 objects.inv                                   |  Bin 1720 -> 1708 bytes
 searchindex.js                                |    2 +-
 user/data.html                                |  102 +-
 user/geometries.html                          |    2 +-
 user/install.html                             |    3 +-
 user/partitions.html                          |    4 +-
 user/quickstart.html                          |    4 +-
 user/recom.html                               |  143 +-
 26 files changed, 1264 insertions(+), 1039 deletions(-)

diff --git a/_images/MN_geopartition_ensamble.gif b/_images/MN_geopartition_ensamble.gif
index 5c127ef14d7c9f5dea7a7f1ff011a67226b6e76b..ef8c6d3e415485b19e916c74a229af78604f1949 100644
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index a6c7f2a0..a60186e1 100644
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diff --git a/_modules/gerrychain/proposals/tree_proposals.html b/_modules/gerrychain/proposals/tree_proposals.html
index 8a942520..75eaaaa9 100644
--- a/_modules/gerrychain/proposals/tree_proposals.html
+++ b/_modules/gerrychain/proposals/tree_proposals.html
@@ -104,7 +104,6 @@ <h1>Source code for gerrychain.proposals.tree_proposals</h1><div class="highligh
     <span class="n">ReselectException</span><span class="p">,</span>
 <span class="p">)</span>
 <span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="n">Callable</span><span class="p">,</span> <span class="n">Optional</span><span class="p">,</span> <span class="n">Dict</span><span class="p">,</span> <span class="n">Union</span>
-<span class="kn">import</span> <span class="nn">warnings</span>
 
 
 <div class="viewcode-block" id="MetagraphError"><a class="viewcode-back" href="../../../full_ref.html#gerrychain.proposals.MetagraphError">[docs]</a><span class="k">class</span> <span class="nc">MetagraphError</span><span class="p">(</span><span class="ne">Exception</span><span class="p">):</span>
@@ -131,7 +130,7 @@ <h1>Source code for gerrychain.proposals.tree_proposals</h1><div class="highligh
     <span class="n">pop_target</span><span class="p">:</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">float</span><span class="p">],</span>
     <span class="n">epsilon</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
     <span class="n">node_repeats</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
-    <span class="n">weight_dict</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">Dict</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+    <span class="n">region_surcharge</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">Dict</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
     <span class="n">method</span><span class="p">:</span> <span class="n">Callable</span> <span class="o">=</span> <span class="n">bipartition_tree</span><span class="p">,</span>
 <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Partition</span><span class="p">:</span>
     <span class="sd">&quot;&quot;&quot;</span>
@@ -173,33 +172,24 @@ <h1>Source code for gerrychain.proposals.tree_proposals</h1><div class="highligh
 <span class="sd">    :type epsilon: float</span>
 <span class="sd">    :param node_repeats: The number of times to repeat the bipartitioning step. Default is 1.</span>
 <span class="sd">    :type node_repeats: int, optional</span>
-<span class="sd">    :param weight_dict: The weight dictionary for the graph used for region-aware</span>
+<span class="sd">    :param region_surcharge: The surcharge dictionary for the graph used for region-aware</span>
 <span class="sd">        partitioning of the grid. Default is None.</span>
-<span class="sd">    :type weight_dict: Optional[Dict], optional</span>
+<span class="sd">    :type region_surcharge: Optional[Dict], optional</span>
 <span class="sd">    :param method: The method used for bipartitioning the tree. Default is</span>
 <span class="sd">        :func:`~gerrychain.tree.bipartition_tree`.</span>
 <span class="sd">    :type method: Callable, optional</span>
 
 <span class="sd">    :returns: The new partition resulting from the ReCom algorithm.</span>
 <span class="sd">    :rtype: Partition</span>
-
-<span class="sd">    :raises ValueWarning: Raised when the sum of the weights in the weight dictionary is</span>
-<span class="sd">        greater than 1.</span>
 <span class="sd">    &quot;&quot;&quot;</span>
 
     <span class="n">bad_district_pairs</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
     <span class="n">n_parts</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">partition</span><span class="p">)</span>
     <span class="n">tot_pairs</span> <span class="o">=</span> <span class="n">n_parts</span> <span class="o">*</span> <span class="p">(</span><span class="n">n_parts</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>  <span class="c1"># n choose 2</span>
 
-    <span class="c1"># Try to add the region aware in if the method accepts the weight dictionary</span>
-    <span class="k">if</span> <span class="s2">&quot;weight_dict&quot;</span> <span class="ow">in</span> <span class="n">signature</span><span class="p">(</span><span class="n">method</span><span class="p">)</span><span class="o">.</span><span class="n">parameters</span><span class="p">:</span>
-        <span class="n">method</span> <span class="o">=</span> <span class="n">partial</span><span class="p">(</span><span class="n">method</span><span class="p">,</span> <span class="n">weight_dict</span><span class="o">=</span><span class="n">weight_dict</span><span class="p">)</span>
-        <span class="k">if</span> <span class="n">weight_dict</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="nb">sum</span><span class="p">(</span><span class="n">weight_dict</span><span class="o">.</span><span class="n">values</span><span class="p">())</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
-            <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
-                <span class="s2">&quot;</span><span class="se">\n</span><span class="s2">The sum of the weights in the weight dictionary is greater than 1.</span><span class="se">\n</span><span class="s2">&quot;</span>
-                <span class="s2">&quot;Please consider normalizing the weights.&quot;</span><span class="p">,</span>
-                <span class="n">ValueWarning</span><span class="p">,</span>
-            <span class="p">)</span>
+    <span class="c1"># Try to add the region aware in if the method accepts the surcharge dictionary</span>
+    <span class="k">if</span> <span class="s2">&quot;region_surcharge&quot;</span> <span class="ow">in</span> <span class="n">signature</span><span class="p">(</span><span class="n">method</span><span class="p">)</span><span class="o">.</span><span class="n">parameters</span><span class="p">:</span>
+        <span class="n">method</span> <span class="o">=</span> <span class="n">partial</span><span class="p">(</span><span class="n">method</span><span class="p">,</span> <span class="n">region_surcharge</span><span class="o">=</span><span class="n">region_surcharge</span><span class="p">)</span>
 
     <span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">bad_district_pairs</span><span class="p">)</span> <span class="o">&lt;</span> <span class="n">tot_pairs</span><span class="p">:</span>
         <span class="k">try</span><span class="p">:</span>
diff --git a/_modules/gerrychain/tree.html b/_modules/gerrychain/tree.html
index d14d8c8b..74ebb4d5 100644
--- a/_modules/gerrychain/tree.html
+++ b/_modules/gerrychain/tree.html
@@ -124,6 +124,7 @@ <h1>Source code for gerrychain.tree</h1><div class="highlight"><pre>
 <span class="kn">from</span> <span class="nn">inspect</span> <span class="kn">import</span> <span class="n">signature</span>
 <span class="kn">import</span> <span class="nn">random</span>
 <span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">deque</span><span class="p">,</span> <span class="n">namedtuple</span>
+<span class="kn">import</span> <span class="nn">itertools</span>
 <span class="kn">from</span> <span class="nn">typing</span> <span class="kn">import</span> <span class="p">(</span>
     <span class="n">Any</span><span class="p">,</span>
     <span class="n">Callable</span><span class="p">,</span>
@@ -148,35 +149,35 @@ <h1>Source code for gerrychain.tree</h1><div class="highlight"><pre>
 
 
 <div class="viewcode-block" id="random_spanning_tree"><a class="viewcode-back" href="../../full_ref.html#gerrychain.tree.random_spanning_tree">[docs]</a><span class="k">def</span> <span class="nf">random_spanning_tree</span><span class="p">(</span>
-    <span class="n">graph</span><span class="p">:</span> <span class="n">nx</span><span class="o">.</span><span class="n">Graph</span><span class="p">,</span> <span class="n">weight_dict</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">Dict</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>
+    <span class="n">graph</span><span class="p">:</span> <span class="n">nx</span><span class="o">.</span><span class="n">Graph</span><span class="p">,</span> <span class="n">region_surcharge</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">Dict</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>
 <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">nx</span><span class="o">.</span><span class="n">Graph</span><span class="p">:</span>
     <span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Builds a spanning tree chosen by Kruskal&#39;s method using random weights.</span>
 
 <span class="sd">    :param graph: The input graph to build the spanning tree from. Should be a Networkx Graph.</span>
 <span class="sd">    :type graph: nx.Graph</span>
-<span class="sd">    :param weight_dict: Dictionary of weights to add to the random weights used in region-aware</span>
-<span class="sd">        variants.</span>
-<span class="sd">    :type weight_dict: Optional[Dict], optional</span>
+<span class="sd">    :param region_surcharge: Dictionary of surcharges to add to the random</span>
+<span class="sd">        weights used in region-aware variants.</span>
+<span class="sd">    :type region_surcharge: Optional[Dict], optional</span>
 
 <span class="sd">    :returns: The maximal spanning tree represented as a Networkx Graph.</span>
 <span class="sd">    :rtype: nx.Graph</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="k">if</span> <span class="n">weight_dict</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-        <span class="n">weight_dict</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
+    <span class="k">if</span> <span class="n">region_surcharge</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">region_surcharge</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">()</span>
 
     <span class="k">for</span> <span class="n">edge</span> <span class="ow">in</span> <span class="n">graph</span><span class="o">.</span><span class="n">edges</span><span class="p">():</span>
         <span class="n">weight</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">()</span>
-        <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">weight_dict</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+        <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">region_surcharge</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
             <span class="k">if</span> <span class="p">(</span>
-                <span class="n">graph</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="n">key</span><span class="p">]</span> <span class="o">==</span> <span class="n">graph</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">]][</span><span class="n">key</span><span class="p">]</span>
+                <span class="n">graph</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="n">key</span><span class="p">]</span> <span class="o">!=</span> <span class="n">graph</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">]][</span><span class="n">key</span><span class="p">]</span>
                 <span class="ow">and</span> <span class="n">graph</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="n">key</span><span class="p">]</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span>
             <span class="p">):</span>
                 <span class="n">weight</span> <span class="o">+=</span> <span class="n">value</span>
 
         <span class="n">graph</span><span class="o">.</span><span class="n">edges</span><span class="p">[</span><span class="n">edge</span><span class="p">][</span><span class="s2">&quot;random_weight&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">weight</span>
 
-    <span class="n">spanning_tree</span> <span class="o">=</span> <span class="n">tree</span><span class="o">.</span><span class="n">maximum_spanning_tree</span><span class="p">(</span>
+    <span class="n">spanning_tree</span> <span class="o">=</span> <span class="n">tree</span><span class="o">.</span><span class="n">minimum_spanning_tree</span><span class="p">(</span>
         <span class="n">graph</span><span class="p">,</span> <span class="n">algorithm</span><span class="o">=</span><span class="s2">&quot;kruskal&quot;</span><span class="p">,</span> <span class="n">weight</span><span class="o">=</span><span class="s2">&quot;random_weight&quot;</span>
     <span class="p">)</span>
     <span class="k">return</span> <span class="n">spanning_tree</span></div>
@@ -295,10 +296,12 @@ <h1>Source code for gerrychain.tree</h1><div class="highlight"><pre>
 
 
 <span class="c1"># Tuple that is used in the find_balanced_edge_cuts function</span>
-<span class="n">Cut</span> <span class="o">=</span> <span class="n">namedtuple</span><span class="p">(</span><span class="s2">&quot;Cut&quot;</span><span class="p">,</span> <span class="s2">&quot;edge subset&quot;</span><span class="p">)</span>
+<span class="n">Cut</span> <span class="o">=</span> <span class="n">namedtuple</span><span class="p">(</span><span class="s2">&quot;Cut&quot;</span><span class="p">,</span> <span class="s2">&quot;edge weight subset&quot;</span><span class="p">)</span>
+<span class="n">Cut</span><span class="o">.</span><span class="fm">__new__</span><span class="o">.</span><span class="vm">__defaults__</span> <span class="o">=</span> <span class="p">(</span><span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">)</span>
 <span class="n">Cut</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="s2">&quot;Represents a cut in a graph.&quot;</span>
-<span class="n">Cut</span><span class="o">.</span><span class="n">edge</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="s2">&quot;The edge where the cut is made.&quot;</span>
-<span class="n">Cut</span><span class="o">.</span><span class="n">subset</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="s2">&quot;The subset of nodes on one side of the cut.&quot;</span>
+<span class="n">Cut</span><span class="o">.</span><span class="n">edge</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="s2">&quot;The edge where the cut is made. Defaults to None.&quot;</span>
+<span class="n">Cut</span><span class="o">.</span><span class="n">weight</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="s2">&quot;The weight assigned to the edge (if any). Defaults to None.&quot;</span>
+<span class="n">Cut</span><span class="o">.</span><span class="n">subset</span><span class="o">.</span><span class="vm">__doc__</span> <span class="o">=</span> <span class="s2">&quot;The (frozen) subset of nodes on one side of the cut. Defaults to None.&quot;</span>
 
 
 <div class="viewcode-block" id="find_balanced_edge_cuts_contraction"><a class="viewcode-back" href="../../full_ref.html#gerrychain.tree.find_balanced_edge_cuts_contraction">[docs]</a><span class="k">def</span> <span class="nf">find_balanced_edge_cuts_contraction</span><span class="p">(</span>
@@ -325,7 +328,14 @@ <h1>Source code for gerrychain.tree</h1><div class="highlight"><pre>
     <span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">leaves</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
         <span class="n">leaf</span> <span class="o">=</span> <span class="n">leaves</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span>
         <span class="k">if</span> <span class="n">h</span><span class="o">.</span><span class="n">has_ideal_population</span><span class="p">(</span><span class="n">leaf</span><span class="p">):</span>
-            <span class="n">cuts</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Cut</span><span class="p">(</span><span class="n">edge</span><span class="o">=</span><span class="p">(</span><span class="n">leaf</span><span class="p">,</span> <span class="n">pred</span><span class="p">[</span><span class="n">leaf</span><span class="p">]),</span> <span class="n">subset</span><span class="o">=</span><span class="n">h</span><span class="o">.</span><span class="n">subsets</span><span class="p">[</span><span class="n">leaf</span><span class="p">]</span><span class="o">.</span><span class="n">copy</span><span class="p">()))</span>
+            <span class="n">e</span> <span class="o">=</span> <span class="p">(</span><span class="n">leaf</span><span class="p">,</span> <span class="n">pred</span><span class="p">[</span><span class="n">leaf</span><span class="p">])</span>
+            <span class="n">cuts</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
+                <span class="n">Cut</span><span class="p">(</span>
+                    <span class="n">edge</span><span class="o">=</span><span class="n">e</span><span class="p">,</span>
+                    <span class="n">weight</span><span class="o">=</span><span class="n">h</span><span class="o">.</span><span class="n">graph</span><span class="o">.</span><span class="n">edges</span><span class="p">[</span><span class="n">e</span><span class="p">]</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;random_weight&quot;</span><span class="p">,</span> <span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">()),</span>
+                    <span class="n">subset</span><span class="o">=</span><span class="nb">frozenset</span><span class="p">(</span><span class="n">h</span><span class="o">.</span><span class="n">subsets</span><span class="p">[</span><span class="n">leaf</span><span class="p">]</span><span class="o">.</span><span class="n">copy</span><span class="p">())</span>
+                <span class="p">)</span>
+            <span class="p">)</span>
         <span class="c1"># Contract the leaf:</span>
         <span class="n">parent</span> <span class="o">=</span> <span class="n">pred</span><span class="p">[</span><span class="n">leaf</span><span class="p">]</span>
         <span class="n">h</span><span class="o">.</span><span class="n">contract_node</span><span class="p">(</span><span class="n">leaf</span><span class="p">,</span> <span class="n">parent</span><span class="p">)</span>
@@ -334,6 +344,68 @@ <h1>Source code for gerrychain.tree</h1><div class="highlight"><pre>
     <span class="k">return</span> <span class="n">cuts</span></div>
 
 
+<span class="k">def</span> <span class="nf">_calc_pops</span><span class="p">(</span><span class="n">succ</span><span class="p">,</span> <span class="n">root</span><span class="p">,</span> <span class="n">h</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Calculates the population of each subtree in the graph</span>
+<span class="sd">    by traversing the graph using a depth-first search.</span>
+
+<span class="sd">    :param succ: The successors of the graph.</span>
+<span class="sd">    :type succ: Dict</span>
+<span class="sd">    :param root: The root node of the graph.</span>
+<span class="sd">    :type root: Any</span>
+<span class="sd">    :param h: The populated graph.</span>
+<span class="sd">    :type h: PopulatedGraph</span>
+
+<span class="sd">    :returns: A dictionary mapping nodes to their subtree populations.</span>
+<span class="sd">    :rtype: Dict</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="n">subtree_pops</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Any</span><span class="p">,</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">float</span><span class="p">]]</span> <span class="o">=</span> <span class="p">{}</span>
+    <span class="n">stack</span> <span class="o">=</span> <span class="n">deque</span><span class="p">(</span><span class="n">n</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">succ</span><span class="p">[</span><span class="n">root</span><span class="p">])</span>
+    <span class="k">while</span> <span class="n">stack</span><span class="p">:</span>
+        <span class="n">next_node</span> <span class="o">=</span> <span class="n">stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+        <span class="k">if</span> <span class="n">next_node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">subtree_pops</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">next_node</span> <span class="ow">in</span> <span class="n">succ</span><span class="p">:</span>
+                <span class="n">children</span> <span class="o">=</span> <span class="n">succ</span><span class="p">[</span><span class="n">next_node</span><span class="p">]</span>
+                <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="n">c</span> <span class="ow">in</span> <span class="n">subtree_pops</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">children</span><span class="p">):</span>
+                    <span class="n">subtree_pops</span><span class="p">[</span><span class="n">next_node</span><span class="p">]</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">subtree_pops</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">children</span><span class="p">)</span>
+                    <span class="n">subtree_pops</span><span class="p">[</span><span class="n">next_node</span><span class="p">]</span> <span class="o">+=</span> <span class="n">h</span><span class="o">.</span><span class="n">population</span><span class="p">[</span><span class="n">next_node</span><span class="p">]</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">next_node</span><span class="p">)</span>
+                    <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">children</span><span class="p">:</span>
+                        <span class="k">if</span> <span class="n">c</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">subtree_pops</span><span class="p">:</span>
+                            <span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">subtree_pops</span><span class="p">[</span><span class="n">next_node</span><span class="p">]</span> <span class="o">=</span> <span class="n">h</span><span class="o">.</span><span class="n">population</span><span class="p">[</span><span class="n">next_node</span><span class="p">]</span>
+
+    <span class="k">return</span> <span class="n">subtree_pops</span>
+
+
+<span class="k">def</span> <span class="nf">_part_nodes</span><span class="p">(</span><span class="n">start</span><span class="p">,</span> <span class="n">succ</span><span class="p">):</span>
+    <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Partitions the nodes of a graph into two sets.</span>
+<span class="sd">    based on the start node and the successors of the graph.</span>
+
+<span class="sd">    :param start: The start node.</span>
+<span class="sd">    :type start: Any</span>
+<span class="sd">    :param succ: The successors of the graph.</span>
+<span class="sd">    :type succ: Dict</span>
+
+<span class="sd">    :returns: A set of nodes for a particular district (only one side of the cut).</span>
+<span class="sd">    :rtype: Set</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="n">nodes</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
+    <span class="n">queue</span> <span class="o">=</span> <span class="n">deque</span><span class="p">([</span><span class="n">start</span><span class="p">])</span>
+    <span class="k">while</span> <span class="n">queue</span><span class="p">:</span>
+        <span class="n">next_node</span> <span class="o">=</span> <span class="n">queue</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+        <span class="k">if</span> <span class="n">next_node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">nodes</span><span class="p">:</span>
+            <span class="n">nodes</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">next_node</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">next_node</span> <span class="ow">in</span> <span class="n">succ</span><span class="p">:</span>
+                <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">succ</span><span class="p">[</span><span class="n">next_node</span><span class="p">]:</span>
+                    <span class="k">if</span> <span class="n">c</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">nodes</span><span class="p">:</span>
+                        <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
+    <span class="k">return</span> <span class="n">nodes</span>
+
+
 <div class="viewcode-block" id="find_balanced_edge_cuts_memoization"><a class="viewcode-back" href="../../full_ref.html#gerrychain.tree.find_balanced_edge_cuts_memoization">[docs]</a><span class="k">def</span> <span class="nf">find_balanced_edge_cuts_memoization</span><span class="p">(</span>
     <span class="n">h</span><span class="p">:</span> <span class="n">PopulatedGraph</span><span class="p">,</span> <span class="n">choice</span><span class="p">:</span> <span class="n">Callable</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">choice</span>
 <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">List</span><span class="p">[</span><span class="n">Cut</span><span class="p">]:</span>
@@ -358,47 +430,29 @@ <h1>Source code for gerrychain.tree</h1><div class="highlight"><pre>
     <span class="n">pred</span> <span class="o">=</span> <span class="n">predecessors</span><span class="p">(</span><span class="n">h</span><span class="o">.</span><span class="n">graph</span><span class="p">,</span> <span class="n">root</span><span class="p">)</span>
     <span class="n">succ</span> <span class="o">=</span> <span class="n">successors</span><span class="p">(</span><span class="n">h</span><span class="o">.</span><span class="n">graph</span><span class="p">,</span> <span class="n">root</span><span class="p">)</span>
     <span class="n">total_pop</span> <span class="o">=</span> <span class="n">h</span><span class="o">.</span><span class="n">tot_pop</span>
-    <span class="n">subtree_pops</span><span class="p">:</span> <span class="n">Dict</span><span class="p">[</span><span class="n">Any</span><span class="p">,</span> <span class="n">Union</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">float</span><span class="p">]]</span> <span class="o">=</span> <span class="p">{}</span>
-    <span class="n">stack</span> <span class="o">=</span> <span class="n">deque</span><span class="p">(</span><span class="n">n</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">succ</span><span class="p">[</span><span class="n">root</span><span class="p">])</span>
-    <span class="k">while</span> <span class="n">stack</span><span class="p">:</span>
-        <span class="n">next_node</span> <span class="o">=</span> <span class="n">stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
-        <span class="k">if</span> <span class="n">next_node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">subtree_pops</span><span class="p">:</span>
-            <span class="k">if</span> <span class="n">next_node</span> <span class="ow">in</span> <span class="n">succ</span><span class="p">:</span>
-                <span class="n">children</span> <span class="o">=</span> <span class="n">succ</span><span class="p">[</span><span class="n">next_node</span><span class="p">]</span>
-                <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="n">c</span> <span class="ow">in</span> <span class="n">subtree_pops</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">children</span><span class="p">):</span>
-                    <span class="n">subtree_pops</span><span class="p">[</span><span class="n">next_node</span><span class="p">]</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">subtree_pops</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">children</span><span class="p">)</span>
-                    <span class="n">subtree_pops</span><span class="p">[</span><span class="n">next_node</span><span class="p">]</span> <span class="o">+=</span> <span class="n">h</span><span class="o">.</span><span class="n">population</span><span class="p">[</span><span class="n">next_node</span><span class="p">]</span>
-                <span class="k">else</span><span class="p">:</span>
-                    <span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">next_node</span><span class="p">)</span>
-                    <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">children</span><span class="p">:</span>
-                        <span class="k">if</span> <span class="n">c</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">subtree_pops</span><span class="p">:</span>
-                            <span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
-            <span class="k">else</span><span class="p">:</span>
-                <span class="n">subtree_pops</span><span class="p">[</span><span class="n">next_node</span><span class="p">]</span> <span class="o">=</span> <span class="n">h</span><span class="o">.</span><span class="n">population</span><span class="p">[</span><span class="n">next_node</span><span class="p">]</span>
+
+    <span class="n">subtree_pops</span> <span class="o">=</span> <span class="n">_calc_pops</span><span class="p">(</span><span class="n">succ</span><span class="p">,</span> <span class="n">root</span><span class="p">,</span> <span class="n">h</span><span class="p">)</span>
 
     <span class="n">cuts</span> <span class="o">=</span> <span class="p">[]</span>
     <span class="k">for</span> <span class="n">node</span><span class="p">,</span> <span class="n">tree_pop</span> <span class="ow">in</span> <span class="n">subtree_pops</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-
-        <span class="k">def</span> <span class="nf">part_nodes</span><span class="p">(</span><span class="n">start</span><span class="p">):</span>
-            <span class="n">nodes</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
-            <span class="n">queue</span> <span class="o">=</span> <span class="n">deque</span><span class="p">([</span><span class="n">start</span><span class="p">])</span>
-            <span class="k">while</span> <span class="n">queue</span><span class="p">:</span>
-                <span class="n">next_node</span> <span class="o">=</span> <span class="n">queue</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
-                <span class="k">if</span> <span class="n">next_node</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">nodes</span><span class="p">:</span>
-                    <span class="n">nodes</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">next_node</span><span class="p">)</span>
-                    <span class="k">if</span> <span class="n">next_node</span> <span class="ow">in</span> <span class="n">succ</span><span class="p">:</span>
-                        <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">succ</span><span class="p">[</span><span class="n">next_node</span><span class="p">]:</span>
-                            <span class="k">if</span> <span class="n">c</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">nodes</span><span class="p">:</span>
-                                <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
-            <span class="k">return</span> <span class="n">nodes</span>
-
         <span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">tree_pop</span> <span class="o">-</span> <span class="n">h</span><span class="o">.</span><span class="n">ideal_pop</span><span class="p">)</span> <span class="o">&lt;=</span> <span class="n">h</span><span class="o">.</span><span class="n">ideal_pop</span> <span class="o">*</span> <span class="n">h</span><span class="o">.</span><span class="n">epsilon</span><span class="p">:</span>
-            <span class="n">cuts</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Cut</span><span class="p">(</span><span class="n">edge</span><span class="o">=</span><span class="p">(</span><span class="n">node</span><span class="p">,</span> <span class="n">pred</span><span class="p">[</span><span class="n">node</span><span class="p">]),</span> <span class="n">subset</span><span class="o">=</span><span class="n">part_nodes</span><span class="p">(</span><span class="n">node</span><span class="p">)))</span>
+            <span class="n">e</span> <span class="o">=</span> <span class="p">(</span><span class="n">node</span><span class="p">,</span> <span class="n">pred</span><span class="p">[</span><span class="n">node</span><span class="p">])</span>
+            <span class="n">wt</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">()</span>
+            <span class="n">cuts</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
+                <span class="n">Cut</span><span class="p">(</span>
+                    <span class="n">edge</span><span class="o">=</span><span class="n">e</span><span class="p">,</span>
+                    <span class="n">weight</span><span class="o">=</span><span class="n">h</span><span class="o">.</span><span class="n">graph</span><span class="o">.</span><span class="n">edges</span><span class="p">[</span><span class="n">e</span><span class="p">]</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;random_weight&quot;</span><span class="p">,</span> <span class="n">wt</span><span class="p">),</span>
+                    <span class="n">subset</span><span class="o">=</span><span class="nb">frozenset</span><span class="p">(</span><span class="n">_part_nodes</span><span class="p">(</span><span class="n">node</span><span class="p">,</span> <span class="n">succ</span><span class="p">))</span>
+                <span class="p">)</span>
+            <span class="p">)</span>
         <span class="k">elif</span> <span class="nb">abs</span><span class="p">((</span><span class="n">total_pop</span> <span class="o">-</span> <span class="n">tree_pop</span><span class="p">)</span> <span class="o">-</span> <span class="n">h</span><span class="o">.</span><span class="n">ideal_pop</span><span class="p">)</span> <span class="o">&lt;=</span> <span class="n">h</span><span class="o">.</span><span class="n">ideal_pop</span> <span class="o">*</span> <span class="n">h</span><span class="o">.</span><span class="n">epsilon</span><span class="p">:</span>
+            <span class="n">e</span> <span class="o">=</span> <span class="p">(</span><span class="n">node</span><span class="p">,</span> <span class="n">pred</span><span class="p">[</span><span class="n">node</span><span class="p">])</span>
+            <span class="n">wt</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">()</span>
             <span class="n">cuts</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
                 <span class="n">Cut</span><span class="p">(</span>
-                    <span class="n">edge</span><span class="o">=</span><span class="p">(</span><span class="n">node</span><span class="p">,</span> <span class="n">pred</span><span class="p">[</span><span class="n">node</span><span class="p">]),</span>
-                    <span class="n">subset</span><span class="o">=</span><span class="nb">set</span><span class="p">(</span><span class="n">h</span><span class="o">.</span><span class="n">graph</span><span class="o">.</span><span class="n">nodes</span><span class="p">)</span> <span class="o">-</span> <span class="n">part_nodes</span><span class="p">(</span><span class="n">node</span><span class="p">),</span>
+                    <span class="n">edge</span><span class="o">=</span><span class="n">e</span><span class="p">,</span>
+                    <span class="n">weight</span><span class="o">=</span><span class="n">h</span><span class="o">.</span><span class="n">graph</span><span class="o">.</span><span class="n">edges</span><span class="p">[</span><span class="n">e</span><span class="p">]</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;random_weight&quot;</span><span class="p">,</span> <span class="n">wt</span><span class="p">),</span>
+                    <span class="n">subset</span><span class="o">=</span><span class="nb">frozenset</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">h</span><span class="o">.</span><span class="n">graph</span><span class="o">.</span><span class="n">nodes</span><span class="p">)</span> <span class="o">-</span> <span class="n">_part_nodes</span><span class="p">(</span><span class="n">node</span><span class="p">,</span> <span class="n">succ</span><span class="p">)),</span>
                 <span class="p">)</span>
             <span class="p">)</span>
     <span class="k">return</span> <span class="n">cuts</span></div>
@@ -423,6 +477,146 @@ <h1>Source code for gerrychain.tree</h1><div class="highlight"><pre>
     <span class="k">pass</span></div>
 
 
+<span class="k">def</span> <span class="nf">_max_weight_choice</span><span class="p">(</span>
+    <span class="n">cut_edge_list</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Cut</span><span class="p">]</span>
+<span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Cut</span><span class="p">:</span>
+    <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Each Cut object in the list is assigned a random weight.</span>
+<span class="sd">    This random weight is either assigned during the call to</span>
+<span class="sd">    the minimum spanning tree algorithm (Kruskal&#39;s) algorithm</span>
+<span class="sd">    or it is generated during the selection of the balanced edges</span>
+<span class="sd">    (cf. :meth:`find_balanced_edge_cuts_memoization` and</span>
+<span class="sd">    :meth:`find_balanced_edge_cuts_contraction`).</span>
+<span class="sd">    This function returns the cut with the highest weight.</span>
+
+<span class="sd">    In the case where a region aware chain is run, this will</span>
+<span class="sd">    preferentially select for cuts that span different regions, rather</span>
+<span class="sd">    than cuts that are interior to that region (the likelihood of this</span>
+<span class="sd">    is generally controlled by the ``region_surcharge`` parameter).</span>
+
+<span class="sd">    In any case where the surcharges are either not set or zero,</span>
+<span class="sd">    this is effectively the same as calling random.choice() on the</span>
+<span class="sd">    list of cuts. Under the above conditions, all of the weights</span>
+<span class="sd">    on the cuts are randomly generated on the interval [0,1], and</span>
+<span class="sd">    there is no outside force that might make the weight assigned</span>
+<span class="sd">    to a particular type of cut higher than another.</span>
+
+<span class="sd">    :param cut_edge_list: A list of Cut objects. Each object has an</span>
+<span class="sd">        edge, a weight, and a subset attribute.</span>
+<span class="sd">    :type cut_edge_list: List[Cut]</span>
+
+<span class="sd">    :returns: The cut with the highest random weight.</span>
+<span class="sd">    :rtype: Cut</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="c1"># Just in case, default to random choice</span>
+    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">cut_edge_list</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">Cut</span><span class="p">)</span> <span class="ow">or</span> <span class="n">cut_edge_list</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">weight</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="k">return</span> <span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="n">cut_edge_list</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="nb">max</span><span class="p">(</span><span class="n">cut_edge_list</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="k">lambda</span> <span class="n">cut</span><span class="p">:</span> <span class="n">cut</span><span class="o">.</span><span class="n">weight</span><span class="p">)</span>
+
+
+<span class="k">def</span> <span class="nf">_power_set_sorted_by_size_then_sum</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
+    <span class="n">power_set</span> <span class="o">=</span> <span class="p">[</span>
+        <span class="n">s</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">d</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">s</span> <span class="ow">in</span> <span class="n">itertools</span><span class="o">.</span><span class="n">combinations</span><span class="p">(</span><span class="n">d</span><span class="o">.</span><span class="n">keys</span><span class="p">(),</span> <span class="n">i</span><span class="p">)</span>
+    <span class="p">]</span>
+
+    <span class="c1"># Sort the subsets in descending order based on</span>
+    <span class="c1"># the sum of their corresponding values in the dictionary</span>
+    <span class="n">sorted_power_set</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span>
+        <span class="n">power_set</span><span class="p">,</span>
+        <span class="n">key</span><span class="o">=</span><span class="k">lambda</span> <span class="n">s</span><span class="p">:</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">s</span><span class="p">),</span> <span class="nb">sum</span><span class="p">(</span><span class="n">d</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">s</span><span class="p">)),</span>
+        <span class="n">reverse</span><span class="o">=</span><span class="kc">True</span>
+    <span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">sorted_power_set</span>
+
+
+<span class="c1"># Note that the populated graph and the region surcharge are passed</span>
+<span class="c1"># by object reference. This means that a copy is not made since we</span>
+<span class="c1"># are not modifying the object in the function, and the speed of</span>
+<span class="c1"># this randomized selection will not suffer for it.</span>
+<span class="k">def</span> <span class="nf">_region_preferred_max_weight_choice</span><span class="p">(</span>
+    <span class="n">populated_graph</span><span class="p">:</span> <span class="n">PopulatedGraph</span><span class="p">,</span>
+    <span class="n">region_surcharge</span><span class="p">:</span> <span class="n">Dict</span><span class="p">,</span>
+    <span class="n">cut_edge_list</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Cut</span><span class="p">]</span>
+<span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Cut</span><span class="p">:</span>
+    <span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    This function is used in the case of a region-aware chain. It</span>
+<span class="sd">    is similar to the as :meth:`_max_weight_choice` function except</span>
+<span class="sd">    that it will preferentially select one of the cuts that has the</span>
+<span class="sd">    highest surcharge. So, if we have a weight dict of the form</span>
+<span class="sd">    ``{region1: wt1, region2: wt2}`` , then this function first looks</span>
+<span class="sd">    for a cut that is a cut edge for both ``region1`` and ``region2``</span>
+<span class="sd">    and then selects the one with the highest weight. If no such cut</span>
+<span class="sd">    exists, then it will then look for a cut that is a cut edge for the</span>
+<span class="sd">    region with the highest surcharge (presumably the region that we care</span>
+<span class="sd">    more about not splitting).</span>
+
+<span class="sd">    In the case of 3 regions, it will first look for a cut that is a</span>
+<span class="sd">    cut edge for all 3 regions, then for a cut that is a cut edge for</span>
+<span class="sd">    2 regions sorted by the highest total surcharge, and then for a cut</span>
+<span class="sd">    that is a cut edge for the region with the highest surcharge.</span>
+
+<span class="sd">    For the case of 4 or more regions, the power set starts to get a bit</span>
+<span class="sd">    large, so we default back to the :meth:`_max_weight_choice` function</span>
+<span class="sd">    and just select the cut with the highest weight, which will still</span>
+<span class="sd">    preferentially select for cuts that span the most regions that we</span>
+<span class="sd">    care about.</span>
+
+<span class="sd">    :param populated_graph: The populated graph.</span>
+<span class="sd">    :type populated_graph: PopulatedGraph</span>
+<span class="sd">    :param region_surcharge: A dictionary of surcharges for the spanning</span>
+<span class="sd">        tree algorithm.</span>
+<span class="sd">    :type region_surcharge: Dict</span>
+<span class="sd">    :param cut_edge_list: A list of Cut objects. Each object has an</span>
+<span class="sd">        edge, a weight, and a subset attribute.</span>
+<span class="sd">    :type cut_edge_list: List[Cut]</span>
+
+<span class="sd">    :returns: A random Cut from the set of possible Cuts with the highest</span>
+<span class="sd">        surcharge.</span>
+<span class="sd">    :rtype: Cut</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">if</span> <span class="p">(</span>
+        <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">region_surcharge</span><span class="p">,</span> <span class="nb">dict</span><span class="p">)</span>
+        <span class="ow">or</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">cut_edge_list</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">Cut</span><span class="p">)</span>
+        <span class="ow">or</span> <span class="n">cut_edge_list</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">weight</span> <span class="ow">is</span> <span class="kc">None</span>
+    <span class="p">):</span>
+        <span class="k">return</span> <span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="n">cut_edge_list</span><span class="p">)</span>
+
+    <span class="c1"># Early return for simple cases</span>
+    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">region_surcharge</span><span class="p">)</span> <span class="o">&lt;</span> <span class="mi">1</span> <span class="ow">or</span> <span class="nb">len</span><span class="p">(</span><span class="n">region_surcharge</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">3</span><span class="p">:</span>
+        <span class="k">return</span> <span class="n">_max_weight_choice</span><span class="p">(</span><span class="n">cut_edge_list</span><span class="p">)</span>
+
+    <span class="c1"># Prepare data for efficient access</span>
+    <span class="n">edge_region_info</span> <span class="o">=</span> <span class="p">{</span>
+        <span class="n">cut</span><span class="p">:</span> <span class="p">{</span>
+            <span class="n">key</span><span class="p">:</span> <span class="p">(</span><span class="n">populated_graph</span><span class="o">.</span><span class="n">graph</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="n">cut</span><span class="o">.</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">key</span><span class="p">),</span>
+                  <span class="n">populated_graph</span><span class="o">.</span><span class="n">graph</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="n">cut</span><span class="o">.</span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">key</span><span class="p">))</span>
+            <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">region_surcharge</span>
+        <span class="p">}</span>
+        <span class="k">for</span> <span class="n">cut</span> <span class="ow">in</span> <span class="n">cut_edge_list</span>
+    <span class="p">}</span>
+
+    <span class="c1"># Generate power set sorted by surcharge, then filter cuts based</span>
+    <span class="c1"># on region matching</span>
+    <span class="n">power_set</span> <span class="o">=</span> <span class="n">_power_set_sorted_by_size_then_sum</span><span class="p">(</span><span class="n">region_surcharge</span><span class="p">)</span>
+    <span class="k">for</span> <span class="n">region_combination</span> <span class="ow">in</span> <span class="n">power_set</span><span class="p">:</span>
+        <span class="n">suitable_cuts</span> <span class="o">=</span> <span class="p">[</span>
+            <span class="n">cut</span> <span class="k">for</span> <span class="n">cut</span> <span class="ow">in</span> <span class="n">cut_edge_list</span>
+            <span class="k">if</span> <span class="nb">all</span><span class="p">(</span>
+                <span class="n">edge_region_info</span><span class="p">[</span><span class="n">cut</span><span class="p">][</span><span class="n">key</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">!=</span> <span class="n">edge_region_info</span><span class="p">[</span><span class="n">cut</span><span class="p">][</span><span class="n">key</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span>
+                <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">region_combination</span>
+            <span class="p">)</span>
+        <span class="p">]</span>
+        <span class="k">if</span> <span class="n">suitable_cuts</span><span class="p">:</span>
+            <span class="k">return</span> <span class="n">_max_weight_choice</span><span class="p">(</span><span class="n">suitable_cuts</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">_max_weight_choice</span><span class="p">(</span><span class="n">cut_edge_list</span><span class="p">)</span>
+
+
 <div class="viewcode-block" id="bipartition_tree"><a class="viewcode-back" href="../../full_ref.html#gerrychain.tree.bipartition_tree">[docs]</a><span class="k">def</span> <span class="nf">bipartition_tree</span><span class="p">(</span>
     <span class="n">graph</span><span class="p">:</span> <span class="n">nx</span><span class="o">.</span><span class="n">Graph</span><span class="p">,</span>
     <span class="n">pop_col</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span>
@@ -431,11 +625,13 @@ <h1>Source code for gerrychain.tree</h1><div class="highlight"><pre>
     <span class="n">node_repeats</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span>
     <span class="n">spanning_tree</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">nx</span><span class="o">.</span><span class="n">Graph</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
     <span class="n">spanning_tree_fn</span><span class="p">:</span> <span class="n">Callable</span> <span class="o">=</span> <span class="n">random_spanning_tree</span><span class="p">,</span>
-    <span class="n">weight_dict</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">Dict</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
+    <span class="n">region_surcharge</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="n">Dict</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span>
     <span class="n">balance_edge_fn</span><span class="p">:</span> <span class="n">Callable</span> <span class="o">=</span> <span class="n">find_balanced_edge_cuts_memoization</span><span class="p">,</span>
     <span class="n">choice</span><span class="p">:</span> <span class="n">Callable</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">,</span>
     <span class="n">max_attempts</span><span class="p">:</span> <span class="n">Optional</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="mi">100000</span><span class="p">,</span>
+    <span class="n">warn_attempts</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">1000</span><span class="p">,</span>
     <span class="n">allow_pair_reselection</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="kc">False</span><span class="p">,</span>
+    <span class="n">cut_choice</span><span class="p">:</span> <span class="n">Callable</span> <span class="o">=</span> <span class="n">_region_preferred_max_weight_choice</span>
 <span class="p">)</span> <span class="o">-&gt;</span> <span class="n">Set</span><span class="p">:</span>
     <span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    This function finds a balanced 2 partition of a graph by drawing a</span>
@@ -464,62 +660,80 @@ <h1>Source code for gerrychain.tree</h1><div class="highlight"><pre>
 <span class="sd">    :param spanning_tree_fn: The random spanning tree algorithm to use if a spanning</span>
 <span class="sd">        tree is not provided. Defaults to :func:`random_spanning_tree`.</span>
 <span class="sd">    :type spanning_tree_fn: Callable, optional</span>
-<span class="sd">    :param weight_dict: A dictionary of weights for the spanning tree algorithm.</span>
+<span class="sd">    :param region_surcharge: A dictionary of surcharges for the spanning tree algorithm.</span>
 <span class="sd">        Defaults to None.</span>
-<span class="sd">    :type weight_dict: Optional[Dict], optional</span>
+<span class="sd">    :type region_surcharge: Optional[Dict], optional</span>
 <span class="sd">    :param balance_edge_fn: The function to find balanced edge cuts. Defaults to</span>
 <span class="sd">        :func:`find_balanced_edge_cuts_memoization`.</span>
 <span class="sd">    :type balance_edge_fn: Callable, optional</span>
-<span class="sd">    :param choice: The function to make a random choice. Can be substituted for testing.</span>
-<span class="sd">        Defaults to :func:`random.choice`.</span>
+<span class="sd">    :param choice: The function to make a random choice of root node for the population</span>
+<span class="sd">        tree. Passed to ``balance_edge_fn``. Can be substituted for testing.</span>
+<span class="sd">        Defaults to :func:`random.random()`.</span>
 <span class="sd">    :type choice: Callable, optional</span>
 <span class="sd">    :param max_attempts: The maximum number of attempts that should be made to bipartition.</span>
 <span class="sd">        Defaults to 10000.</span>
 <span class="sd">    :type max_attempts: Optional[int], optional</span>
+<span class="sd">    :param warn_attempts: The number of attempts after which a warning is issued if a balanced</span>
+<span class="sd">        cut cannot be found. Defaults to 1000.</span>
+<span class="sd">    :type warn_attempts: int, optional</span>
 <span class="sd">    :param allow_pair_reselection: Whether we would like to return an error to the calling</span>
 <span class="sd">        function to ask it to reselect the pair of nodes to try and recombine. Defaults to False.</span>
 <span class="sd">    :type allow_pair_reselection: bool, optional</span>
+<span class="sd">    :param cut_choice: The function used to select the cut edge from the list of possible</span>
+<span class="sd">        balanced cuts. Defaults to :meth:`_region_preferred_max_weight_choice` .</span>
+<span class="sd">    :type cut_choice: Callable, optional</span>
 
 <span class="sd">    :returns: A subset of nodes of ``graph`` (whose induced subgraph is connected). The other</span>
 <span class="sd">        part of the partition is the complement of this subset.</span>
 <span class="sd">    :rtype: Set</span>
 
-<span class="sd">    :raises BipartitionWarning: If a possible cut cannot be found after 50 attempts.</span>
+<span class="sd">    :raises BipartitionWarning: If a possible cut cannot be found after 1000 attempts.</span>
 <span class="sd">    :raises RuntimeError: If a possible cut cannot be found after the maximum number of attempts</span>
 <span class="sd">        given by ``max_attempts``.</span>
 <span class="sd">    &quot;&quot;&quot;</span>
-    <span class="c1"># Try to add the region-aware in if the spanning_tree_fn accepts a weight dictionary</span>
-    <span class="k">if</span> <span class="s2">&quot;weight_dict&quot;</span> <span class="ow">in</span> <span class="n">signature</span><span class="p">(</span><span class="n">spanning_tree_fn</span><span class="p">)</span><span class="o">.</span><span class="n">parameters</span><span class="p">:</span>
-        <span class="n">spanning_tree_fn</span> <span class="o">=</span> <span class="n">partial</span><span class="p">(</span><span class="n">spanning_tree_fn</span><span class="p">,</span> <span class="n">weight_dict</span><span class="o">=</span><span class="n">weight_dict</span><span class="p">)</span>
+    <span class="c1"># Try to add the region-aware in if the spanning_tree_fn accepts a surcharge dictionary</span>
+    <span class="k">if</span> <span class="s2">&quot;region_surcharge&quot;</span> <span class="ow">in</span> <span class="n">signature</span><span class="p">(</span><span class="n">spanning_tree_fn</span><span class="p">)</span><span class="o">.</span><span class="n">parameters</span><span class="p">:</span>
+        <span class="n">spanning_tree_fn</span> <span class="o">=</span> <span class="n">partial</span><span class="p">(</span><span class="n">spanning_tree_fn</span><span class="p">,</span> <span class="n">region_surcharge</span><span class="o">=</span><span class="n">region_surcharge</span><span class="p">)</span>
 
     <span class="n">populations</span> <span class="o">=</span> <span class="p">{</span><span class="n">node</span><span class="p">:</span> <span class="n">graph</span><span class="o">.</span><span class="n">nodes</span><span class="p">[</span><span class="n">node</span><span class="p">][</span><span class="n">pop_col</span><span class="p">]</span> <span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">graph</span><span class="o">.</span><span class="n">node_indices</span><span class="p">}</span>
 
-    <span class="n">possible_cuts</span> <span class="o">=</span> <span class="p">[]</span>
+    <span class="n">possible_cuts</span><span class="p">:</span> <span class="n">List</span><span class="p">[</span><span class="n">Cut</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
     <span class="k">if</span> <span class="n">spanning_tree</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
         <span class="n">spanning_tree</span> <span class="o">=</span> <span class="n">spanning_tree_fn</span><span class="p">(</span><span class="n">graph</span><span class="p">)</span>
 
     <span class="n">restarts</span> <span class="o">=</span> <span class="mi">0</span>
     <span class="n">attempts</span> <span class="o">=</span> <span class="mi">0</span>
+
     <span class="k">while</span> <span class="n">max_attempts</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">attempts</span> <span class="o">&lt;</span> <span class="n">max_attempts</span><span class="p">:</span>
         <span class="k">if</span> <span class="n">restarts</span> <span class="o">==</span> <span class="n">node_repeats</span><span class="p">:</span>
             <span class="n">spanning_tree</span> <span class="o">=</span> <span class="n">spanning_tree_fn</span><span class="p">(</span><span class="n">graph</span><span class="p">)</span>
             <span class="n">restarts</span> <span class="o">=</span> <span class="mi">0</span>
         <span class="n">h</span> <span class="o">=</span> <span class="n">PopulatedGraph</span><span class="p">(</span><span class="n">spanning_tree</span><span class="p">,</span> <span class="n">populations</span><span class="p">,</span> <span class="n">pop_target</span><span class="p">,</span> <span class="n">epsilon</span><span class="p">)</span>
+
+        <span class="n">is_region_cut</span> <span class="o">=</span> <span class="p">(</span>
+            <span class="s2">&quot;region_surcharge&quot;</span> <span class="ow">in</span> <span class="n">signature</span><span class="p">(</span><span class="n">cut_choice</span><span class="p">)</span><span class="o">.</span><span class="n">parameters</span>
+            <span class="ow">and</span> <span class="s2">&quot;populated_graph&quot;</span> <span class="ow">in</span> <span class="n">signature</span><span class="p">(</span><span class="n">cut_choice</span><span class="p">)</span><span class="o">.</span><span class="n">parameters</span>
+        <span class="p">)</span>
+
+        <span class="c1"># This returns a list of Cut objects with attributes edge and subset</span>
         <span class="n">possible_cuts</span> <span class="o">=</span> <span class="n">balance_edge_fn</span><span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">choice</span><span class="o">=</span><span class="n">choice</span><span class="p">)</span>
 
         <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">possible_cuts</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
-            <span class="k">return</span> <span class="n">choice</span><span class="p">(</span><span class="n">possible_cuts</span><span class="p">)</span><span class="o">.</span><span class="n">subset</span>
+            <span class="k">if</span> <span class="n">is_region_cut</span><span class="p">:</span>
+                <span class="k">return</span> <span class="n">cut_choice</span><span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">region_surcharge</span><span class="p">,</span> <span class="n">possible_cuts</span><span class="p">)</span><span class="o">.</span><span class="n">subset</span>
+
+            <span class="k">return</span> <span class="n">cut_choice</span><span class="p">(</span><span class="n">possible_cuts</span><span class="p">)</span><span class="o">.</span><span class="n">subset</span>
 
         <span class="n">restarts</span> <span class="o">+=</span> <span class="mi">1</span>
         <span class="n">attempts</span> <span class="o">+=</span> <span class="mi">1</span>
 
         <span class="c1"># Don&#39;t forget to change the documentation if you change this number</span>
-        <span class="k">if</span> <span class="n">attempts</span> <span class="o">==</span> <span class="mi">50</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">allow_pair_reselection</span><span class="p">:</span>
+        <span class="k">if</span> <span class="n">attempts</span> <span class="o">==</span> <span class="n">warn_attempts</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">allow_pair_reselection</span><span class="p">:</span>
             <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
-                <span class="s2">&quot;</span><span class="se">\n</span><span class="s2">Failed to find a balanced cut after 50 attempts.</span><span class="se">\n</span><span class="s2">&quot;</span>
+                <span class="sa">f</span><span class="s2">&quot;</span><span class="se">\n</span><span class="s2">Failed to find a balanced cut after </span><span class="si">{warn_attempts}</span><span class="s2"> attempts.</span><span class="se">\n</span><span class="s2">&quot;</span>
                 <span class="s2">&quot;If possible, consider enabling pair reselection within your</span><span class="se">\n</span><span class="s2">&quot;</span>
                 <span class="s2">&quot;MarkovChain proposal method to allow the algorithm to select</span><span class="se">\n</span><span class="s2">&quot;</span>
-                <span class="s2">&quot;a different pair of districts to try and recombine.&quot;</span><span class="p">,</span>
+                <span class="s2">&quot;a different pair of districts for recombination.&quot;</span><span class="p">,</span>
                 <span class="n">BipartitionWarning</span><span class="p">,</span>
             <span class="p">)</span>
 
@@ -590,9 +804,9 @@ <h1>Source code for gerrychain.tree</h1><div class="highlight"><pre>
     <span class="k">if</span> <span class="n">spanning_tree</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
         <span class="n">spanning_tree</span> <span class="o">=</span> <span class="n">spanning_tree_fn</span><span class="p">(</span><span class="n">graph</span><span class="p">)</span>
 
-    <span class="n">repeat</span> <span class="o">=</span> <span class="kc">True</span>
     <span class="n">restarts</span> <span class="o">=</span> <span class="mi">0</span>
     <span class="n">attempts</span> <span class="o">=</span> <span class="mi">0</span>
+
     <span class="k">while</span> <span class="n">max_attempts</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">attempts</span> <span class="o">&lt;</span> <span class="n">max_attempts</span><span class="p">:</span>
         <span class="k">if</span> <span class="n">restarts</span> <span class="o">==</span> <span class="n">node_repeats</span><span class="p">:</span>
             <span class="n">spanning_tree</span> <span class="o">=</span> <span class="n">spanning_tree_fn</span><span class="p">(</span><span class="n">graph</span><span class="p">)</span>
@@ -600,9 +814,7 @@ <h1>Source code for gerrychain.tree</h1><div class="highlight"><pre>
         <span class="n">h</span> <span class="o">=</span> <span class="n">PopulatedGraph</span><span class="p">(</span><span class="n">spanning_tree</span><span class="p">,</span> <span class="n">populations</span><span class="p">,</span> <span class="n">pop_target</span><span class="p">,</span> <span class="n">epsilon</span><span class="p">)</span>
         <span class="n">possible_cuts</span> <span class="o">=</span> <span class="n">balance_edge_fn</span><span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">choice</span><span class="o">=</span><span class="n">choice</span><span class="p">)</span>
 
-        <span class="n">repeat</span> <span class="o">=</span> <span class="n">repeat_until_valid</span>
-
-        <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">repeat</span> <span class="ow">and</span> <span class="nb">len</span><span class="p">(</span><span class="n">possible_cuts</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">):</span>
+        <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="n">repeat_until_valid</span> <span class="ow">and</span> <span class="nb">len</span><span class="p">(</span><span class="n">possible_cuts</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">):</span>
             <span class="k">return</span> <span class="n">possible_cuts</span>
 
         <span class="n">restarts</span> <span class="o">+=</span> <span class="mi">1</span>
diff --git a/_sources/user/data.rst.txt b/_sources/user/data.rst.txt
index 71480c85..f6007874 100644
--- a/_sources/user/data.rst.txt
+++ b/_sources/user/data.rst.txt
@@ -24,7 +24,7 @@ Writing Data to JSONL
 .. raw:: html
 
     <div class="center-container">
-      <a href="https://github.com/mggg/GerryChain/blob/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
+      <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
     </div>
     <br style="line-height: 5px;">
 
@@ -217,42 +217,40 @@ which will produce:
 +-----+------+---------------+------------+----------+-------------+
 |     | step | district_name | population |   area   | n_cut_edges |
 +=====+======+===============+============+==========+=============+
-| 198 |  11  |      3        |   699433   | 0.831304 |    2162     |
+| 198 |  11  |       3       |   704364   | 0.883639 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 199 |  11  |      10       |   700040   | 1.562749 |    2162     |
+| 199 |  11  |       10      |   709547   | 2.228103 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 200 |  11  |      9        |   702500   | 1.579113 |    2162     |
+| 200 |  11  |       9       |   712201   | 0.801655 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 201 |  11  |      5        |   695917   | 3.012263 |    2162     |
+| 201 |  11  |       5       |   699705   | 1.639986 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 202 |  11  |      15       |   700895   | 1.616416 |    2162     |
+| 202 |  11  |       15      |   706694   | 0.744557 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 203 |  11  |      6        |   705782   | 0.239069 |    2162     |
+| 203 |  11  |       6       |   708502   | 0.351298 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 204 |  11  |      11       |   709813   | 0.357564 |    2162     |
+| 204 |  11  |       11      |   705406   | 0.948691 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 205 |  11  |      8        |   705689   | 0.199275 |    2162     |
+| 205 |  11  |       8       |   702576   | 0.109261 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 206 |  11  |      4        |   705669   | 0.418513 |    2162     |
+| 206 |  11  |       4       |   705669   | 0.418513 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 207 |  11  |      18       |   706380   | 0.421818 |    2162     |
+| 207 |  11  |       18      |   705847   | 0.569159 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 208 |  11  |      12       |   713452   | 0.856847 |    2162     |
+| 208 |  11  |       12      |   695032   | 2.954248 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 209 |  11  |      17       |   706041   | 0.622091 |    2162     |
+| 209 |  11  |       17      |   695142   | 0.237470 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 210 |  11  |      7        |   697675   | 0.329930 |    2162     |
+| 210 |  11  |       7       |   711035   | 0.018885 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 211 |  11  |      16       |   716162   | 0.194045 |    2162     |
+| 211 |  11  |       16      |   699557   | 0.283365 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 212 |  11  |      14       |   704993   | 0.207707 |    2162     |
+| 212 |  11  |       14      |   705526   | 0.060366 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 213 |  11  |      13       |   705028   | 0.042608 |    2162     |
+| 213 |  11  |       13      |   705028   | 0.042608 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 214 |  11  |      2        |   710286   | 0.021872 |    2162     |
+| 214 |  11  |       2       |   705218   | 0.021515 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
-| 215 |  11  |      1        |   699174   | 0.021139 |    2162     |
+| 215 |  11  |       1       |   707880   | 0.221007 |    2103     |
 +-----+------+---------------+------------+----------+-------------+
 
-
-
diff --git a/_sources/user/geometries.rst.txt b/_sources/user/geometries.rst.txt
index d55751ce..f6c11875 100644
--- a/_sources/user/geometries.rst.txt
+++ b/_sources/user/geometries.rst.txt
@@ -35,7 +35,7 @@ Loading and Running a Plan
 .. raw:: html
 
     <div class="center-container">
-      <a href="https://github.com/mggg/GerryChain/blob/main/docs/_static/MN.zip" class="download-badge" download>Download MN File</a>
+      <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/MN.zip" class="download-badge" download>Download MN File</a>
     </div>
     <br style="line-height: 5px;">
 
diff --git a/_sources/user/install.rst.txt b/_sources/user/install.rst.txt
index 3e8f5a31..3c805a91 100644
--- a/_sources/user/install.rst.txt
+++ b/_sources/user/install.rst.txt
@@ -9,6 +9,7 @@ The most recent version of GerryChain (as of January 2024) supports
 - Python 3.9
 - Python 3.10
 - Python 3.11
+- Python 3.12
 
 If you do not have one of these versions installed on you machine, we
 recommend that you go to the 
@@ -135,7 +136,7 @@ This approach sometimes fails due to compatibility issues between our
 different Python GIS dependencies, like ``geopandas``, ``pyproj``,
 ``fiona``, and ``shapely``. If you run into this issue, try installing
 the dependencies using the 
-`geo_settings.txt <https://github.com/mggg/GerryChain/blob/main/docs/geo_settings.txt>`_
+`geo_settings.txt <https://github.com/mggg/GerryChain/raw/main/docs/geo_settings.txt>`_
 file. To do this, run ``pip install -r geo_settings.txt`` from the
 command line.
 
diff --git a/_sources/user/partitions.rst.txt b/_sources/user/partitions.rst.txt
index 3241c539..2bbe049b 100644
--- a/_sources/user/partitions.rst.txt
+++ b/_sources/user/partitions.rst.txt
@@ -4,7 +4,7 @@ Working with Partitions
 .. raw:: html
 
     <div class="center-container">
-      <a href="https://github.com/mggg/GerryChain/blob/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
+      <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
     </div>
     <br style="line-height: 5px;">
 
@@ -17,7 +17,7 @@ GerryChain ``Partition`` object.
     from gerrychain.updaters import cut_edges
 
 We'll use our 
-`Pennsylvania VTD json <https://github.com/mggg/GerryChain/blob/main/docs/_static/PA_VTDs.json>`_ 
+`Pennsylvania VTD json <https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json>`_ 
 to create the graph we'll use in these examples.
 
 .. code-block:: python
diff --git a/_sources/user/quickstart.rst.txt b/_sources/user/quickstart.rst.txt
index b5cdf8ce..5a6f4af9 100644
--- a/_sources/user/quickstart.rst.txt
+++ b/_sources/user/quickstart.rst.txt
@@ -13,7 +13,7 @@ What you'll need
 Before we can start running Markov chains, you'll need to:
 
 * Install ``gerrychain`` from PyPI. See the :doc:`installation guide <./install>` for instructions.
-* Download `this example json of Pennsylvania's VTDs <https://github.com/mggg/GerryChain/blob/main/docs/_static/PA_VTDs.json>`_.
+* Download `this example json of Pennsylvania's VTDs <https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json>`_.
 * Open your preferred Python environment (e.g. JupyterLab, IPython, or a ``.py`` file
   in your favorite editor) in the directory containing the ``PA_VTDs.json`` file
   that you downloaded.
@@ -43,7 +43,7 @@ Creating the initial partition
 .. raw:: html
 
     <div class="center-container">
-      <a href="https://github.com/mggg/GerryChain/blob/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
+      <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
     </div>
     <br style="line-height: 5px;">
 
diff --git a/_sources/user/recom.rst.txt b/_sources/user/recom.rst.txt
index 5e45f9b9..a3c76e77 100644
--- a/_sources/user/recom.rst.txt
+++ b/_sources/user/recom.rst.txt
@@ -28,7 +28,7 @@ A Simple Recom Chain
 .. raw:: html
 
     <div class="center-container">
-      <a href="https://github.com/mggg/GerryChain/blob/main/docs/_static/gerrymandria.json" class="download-badge" download>
+      <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/gerrymandria.json" class="download-badge" download>
         Download GerryMandria File
       </a>
     </div>
@@ -49,7 +49,7 @@ the first thing to do is to import the required packages:
 
     # Set the random seed so that the results are reproducible!
     import random
-    random.seed(42)
+    random.seed(2024)
 
 Now we set up the initial partition:
 
@@ -94,7 +94,7 @@ We can now set up the chain:
         constraints=[contiguous],
         accept=accept.always_accept,
         initial_state=initial_partition,
-        total_steps=20
+        total_steps=40
     )
 
 and run it with
@@ -131,12 +131,12 @@ bad idea to do this for a chain with a large number of steps).
         pos = {node :(data['x'],data['y']) for node, data in graph.nodes(data=True)}
         node_colors = [mcm.tab20(int(assignment_list[i][node]) % 20) for node in graph.nodes()]
         node_labels = {node: str(assignment_list[i][node]) for node in graph.nodes()}
-        
+
         nx.draw_networkx_nodes(graph, pos, node_color=node_colors)
         nx.draw_networkx_edges(graph, pos)
         nx.draw_networkx_labels(graph, pos, labels=node_labels)
         plt.axis('off')
-        
+
         buffer = io.BytesIO()
         plt.savefig(buffer, format='png')
         buffer.seek(0)
@@ -176,7 +176,7 @@ Fortunately, ``gerrychain`` has a built-in functionality that allows for
 region-aware ReCom chains which create ensembles
 of districting plans that try to keep particular regions of interest together.
 And it only takes one extra line of code: we simply update
-our proposal to include a ``weight_dict`` which increases the importance of the
+our proposal to include a ``region_surcharge`` which increases the importance of the
 edges within the municipalities.
 
 .. code-block:: python
@@ -187,7 +187,7 @@ edges within the municipalities.
         pop_target=ideal_population,
         epsilon=0.01,
         node_repeats=2,
-        weight_dict={"muni": 0.8},
+        region_surcharge={"muni": 1.0},
     )
 
 And this will produce the following ensemble:
@@ -210,7 +210,7 @@ and so it is not going to be possible to keep all of the water districts togethe
 and all of the municipalities together in one plan. However, we can try to keep
 the water districts together as much as possible, and then, within those water
 districts, try to be sensitive to the boundaries of the municipalities. Again, 
-this only requires for us to edit the ``weight_dict`` parameter of the proposal
+this only requires for us to edit the ``region_surcharge`` parameter of the proposal
 
 .. code-block:: python
 
@@ -220,7 +220,7 @@ this only requires for us to edit the ``weight_dict`` parameter of the proposal
         pop_target=ideal_population,
         epsilon=0.01,
         node_repeats=2,
-        weight_dict={"muni": 0.2, "water": 0.8},
+        region_surcharge={"muni": 0.2, "water": 0.8},
     )
 
 Since we are trying to be sensitive to multiple bits of information, we should probably
@@ -236,7 +236,7 @@ also increase the length of our chain to make sure that we have time to mix prop
         total_steps=10000
     )
 
-Then, we can run the chain and look at the last 20 assignments in the ensemble
+Then, we can run the chain and look at the last 40 assignments in the ensemble
 
 .. image:: ./images/gerrymandria_water_muni_ensamble.gif
     :width: 400px
@@ -251,45 +251,106 @@ while also being sensitive to the municipalities
     :align: center
 
     The last map in the ensemble from the 10000 step region-aware ReCom chain with
-    weights of 0.2 for the municipalities and 0.8 for the water districts.
+    surcharges of 0.2 for the municipalities and 0.8 for the water districts.
 
 .. raw:: html
 
    <div style="display: flex; justify-content: space-around;">
        <figure style="text-align: center;">
-           <img src="../_images/gerrymandria_cities.png" style="width: 100%;">
+           <img src="../../_images/gerrymandria_cities.png" style="width: 100%;">
            <figcaption><em>Municipalities of Gerrymandria</em></figcaption>
        </figure>
        <figure style="text-align: center;">
-           <img src="../_images/gerrymandria_water.png" style="width: 100%;">
+           <img src="../../_images/gerrymandria_water.png" style="width: 100%;">
            <figcaption><em>Water Districts of GerryMandria</em><figcaption>
        </figure>
    </div>
 
 
-.. _weight-dict-warning:
+How the Region Aware Implementation Works
+-----------------------------------------
+
+When working with region-aware ReCom chains, it is worth knowing how the spanning tree
+of the dual graph is being split. Weights from the interval :math:`[0,1]` are randomly
+assigned to the edges of the graph and then the surcharges are applied to the edges in
+the graph that span different regions specified by the ``region_surcharge`` dictionary.
+So if we have ``region_surcharge={"muni": 0.2, "water": 0.8}``, then the edges that
+span different municipalities will be upweighted by 0.2 and the edges that span different
+water districts will be upweighted by 0.8. We then draw a minimum spanning tree using
+by greedily selecting the lowest-weight edges via Kruskal's algorithm. The surcharges on
+the edges helps ensure that the algorithm picks the edges interior to the region
+before it picks the edges that bridge different regions. 
+
+This makes it very likely that each region is largely contained in a connected subtree
+attached to a bridge node. Thus, when we make a cut, the regions attached to the
+bridge node are more likely to be (mostly) preserved in the subtree on either side
+of the cut.
+
+In the implementation of :meth:`~gerrychain.tree.biparition_tree` we further bias this
+choice by deterministically cutting bridge edges first (when possible). In the event that
+multiple types of regions are specified, the surcharges are added together, and edges are
+selected first by the number of types of regions that they span, and then by the
+surcharge added to those weights. So, if we have a region surcharge dictionary of
+``{"a": 1, "b": 4, "c": 2}`` then we we look for edges according to the order
+
+- ("a", "b", "c")
+- ("b", "c")
+- ("a", "b")
+- ("a", "c")
+- ("b")
+- ("c")
+- ("a")
+- random
+
+where the tuples indicate that a desired cut edge bridges both types of region in
+the tuple. In the event that this is not the desired behaviour, then the user can simply
+alter the ``cut_choice`` function in the constraints to be different. So, if the user
+would prefer the cut edge to be a random edge with no deference to bridge edges,
+then they might use ``random.choice()`` in the following way:
+
+.. code-block:: python
+
+    proposal = partial(
+        recom,
+        pop_col="TOTPOP",
+        pop_target=ideal_population,
+        epsilon=0.01,
+        node_repeats=1,
+        region_surcharge={
+            "muni": 2.0,
+            "water_dist": 2.0
+        },
+        method = partial(
+            bipartition_tree,
+            cut_choice = random.choice,
+        )
+    )
+
+**Note**: When ``region_surcharge`` is not specified, ``bipartition_tree`` will behave as if
+``cut_choice`` is set to ``random.choice``.
+
 
-.. attention::
+.. .. attention::
 
-  The ``weight_dict`` parameter is a dictionary that assigns a weight to each
-  edge within a particular region that is determined by the keys of the dictionary.
-  In the event that multiple regions are specified, the weights are added together,
-  and if the weights add to more than 1, then the following warning will be printed 
-  to the user:
+..   The ``region_surcharge`` parameter is a dictionary that assigns a surcharge to each
+..   edge within a particular region that is determined by the keys of the dictionary.
+..   In the event that multiple regions are specified, the surcharges are added together,
+..   and if the surcharges add to more than 1, then the following warning will be printed 
+..   to the user:
 
-  .. code-block:: console
+..   .. code-block:: console
     
-    ValueWarning: 
-    The sum of the weights in the weight dictionary is greater than 1.
-    Please consider normalizing the weights.
+..     ValueWarning: 
+..     The sum of the surcharges in the surcharge dictionary is greater than 1.
+..     Please consider normalizing the surcharges.
 
-  It is generally inadvisable to set the weight of a region to 1 or more. When
-  using :meth:`~gerrychain.proposals.recom` with a ``weight_dict``, the proposal
-  will try to draw a minimum spanning tree using Kruskal's algorithm where,
-  the weights are in the range :math:`[0,1]`, then the weights from the weight
-  dictionary are added to them. In the event that
-  many edges within the tree have a weight above 1, then it can sometimes
-  cause the biparitioning step to stall.
+..   It is generally inadvisable to set the surcharge of a region to 1 or more. When
+..   using :meth:`~gerrychain.proposals.recom` with a ``region_surcharge``, the proposal
+..   will try to draw a minimum spanning tree using Kruskal's algorithm where,
+..   the surcharges are in the range :math:`[0,1]`, then the surcharges from the surcharge
+..   dictionary are added to them. In the event that
+..   many edges within the tree have a surcharge above 1, then it can sometimes
+..   cause the bipartitioning step to stall.
 
 
 What to do if the Chain Gets Stuck
@@ -311,7 +372,7 @@ district, then the chain will get stuck and throw an error. Here is the setup:
     from gerrychain.constraints import contiguous
     from functools import partial
     import random
-    random.seed(42)
+    random.seed(0)
 
     graph = Graph.from_json("./gerrymandria.json")
 
@@ -334,7 +395,14 @@ district, then the chain will get stuck and throw an error. Here is the setup:
         pop_target=ideal_population,
         epsilon=0.01,
         node_repeats=1,
-        weight_dict={"muni": 1.0, "water_dist": 1.0},
+        region_surcharge={
+            "muni": 2.0,
+            "water_dist": 2.0
+        },
+        method = partial(
+            bipartition_tree, 
+            max_attempts=100,
+        )
     )
 
     recom_chain = MarkovChain(
@@ -342,23 +410,19 @@ district, then the chain will get stuck and throw an error. Here is the setup:
         constraints=[contiguous],
         accept=accept.always_accept,
         initial_state=initial_partition,
-        total_steps=20
+        total_steps=20,
     )
 
     assignment_list = []
 
     for i, item in enumerate(recom_chain):
         print(f"Finished step {i + 1}/{len(recom_chain)}", end="\r")
-        assignment_list.append(item.assignment)
+        assignment_list.append(item.assignment))
 
 This will output the following sequence of warnings and errors
 
 .. code-block:: console
 
-    ValueWarning: 
-    The sum of the weights in the weight dictionary is greater than 1.
-    Please consider normalizing the weights.
-
     BipartitionWarning: 
     Failed to find a balanced cut after 50 attempts.
     If possible, consider enabling pair reselection within your
@@ -374,12 +438,6 @@ Let's break down what is happening in each of these:
 .. raw:: html
 
   <ul>
-    <li><strong>ValueWarning</strong> 
-      This is just telling us that we have made an ill-advised
-      choice of weights for our regions. See <a href="#weight-dict-warning">the above warning</a> 
-      for more information.
-    </li>
-    <br style="line-height: 5px;">
     <li><strong>BipartitionWarning</strong>
       This is telling us that somewhere along the way, 
       we picked a pair of districts that were difficult to bipartition underneath
@@ -419,7 +477,10 @@ node repeats:
         pop_target=ideal_population,
         epsilon=0.01,
         node_repeats=100,
-        weight_dict={"muni": 1.0, "water_dist": 1.0},
+        region_surcharge={
+            "muni": 1.0, 
+            "water_dist": 1.0
+        },
     )
 
 Running this code, we can see that we get stuck once again, so this was not the fix.
@@ -427,7 +488,11 @@ Let's try to enable reselection instead:
 
 .. code-block:: python 
 
-    method = partial(bipartition_tree, allow_pair_reselection=True)
+    method = partial(
+        bipartition_tree,
+        max_attempts=100,
+        allow_pair_reselection=True
+    )
 
     proposal = partial(
         recom,
@@ -435,7 +500,10 @@ Let's try to enable reselection instead:
         pop_target=ideal_population,
         epsilon=0.01,
         node_repeats=1,
-        weight_dict={"muni": 1.0, "water_dist": 1.0},
+        region_surcharge={
+            "muni": 1.0,
+            "water_dist": 1.0
+        },
         method=method
     )
 
@@ -473,7 +541,7 @@ Setting up the initial districting plan
 .. raw:: html
 
     <div class="center-container">
-      <a href="https://github.com/mggg/GerryChain/blob/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
+      <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
     </div>
     <br style="line-height: 5px;">
 
diff --git a/api.html b/api.html
index bb802a8a..1c7aabe7 100644
--- a/api.html
+++ b/api.html
@@ -155,7 +155,7 @@ <h2><a class="toc-backref" href="#id6">Adjacency graphs</a><a class="headerlink"
 </div>
 <dl class="method">
 <dt id="gerrychain.graph.graph.Graph.add_data">
-<code class="sig-name descname">add_data</code><span class="sig-paren">(</span><em class="sig-param">df: &lt;Mock name='mock.DataFrame' id='140048407164816'&gt;</em>, <em class="sig-param">columns: Optional[Iterable[str]] = None</em><span class="sig-paren">)</span> &#x2192; None<a class="reference internal" href="_modules/gerrychain/graph/graph.html#Graph.add_data"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#gerrychain.graph.graph.Graph.add_data" title="Permalink to this definition">¶</a></dt>
+<code class="sig-name descname">add_data</code><span class="sig-paren">(</span><em class="sig-param">df: &lt;Mock name='mock.DataFrame' id='140565501544864'&gt;</em>, <em class="sig-param">columns: Optional[Iterable[str]] = None</em><span class="sig-paren">)</span> &#x2192; None<a class="reference internal" href="_modules/gerrychain/graph/graph.html#Graph.add_data"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#gerrychain.graph.graph.Graph.add_data" title="Permalink to this definition">¶</a></dt>
 <dd><p>Add columns of a DataFrame to a graph as node attributes
 by matching the DataFrame’s index to node ids.</p>
 <dl class="field-list simple">
@@ -211,7 +211,7 @@ <h2><a class="toc-backref" href="#id6">Adjacency graphs</a><a class="headerlink"
 
 <dl class="method">
 <dt id="gerrychain.graph.graph.Graph.from_geodataframe">
-<em class="property">classmethod </em><code class="sig-name descname">from_geodataframe</code><span class="sig-paren">(</span><em class="sig-param">dataframe: &lt;Mock name='mock.DataFrame' id='140048407164816'&gt;</em>, <em class="sig-param">adjacency: str = 'rook'</em>, <em class="sig-param">cols_to_add: Optional[List[str]] = None</em>, <em class="sig-param">reproject: bool = False</em>, <em class="sig-param">ignore_errors: bool = False</em><span class="sig-paren">)</span> &#x2192; gerrychain.graph.graph.Graph<a class="reference internal" href="_modules/gerrychain/graph/graph.html#Graph.from_geodataframe"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#gerrychain.graph.graph.Graph.from_geodataframe" title="Permalink to this definition">¶</a></dt>
+<em class="property">classmethod </em><code class="sig-name descname">from_geodataframe</code><span class="sig-paren">(</span><em class="sig-param">dataframe: &lt;Mock name='mock.DataFrame' id='140565501544864'&gt;</em>, <em class="sig-param">adjacency: str = 'rook'</em>, <em class="sig-param">cols_to_add: Optional[List[str]] = None</em>, <em class="sig-param">reproject: bool = False</em>, <em class="sig-param">ignore_errors: bool = False</em><span class="sig-paren">)</span> &#x2192; gerrychain.graph.graph.Graph<a class="reference internal" href="_modules/gerrychain/graph/graph.html#Graph.from_geodataframe"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#gerrychain.graph.graph.Graph.from_geodataframe" title="Permalink to this definition">¶</a></dt>
 <dd><p>Creates the adjacency <a class="reference internal" href="#gerrychain.graph.graph.Graph" title="gerrychain.graph.graph.Graph"><code class="xref py py-class docutils literal notranslate"><span class="pre">Graph</span></code></a> of geometries described by <cite>dataframe</cite>.
 The areas of the polygons are included as node attributes (with key <cite>area</cite>).
 The shared perimeter of neighboring polygons are included as edge attributes
@@ -311,7 +311,7 @@ <h2><a class="toc-backref" href="#id6">Adjacency graphs</a><a class="headerlink"
 
 <dl class="method">
 <dt id="gerrychain.graph.graph.Graph.join">
-<code class="sig-name descname">join</code><span class="sig-paren">(</span><em class="sig-param">dataframe: &lt;Mock name='mock.DataFrame' id='140048407164816'&gt;</em>, <em class="sig-param">columns: Optional[List[str]] = None</em>, <em class="sig-param">left_index: Optional[str] = None</em>, <em class="sig-param">right_index: Optional[str] = None</em><span class="sig-paren">)</span> &#x2192; None<a class="reference internal" href="_modules/gerrychain/graph/graph.html#Graph.join"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#gerrychain.graph.graph.Graph.join" title="Permalink to this definition">¶</a></dt>
+<code class="sig-name descname">join</code><span class="sig-paren">(</span><em class="sig-param">dataframe: &lt;Mock name='mock.DataFrame' id='140565501544864'&gt;</em>, <em class="sig-param">columns: Optional[List[str]] = None</em>, <em class="sig-param">left_index: Optional[str] = None</em>, <em class="sig-param">right_index: Optional[str] = None</em><span class="sig-paren">)</span> &#x2192; None<a class="reference internal" href="_modules/gerrychain/graph/graph.html#Graph.join"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#gerrychain.graph.graph.Graph.join" title="Permalink to this definition">¶</a></dt>
 <dd><p>Add data from a dataframe to the graph, matching nodes to rows when
 the node’s <cite>left_index</cite> attribute equals the row’s <cite>right_index</cite> value.</p>
 <dl class="field-list simple">
@@ -600,7 +600,7 @@ <h2><a class="toc-backref" href="#id8">Markov chains</a><a class="headerlink" hr
 <span id="proposals"></span><h2><a class="toc-backref" href="#id9">Proposals</a><a class="headerlink" href="#module-gerrychain.proposals" title="Permalink to this headline">¶</a></h2>
 <dl class="function">
 <dt id="gerrychain.proposals.recom">
-<code class="sig-prename descclassname">gerrychain.proposals.</code><code class="sig-name descname">recom</code><span class="sig-paren">(</span><em class="sig-param">partition: gerrychain.partition.partition.Partition, pop_col: str, pop_target: Union[int, float], epsilon: float, node_repeats: int = 1, weight_dict: Optional[Dict] = None, method: Callable = &lt;function bipartition_tree&gt;</em><span class="sig-paren">)</span> &#x2192; gerrychain.partition.partition.Partition<a class="reference internal" href="_modules/gerrychain/proposals/tree_proposals.html#recom"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#gerrychain.proposals.recom" title="Permalink to this definition">¶</a></dt>
+<code class="sig-prename descclassname">gerrychain.proposals.</code><code class="sig-name descname">recom</code><span class="sig-paren">(</span><em class="sig-param">partition: gerrychain.partition.partition.Partition, pop_col: str, pop_target: Union[int, float], epsilon: float, node_repeats: int = 1, region_surcharge: Optional[Dict] = None, method: Callable = &lt;function bipartition_tree&gt;</em><span class="sig-paren">)</span> &#x2192; gerrychain.partition.partition.Partition<a class="reference internal" href="_modules/gerrychain/proposals/tree_proposals.html#recom"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#gerrychain.proposals.recom" title="Permalink to this definition">¶</a></dt>
 <dd><p>ReCom (short for ReCombination) is a Markov Chain Monte Carlo (MCMC) algorithm
 used for redistricting. At each step of the algorithm, a pair of adjacent districts
 is selected at random and merged into a single district. The region is then split
@@ -634,7 +634,7 @@ <h2><a class="toc-backref" href="#id8">Markov chains</a><a class="headerlink" hr
 <li><p><strong>epsilon</strong> (<em>float</em>) – The epsilon value for population deviation as a percentage of the
 target population.</p></li>
 <li><p><strong>node_repeats</strong> (<em>int</em><em>, </em><em>optional</em>) – The number of times to repeat the bipartitioning step. Default is 1.</p></li>
-<li><p><strong>weight_dict</strong> (<em>Optional</em><em>[</em><em>Dict</em><em>]</em><em>, </em><em>optional</em>) – The weight dictionary for the graph used for region-aware
+<li><p><strong>region_surcharge</strong> (<em>Optional</em><em>[</em><em>Dict</em><em>]</em><em>, </em><em>optional</em>) – The surcharge dictionary for the graph used for region-aware
 partitioning of the grid. Default is None.</p></li>
 <li><p><strong>method</strong> (<em>Callable</em><em>, </em><em>optional</em>) – The method used for bipartitioning the tree. Default is
 <a class="reference internal" href="#gerrychain.tree.bipartition_tree" title="gerrychain.tree.bipartition_tree"><code class="xref py py-func docutils literal notranslate"><span class="pre">bipartition_tree()</span></code></a>.</p></li>
@@ -646,10 +646,6 @@ <h2><a class="toc-backref" href="#id8">Markov chains</a><a class="headerlink" hr
 <dt class="field-odd">Return type</dt>
 <dd class="field-odd"><p><a class="reference internal" href="#gerrychain.partition.Partition" title="gerrychain.partition.Partition">Partition</a></p>
 </dd>
-<dt class="field-even">Raises</dt>
-<dd class="field-even"><p><strong>ValueWarning</strong> – Raised when the sum of the weights in the weight dictionary is
-greater than 1.</p>
-</dd>
 </dl>
 </dd></dl>
 
@@ -1328,7 +1324,7 @@ <h2><a class="toc-backref" href="#id8">Markov chains</a><a class="headerlink" hr
 
 <dl class="class">
 <dt id="gerrychain.updaters.DataTally">
-<em class="property">class </em><code class="sig-prename descclassname">gerrychain.updaters.</code><code class="sig-name descname">DataTally</code><span class="sig-paren">(</span><em class="sig-param">data: Union[Dict, &lt;Mock name='mock.Series' id='140048407164912'&gt;, str], alias: str</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/gerrychain/updaters/tally.html#DataTally"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#gerrychain.updaters.DataTally" title="Permalink to this definition">¶</a></dt>
+<em class="property">class </em><code class="sig-prename descclassname">gerrychain.updaters.</code><code class="sig-name descname">DataTally</code><span class="sig-paren">(</span><em class="sig-param">data: Union[Dict, &lt;Mock name='mock.Series' id='140565501545008'&gt;, str], alias: str</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/gerrychain/updaters/tally.html#DataTally"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#gerrychain.updaters.DataTally" title="Permalink to this definition">¶</a></dt>
 <dd><p>An updater for tallying numerical data that is not necessarily stored as
 node attributes</p>
 <dl class="field-list simple">
@@ -2155,17 +2151,23 @@ <h2><a class="toc-backref" href="#id14">Spanning tree methods</a><a class="heade
 <dt id="gerrychain.tree.Cut">
 <em class="property">class </em><code class="sig-prename descclassname">gerrychain.tree.</code><code class="sig-name descname">Cut</code><a class="headerlink" href="#gerrychain.tree.Cut" title="Permalink to this definition">¶</a></dt>
 <dd><p>Represents a cut in a graph.</p>
-<p>Create new instance of Cut(edge, subset)</p>
+<p>Create new instance of Cut(edge, weight, subset)</p>
 <dl class="attribute">
 <dt id="gerrychain.tree.Cut.edge">
 <code class="sig-name descname">edge</code><a class="headerlink" href="#gerrychain.tree.Cut.edge" title="Permalink to this definition">¶</a></dt>
-<dd><p>The edge where the cut is made.</p>
+<dd><p>The edge where the cut is made. Defaults to None.</p>
 </dd></dl>
 
 <dl class="attribute">
 <dt id="gerrychain.tree.Cut.subset">
 <code class="sig-name descname">subset</code><a class="headerlink" href="#gerrychain.tree.Cut.subset" title="Permalink to this definition">¶</a></dt>
-<dd><p>The subset of nodes on one side of the cut.</p>
+<dd><p>The (frozen) subset of nodes on one side of the cut. Defaults to None.</p>
+</dd></dl>
+
+<dl class="attribute">
+<dt id="gerrychain.tree.Cut.weight">
+<code class="sig-name descname">weight</code><a class="headerlink" href="#gerrychain.tree.Cut.weight" title="Permalink to this definition">¶</a></dt>
+<dd><p>The weight assigned to the edge (if any). Defaults to None.</p>
 </dd></dl>
 
 </dd></dl>
@@ -2209,7 +2211,7 @@ <h2><a class="toc-backref" href="#id14">Spanning tree methods</a><a class="heade
 
 <dl class="function">
 <dt id="gerrychain.tree.bipartition_tree">
-<code class="sig-prename descclassname">gerrychain.tree.</code><code class="sig-name descname">bipartition_tree</code><span class="sig-paren">(</span><em class="sig-param">graph: networkx.classes.graph.Graph, pop_col: str, pop_target: Union[int, float], epsilon: float, node_repeats: int = 1, spanning_tree: Optional[networkx.classes.graph.Graph] = None, spanning_tree_fn: Callable = &lt;function random_spanning_tree&gt;, weight_dict: Optional[Dict] = None, balance_edge_fn: Callable = &lt;function find_balanced_edge_cuts_memoization&gt;, choice: Callable = &lt;bound method Random.choice of &lt;random.Random object&gt;&gt;, max_attempts: Optional[int] = 100000, allow_pair_reselection: bool = False</em><span class="sig-paren">)</span> &#x2192; Set<a class="reference internal" href="_modules/gerrychain/tree.html#bipartition_tree"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#gerrychain.tree.bipartition_tree" title="Permalink to this definition">¶</a></dt>
+<code class="sig-prename descclassname">gerrychain.tree.</code><code class="sig-name descname">bipartition_tree</code><span class="sig-paren">(</span><em class="sig-param">graph: networkx.classes.graph.Graph, pop_col: str, pop_target: Union[int, float], epsilon: float, node_repeats: int = 1, spanning_tree: Optional[networkx.classes.graph.Graph] = None, spanning_tree_fn: Callable = &lt;function random_spanning_tree&gt;, region_surcharge: Optional[Dict] = None, balance_edge_fn: Callable = &lt;function find_balanced_edge_cuts_memoization&gt;, choice: Callable = &lt;bound method Random.choice of &lt;random.Random object&gt;&gt;, max_attempts: Optional[int] = 100000, warn_attempts: int = 1000, allow_pair_reselection: bool = False, cut_choice: Callable = &lt;function _region_preferred_max_weight_choice&gt;</em><span class="sig-paren">)</span> &#x2192; Set<a class="reference internal" href="_modules/gerrychain/tree.html#bipartition_tree"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#gerrychain.tree.bipartition_tree" title="Permalink to this definition">¶</a></dt>
 <dd><p>This function finds a balanced 2 partition of a graph by drawing a
 spanning tree and finding an edge to cut that leaves at most an epsilon
 imbalance between the populations of the parts. If a root fails, new roots
@@ -2230,16 +2232,21 @@ <h2><a class="toc-backref" href="#id14">Spanning tree methods</a><a class="heade
 algorithm chooses a new root and for testing).</p></li>
 <li><p><strong>spanning_tree_fn</strong> (<em>Callable</em><em>, </em><em>optional</em>) – The random spanning tree algorithm to use if a spanning
 tree is not provided. Defaults to <a class="reference internal" href="#gerrychain.tree.random_spanning_tree" title="gerrychain.tree.random_spanning_tree"><code class="xref py py-func docutils literal notranslate"><span class="pre">random_spanning_tree()</span></code></a>.</p></li>
-<li><p><strong>weight_dict</strong> (<em>Optional</em><em>[</em><em>Dict</em><em>]</em><em>, </em><em>optional</em>) – A dictionary of weights for the spanning tree algorithm.
+<li><p><strong>region_surcharge</strong> (<em>Optional</em><em>[</em><em>Dict</em><em>]</em><em>, </em><em>optional</em>) – A dictionary of surcharges for the spanning tree algorithm.
 Defaults to None.</p></li>
 <li><p><strong>balance_edge_fn</strong> (<em>Callable</em><em>, </em><em>optional</em>) – The function to find balanced edge cuts. Defaults to
 <a class="reference internal" href="#gerrychain.tree.find_balanced_edge_cuts_memoization" title="gerrychain.tree.find_balanced_edge_cuts_memoization"><code class="xref py py-func docutils literal notranslate"><span class="pre">find_balanced_edge_cuts_memoization()</span></code></a>.</p></li>
-<li><p><strong>choice</strong> (<em>Callable</em><em>, </em><em>optional</em>) – The function to make a random choice. Can be substituted for testing.
-Defaults to <code class="xref py py-func docutils literal notranslate"><span class="pre">random.choice()</span></code>.</p></li>
+<li><p><strong>choice</strong> (<em>Callable</em><em>, </em><em>optional</em>) – The function to make a random choice of root node for the population
+tree. Passed to <code class="docutils literal notranslate"><span class="pre">balance_edge_fn</span></code>. Can be substituted for testing.
+Defaults to <code class="xref py py-func docutils literal notranslate"><span class="pre">random.random()</span></code>.</p></li>
 <li><p><strong>max_attempts</strong> (<em>Optional</em><em>[</em><em>int</em><em>]</em><em>, </em><em>optional</em>) – The maximum number of attempts that should be made to bipartition.
 Defaults to 10000.</p></li>
+<li><p><strong>warn_attempts</strong> (<em>int</em><em>, </em><em>optional</em>) – The number of attempts after which a warning is issued if a balanced
+cut cannot be found. Defaults to 1000.</p></li>
 <li><p><strong>allow_pair_reselection</strong> (<em>bool</em><em>, </em><em>optional</em>) – Whether we would like to return an error to the calling
 function to ask it to reselect the pair of nodes to try and recombine. Defaults to False.</p></li>
+<li><p><strong>cut_choice</strong> (<em>Callable</em><em>, </em><em>optional</em>) – The function used to select the cut edge from the list of possible
+balanced cuts. Defaults to <code class="xref py py-meth docutils literal notranslate"><span class="pre">_region_preferred_max_weight_choice()</span></code> .</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns</dt>
@@ -2251,7 +2258,7 @@ <h2><a class="toc-backref" href="#id14">Spanning tree methods</a><a class="heade
 </dd>
 <dt class="field-even">Raises</dt>
 <dd class="field-even"><ul class="simple">
-<li><p><a class="reference internal" href="#gerrychain.tree.BipartitionWarning" title="gerrychain.tree.BipartitionWarning"><strong>BipartitionWarning</strong></a> – If a possible cut cannot be found after 50 attempts.</p></li>
+<li><p><a class="reference internal" href="#gerrychain.tree.BipartitionWarning" title="gerrychain.tree.BipartitionWarning"><strong>BipartitionWarning</strong></a> – If a possible cut cannot be found after 1000 attempts.</p></li>
 <li><p><strong>RuntimeError</strong> – If a possible cut cannot be found after the maximum number of attempts
 given by <code class="docutils literal notranslate"><span class="pre">max_attempts</span></code>.</p></li>
 </ul>
@@ -2406,14 +2413,14 @@ <h2><a class="toc-backref" href="#id14">Spanning tree methods</a><a class="heade
 
 <dl class="function">
 <dt id="gerrychain.tree.random_spanning_tree">
-<code class="sig-prename descclassname">gerrychain.tree.</code><code class="sig-name descname">random_spanning_tree</code><span class="sig-paren">(</span><em class="sig-param">graph: networkx.classes.graph.Graph</em>, <em class="sig-param">weight_dict: Optional[Dict] = None</em><span class="sig-paren">)</span> &#x2192; networkx.classes.graph.Graph<a class="reference internal" href="_modules/gerrychain/tree.html#random_spanning_tree"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#gerrychain.tree.random_spanning_tree" title="Permalink to this definition">¶</a></dt>
+<code class="sig-prename descclassname">gerrychain.tree.</code><code class="sig-name descname">random_spanning_tree</code><span class="sig-paren">(</span><em class="sig-param">graph: networkx.classes.graph.Graph</em>, <em class="sig-param">region_surcharge: Optional[Dict] = None</em><span class="sig-paren">)</span> &#x2192; networkx.classes.graph.Graph<a class="reference internal" href="_modules/gerrychain/tree.html#random_spanning_tree"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#gerrychain.tree.random_spanning_tree" title="Permalink to this definition">¶</a></dt>
 <dd><p>Builds a spanning tree chosen by Kruskal’s method using random weights.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters</dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>graph</strong> (<em>nx.Graph</em>) – The input graph to build the spanning tree from. Should be a Networkx Graph.</p></li>
-<li><p><strong>weight_dict</strong> (<em>Optional</em><em>[</em><em>Dict</em><em>]</em><em>, </em><em>optional</em>) – Dictionary of weights to add to the random weights used in region-aware
-variants.</p></li>
+<li><p><strong>region_surcharge</strong> (<em>Optional</em><em>[</em><em>Dict</em><em>]</em><em>, </em><em>optional</em>) – Dictionary of surcharges to add to the random
+weights used in region-aware variants.</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns</dt>
diff --git a/full_ref.html b/full_ref.html
index 28105e9f..2be9fdcc 100644
--- a/full_ref.html
+++ b/full_ref.html
@@ -630,17 +630,23 @@ <h2>Tree<a class="headerlink" href="#tree" title="Permalink to this headline">¶
 <em class="property">class </em><code class="sig-prename descclassname">gerrychain.tree.</code><code class="sig-name descname">Cut</code></dt>
 <dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">tuple</span></code></p>
 <p>Represents a cut in a graph.</p>
-<p>Create new instance of Cut(edge, subset)</p>
+<p>Create new instance of Cut(edge, weight, subset)</p>
 <dl class="attribute">
 <dt>
 <code class="sig-name descname">edge</code></dt>
-<dd><p>The edge where the cut is made.</p>
+<dd><p>The edge where the cut is made. Defaults to None.</p>
 </dd></dl>
 
 <dl class="attribute">
 <dt>
 <code class="sig-name descname">subset</code></dt>
-<dd><p>The subset of nodes on one side of the cut.</p>
+<dd><p>The (frozen) subset of nodes on one side of the cut. Defaults to None.</p>
+</dd></dl>
+
+<dl class="attribute">
+<dt>
+<code class="sig-name descname">weight</code></dt>
+<dd><p>The weight assigned to the edge (if any). Defaults to None.</p>
 </dd></dl>
 
 </dd></dl>
@@ -701,7 +707,7 @@ <h2>Tree<a class="headerlink" href="#tree" title="Permalink to this headline">¶
 
 <dl class="function">
 <dt>
-<code class="sig-prename descclassname">gerrychain.tree.</code><code class="sig-name descname">bipartition_tree</code><span class="sig-paren">(</span><em class="sig-param">graph: networkx.classes.graph.Graph, pop_col: str, pop_target: Union[int, float], epsilon: float, node_repeats: int = 1, spanning_tree: Optional[networkx.classes.graph.Graph] = None, spanning_tree_fn: Callable = &lt;function random_spanning_tree&gt;, weight_dict: Optional[Dict] = None, balance_edge_fn: Callable = &lt;function find_balanced_edge_cuts_memoization&gt;, choice: Callable = &lt;bound method Random.choice of &lt;random.Random object&gt;&gt;, max_attempts: Optional[int] = 100000, allow_pair_reselection: bool = False</em><span class="sig-paren">)</span> &#x2192; Set<a class="reference internal" href="_modules/gerrychain/tree.html#bipartition_tree"><span class="viewcode-link">[source]</span></a></dt>
+<code class="sig-prename descclassname">gerrychain.tree.</code><code class="sig-name descname">bipartition_tree</code><span class="sig-paren">(</span><em class="sig-param">graph: networkx.classes.graph.Graph, pop_col: str, pop_target: Union[int, float], epsilon: float, node_repeats: int = 1, spanning_tree: Optional[networkx.classes.graph.Graph] = None, spanning_tree_fn: Callable = &lt;function random_spanning_tree&gt;, region_surcharge: Optional[Dict] = None, balance_edge_fn: Callable = &lt;function find_balanced_edge_cuts_memoization&gt;, choice: Callable = &lt;bound method Random.choice of &lt;random.Random object&gt;&gt;, max_attempts: Optional[int] = 100000, warn_attempts: int = 1000, allow_pair_reselection: bool = False, cut_choice: Callable = &lt;function _region_preferred_max_weight_choice&gt;</em><span class="sig-paren">)</span> &#x2192; Set<a class="reference internal" href="_modules/gerrychain/tree.html#bipartition_tree"><span class="viewcode-link">[source]</span></a></dt>
 <dd><p>This function finds a balanced 2 partition of a graph by drawing a
 spanning tree and finding an edge to cut that leaves at most an epsilon
 imbalance between the populations of the parts. If a root fails, new roots
@@ -722,16 +728,21 @@ <h2>Tree<a class="headerlink" href="#tree" title="Permalink to this headline">¶
 algorithm chooses a new root and for testing).</p></li>
 <li><p><strong>spanning_tree_fn</strong> (<em>Callable</em><em>, </em><em>optional</em>) – The random spanning tree algorithm to use if a spanning
 tree is not provided. Defaults to <a class="reference internal" href="api.html#gerrychain.tree.random_spanning_tree" title="gerrychain.tree.random_spanning_tree"><code class="xref py py-func docutils literal notranslate"><span class="pre">random_spanning_tree()</span></code></a>.</p></li>
-<li><p><strong>weight_dict</strong> (<em>Optional</em><em>[</em><em>Dict</em><em>]</em><em>, </em><em>optional</em>) – A dictionary of weights for the spanning tree algorithm.
+<li><p><strong>region_surcharge</strong> (<em>Optional</em><em>[</em><em>Dict</em><em>]</em><em>, </em><em>optional</em>) – A dictionary of surcharges for the spanning tree algorithm.
 Defaults to None.</p></li>
 <li><p><strong>balance_edge_fn</strong> (<em>Callable</em><em>, </em><em>optional</em>) – The function to find balanced edge cuts. Defaults to
 <a class="reference internal" href="api.html#gerrychain.tree.find_balanced_edge_cuts_memoization" title="gerrychain.tree.find_balanced_edge_cuts_memoization"><code class="xref py py-func docutils literal notranslate"><span class="pre">find_balanced_edge_cuts_memoization()</span></code></a>.</p></li>
-<li><p><strong>choice</strong> (<em>Callable</em><em>, </em><em>optional</em>) – The function to make a random choice. Can be substituted for testing.
-Defaults to <code class="xref py py-func docutils literal notranslate"><span class="pre">random.choice()</span></code>.</p></li>
+<li><p><strong>choice</strong> (<em>Callable</em><em>, </em><em>optional</em>) – The function to make a random choice of root node for the population
+tree. Passed to <code class="docutils literal notranslate"><span class="pre">balance_edge_fn</span></code>. Can be substituted for testing.
+Defaults to <code class="xref py py-func docutils literal notranslate"><span class="pre">random.random()</span></code>.</p></li>
 <li><p><strong>max_attempts</strong> (<em>Optional</em><em>[</em><em>int</em><em>]</em><em>, </em><em>optional</em>) – The maximum number of attempts that should be made to bipartition.
 Defaults to 10000.</p></li>
+<li><p><strong>warn_attempts</strong> (<em>int</em><em>, </em><em>optional</em>) – The number of attempts after which a warning is issued if a balanced
+cut cannot be found. Defaults to 1000.</p></li>
 <li><p><strong>allow_pair_reselection</strong> (<em>bool</em><em>, </em><em>optional</em>) – Whether we would like to return an error to the calling
 function to ask it to reselect the pair of nodes to try and recombine. Defaults to False.</p></li>
+<li><p><strong>cut_choice</strong> (<em>Callable</em><em>, </em><em>optional</em>) – The function used to select the cut edge from the list of possible
+balanced cuts. Defaults to <code class="xref py py-meth docutils literal notranslate"><span class="pre">_region_preferred_max_weight_choice()</span></code> .</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns</dt>
@@ -743,7 +754,7 @@ <h2>Tree<a class="headerlink" href="#tree" title="Permalink to this headline">¶
 </dd>
 <dt class="field-even">Raises</dt>
 <dd class="field-even"><ul class="simple">
-<li><p><a class="reference internal" href="api.html#gerrychain.tree.BipartitionWarning" title="gerrychain.tree.BipartitionWarning"><strong>BipartitionWarning</strong></a> – If a possible cut cannot be found after 50 attempts.</p></li>
+<li><p><a class="reference internal" href="api.html#gerrychain.tree.BipartitionWarning" title="gerrychain.tree.BipartitionWarning"><strong>BipartitionWarning</strong></a> – If a possible cut cannot be found after 1000 attempts.</p></li>
 <li><p><strong>RuntimeError</strong> – If a possible cut cannot be found after the maximum number of attempts
 given by <code class="docutils literal notranslate"><span class="pre">max_attempts</span></code>.</p></li>
 </ul>
@@ -903,14 +914,14 @@ <h2>Tree<a class="headerlink" href="#tree" title="Permalink to this headline">¶
 
 <dl class="function">
 <dt>
-<code class="sig-prename descclassname">gerrychain.tree.</code><code class="sig-name descname">random_spanning_tree</code><span class="sig-paren">(</span><em class="sig-param">graph: networkx.classes.graph.Graph</em>, <em class="sig-param">weight_dict: Optional[Dict] = None</em><span class="sig-paren">)</span> &#x2192; networkx.classes.graph.Graph<a class="reference internal" href="_modules/gerrychain/tree.html#random_spanning_tree"><span class="viewcode-link">[source]</span></a></dt>
+<code class="sig-prename descclassname">gerrychain.tree.</code><code class="sig-name descname">random_spanning_tree</code><span class="sig-paren">(</span><em class="sig-param">graph: networkx.classes.graph.Graph</em>, <em class="sig-param">region_surcharge: Optional[Dict] = None</em><span class="sig-paren">)</span> &#x2192; networkx.classes.graph.Graph<a class="reference internal" href="_modules/gerrychain/tree.html#random_spanning_tree"><span class="viewcode-link">[source]</span></a></dt>
 <dd><p>Builds a spanning tree chosen by Kruskal’s method using random weights.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters</dt>
 <dd class="field-odd"><ul class="simple">
 <li><p><strong>graph</strong> (<em>nx.Graph</em>) – The input graph to build the spanning tree from. Should be a Networkx Graph.</p></li>
-<li><p><strong>weight_dict</strong> (<em>Optional</em><em>[</em><em>Dict</em><em>]</em><em>, </em><em>optional</em>) – Dictionary of weights to add to the random weights used in region-aware
-variants.</p></li>
+<li><p><strong>region_surcharge</strong> (<em>Optional</em><em>[</em><em>Dict</em><em>]</em><em>, </em><em>optional</em>) – Dictionary of surcharges to add to the random
+weights used in region-aware variants.</p></li>
 </ul>
 </dd>
 <dt class="field-even">Returns</dt>
@@ -1585,7 +1596,7 @@ <h2>Graph<a class="headerlink" href="#graph" title="Permalink to this headline">
 
 <dl class="function">
 <dt>
-<code class="sig-prename descclassname">gerrychain.graph.adjacency.</code><code class="sig-name descname">neighbors</code><span class="sig-paren">(</span><em class="sig-param">df: &lt;Mock name='mock.GeoDataFrame' id='140048407617888'&gt;</em>, <em class="sig-param">adjacency: str</em><span class="sig-paren">)</span> &#x2192; Dict<a class="reference internal" href="_modules/gerrychain/graph/adjacency.html#neighbors"><span class="viewcode-link">[source]</span></a></dt>
+<code class="sig-prename descclassname">gerrychain.graph.adjacency.</code><code class="sig-name descname">neighbors</code><span class="sig-paren">(</span><em class="sig-param">df: &lt;Mock name='mock.GeoDataFrame' id='140565501473552'&gt;</em>, <em class="sig-param">adjacency: str</em><span class="sig-paren">)</span> &#x2192; Dict<a class="reference internal" href="_modules/gerrychain/graph/adjacency.html#neighbors"><span class="viewcode-link">[source]</span></a></dt>
 <dd></dd></dl>
 
 <dl class="function">
@@ -1691,7 +1702,7 @@ <h2>Graph<a class="headerlink" href="#graph" title="Permalink to this headline">
 
 <dl class="function">
 <dt>
-<code class="sig-prename descclassname">gerrychain.graph.geo.</code><code class="sig-name descname">identify_utm_zone</code><span class="sig-paren">(</span><em class="sig-param">df: &lt;Mock name='mock.GeoDataFrame' id='140048407617888'&gt;</em><span class="sig-paren">)</span> &#x2192; int<a class="reference internal" href="_modules/gerrychain/graph/geo.html#identify_utm_zone"><span class="viewcode-link">[source]</span></a></dt>
+<code class="sig-prename descclassname">gerrychain.graph.geo.</code><code class="sig-name descname">identify_utm_zone</code><span class="sig-paren">(</span><em class="sig-param">df: &lt;Mock name='mock.GeoDataFrame' id='140565501473552'&gt;</em><span class="sig-paren">)</span> &#x2192; int<a class="reference internal" href="_modules/gerrychain/graph/geo.html#identify_utm_zone"><span class="viewcode-link">[source]</span></a></dt>
 <dd><p>Given a GeoDataFrame, identify the Universal Transverse Mercator zone
 number for the centroid of the geometries in the dataframe.</p>
 </dd></dl>
@@ -1851,7 +1862,7 @@ <h2>Graph<a class="headerlink" href="#graph" title="Permalink to this headline">
 </div>
 <dl class="method">
 <dt>
-<code class="sig-name descname">add_data</code><span class="sig-paren">(</span><em class="sig-param">df: &lt;Mock name='mock.DataFrame' id='140048407164816'&gt;</em>, <em class="sig-param">columns: Optional[Iterable[str]] = None</em><span class="sig-paren">)</span> &#x2192; None<a class="reference internal" href="_modules/gerrychain/graph/graph.html#Graph.add_data"><span class="viewcode-link">[source]</span></a></dt>
+<code class="sig-name descname">add_data</code><span class="sig-paren">(</span><em class="sig-param">df: &lt;Mock name='mock.DataFrame' id='140565501544864'&gt;</em>, <em class="sig-param">columns: Optional[Iterable[str]] = None</em><span class="sig-paren">)</span> &#x2192; None<a class="reference internal" href="_modules/gerrychain/graph/graph.html#Graph.add_data"><span class="viewcode-link">[source]</span></a></dt>
 <dd><p>Add columns of a DataFrame to a graph as node attributes
 by matching the DataFrame’s index to node ids.</p>
 <dl class="field-list simple">
@@ -1912,7 +1923,7 @@ <h2>Graph<a class="headerlink" href="#graph" title="Permalink to this headline">
 
 <dl class="method">
 <dt>
-<em class="property">classmethod </em><code class="sig-name descname">from_geodataframe</code><span class="sig-paren">(</span><em class="sig-param">dataframe: &lt;Mock name='mock.DataFrame' id='140048407164816'&gt;</em>, <em class="sig-param">adjacency: str = 'rook'</em>, <em class="sig-param">cols_to_add: Optional[List[str]] = None</em>, <em class="sig-param">reproject: bool = False</em>, <em class="sig-param">ignore_errors: bool = False</em><span class="sig-paren">)</span> &#x2192; gerrychain.graph.graph.Graph<a class="reference internal" href="_modules/gerrychain/graph/graph.html#Graph.from_geodataframe"><span class="viewcode-link">[source]</span></a></dt>
+<em class="property">classmethod </em><code class="sig-name descname">from_geodataframe</code><span class="sig-paren">(</span><em class="sig-param">dataframe: &lt;Mock name='mock.DataFrame' id='140565501544864'&gt;</em>, <em class="sig-param">adjacency: str = 'rook'</em>, <em class="sig-param">cols_to_add: Optional[List[str]] = None</em>, <em class="sig-param">reproject: bool = False</em>, <em class="sig-param">ignore_errors: bool = False</em><span class="sig-paren">)</span> &#x2192; gerrychain.graph.graph.Graph<a class="reference internal" href="_modules/gerrychain/graph/graph.html#Graph.from_geodataframe"><span class="viewcode-link">[source]</span></a></dt>
 <dd><p>Creates the adjacency <a class="reference internal" href="api.html#gerrychain.graph.graph.Graph" title="gerrychain.graph.graph.Graph"><code class="xref py py-class docutils literal notranslate"><span class="pre">Graph</span></code></a> of geometries described by <cite>dataframe</cite>.
 The areas of the polygons are included as node attributes (with key <cite>area</cite>).
 The shared perimeter of neighboring polygons are included as edge attributes
@@ -2012,7 +2023,7 @@ <h2>Graph<a class="headerlink" href="#graph" title="Permalink to this headline">
 
 <dl class="method">
 <dt>
-<code class="sig-name descname">join</code><span class="sig-paren">(</span><em class="sig-param">dataframe: &lt;Mock name='mock.DataFrame' id='140048407164816'&gt;</em>, <em class="sig-param">columns: Optional[List[str]] = None</em>, <em class="sig-param">left_index: Optional[str] = None</em>, <em class="sig-param">right_index: Optional[str] = None</em><span class="sig-paren">)</span> &#x2192; None<a class="reference internal" href="_modules/gerrychain/graph/graph.html#Graph.join"><span class="viewcode-link">[source]</span></a></dt>
+<code class="sig-name descname">join</code><span class="sig-paren">(</span><em class="sig-param">dataframe: &lt;Mock name='mock.DataFrame' id='140565501544864'&gt;</em>, <em class="sig-param">columns: Optional[List[str]] = None</em>, <em class="sig-param">left_index: Optional[str] = None</em>, <em class="sig-param">right_index: Optional[str] = None</em><span class="sig-paren">)</span> &#x2192; None<a class="reference internal" href="_modules/gerrychain/graph/graph.html#Graph.join"><span class="viewcode-link">[source]</span></a></dt>
 <dd><p>Add data from a dataframe to the graph, matching nodes to rows when
 the node’s <cite>left_index</cite> attribute equals the row’s <cite>right_index</cite> value.</p>
 <dl class="field-list simple">
@@ -2100,7 +2111,7 @@ <h2>Graph<a class="headerlink" href="#graph" title="Permalink to this headline">
 
 <dl class="function">
 <dt>
-<code class="sig-prename descclassname">gerrychain.graph.graph.</code><code class="sig-name descname">add_boundary_perimeters</code><span class="sig-paren">(</span><em class="sig-param">graph: gerrychain.graph.graph.Graph</em>, <em class="sig-param">geometries: &lt;Mock name='mock.Series' id='140048407164912'&gt;</em><span class="sig-paren">)</span> &#x2192; None<a class="reference internal" href="_modules/gerrychain/graph/graph.html#add_boundary_perimeters"><span class="viewcode-link">[source]</span></a></dt>
+<code class="sig-prename descclassname">gerrychain.graph.graph.</code><code class="sig-name descname">add_boundary_perimeters</code><span class="sig-paren">(</span><em class="sig-param">graph: gerrychain.graph.graph.Graph</em>, <em class="sig-param">geometries: &lt;Mock name='mock.Series' id='140565501545008'&gt;</em><span class="sig-paren">)</span> &#x2192; None<a class="reference internal" href="_modules/gerrychain/graph/graph.html#add_boundary_perimeters"><span class="viewcode-link">[source]</span></a></dt>
 <dd><p>Add shared perimeter between nodes and the total geometry boundary.</p>
 <dl class="field-list simple">
 <dt class="field-odd">Parameters</dt>
@@ -2120,7 +2131,7 @@ <h2>Graph<a class="headerlink" href="#graph" title="Permalink to this headline">
 
 <dl class="function">
 <dt>
-<code class="sig-prename descclassname">gerrychain.graph.graph.</code><code class="sig-name descname">check_dataframe</code><span class="sig-paren">(</span><em class="sig-param">df: &lt;Mock name='mock.DataFrame' id='140048407164816'&gt;</em><span class="sig-paren">)</span> &#x2192; None<a class="reference internal" href="_modules/gerrychain/graph/graph.html#check_dataframe"><span class="viewcode-link">[source]</span></a></dt>
+<code class="sig-prename descclassname">gerrychain.graph.graph.</code><code class="sig-name descname">check_dataframe</code><span class="sig-paren">(</span><em class="sig-param">df: &lt;Mock name='mock.DataFrame' id='140565501544864'&gt;</em><span class="sig-paren">)</span> &#x2192; None<a class="reference internal" href="_modules/gerrychain/graph/graph.html#check_dataframe"><span class="viewcode-link">[source]</span></a></dt>
 <dd><dl class="field-list simple">
 <dt class="field-odd">Returns</dt>
 <dd class="field-odd"><p>None</p>
@@ -2516,7 +2527,7 @@ <h2>Partition<a class="headerlink" href="#partition" title="Permalink to this he
 
 <dl class="method">
 <dt>
-<code class="sig-name descname">to_series</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; &lt;Mock name='mock.Series' id='140048407164912'&gt;<a class="reference internal" href="_modules/gerrychain/partition/assignment.html#Assignment.to_series"><span class="viewcode-link">[source]</span></a></dt>
+<code class="sig-name descname">to_series</code><span class="sig-paren">(</span><span class="sig-paren">)</span> &#x2192; &lt;Mock name='mock.Series' id='140565501545008'&gt;<a class="reference internal" href="_modules/gerrychain/partition/assignment.html#Assignment.to_series"><span class="viewcode-link">[source]</span></a></dt>
 <dd><dl class="field-list simple">
 <dt class="field-odd">Returns</dt>
 <dd class="field-odd"><p>The assignment as a <code class="xref py py-class docutils literal notranslate"><span class="pre">pandas.Series</span></code>.</p>
@@ -3139,7 +3150,7 @@ <h2>Proposals<a class="headerlink" href="#proposals" title="Permalink to this he
 
 <dl class="function">
 <dt>
-<code class="sig-prename descclassname">gerrychain.proposals.tree_proposals.</code><code class="sig-name descname">recom</code><span class="sig-paren">(</span><em class="sig-param">partition: gerrychain.partition.partition.Partition, pop_col: str, pop_target: Union[int, float], epsilon: float, node_repeats: int = 1, weight_dict: Optional[Dict] = None, method: Callable = &lt;function bipartition_tree&gt;</em><span class="sig-paren">)</span> &#x2192; gerrychain.partition.partition.Partition<a class="reference internal" href="_modules/gerrychain/proposals/tree_proposals.html#recom"><span class="viewcode-link">[source]</span></a></dt>
+<code class="sig-prename descclassname">gerrychain.proposals.tree_proposals.</code><code class="sig-name descname">recom</code><span class="sig-paren">(</span><em class="sig-param">partition: gerrychain.partition.partition.Partition, pop_col: str, pop_target: Union[int, float], epsilon: float, node_repeats: int = 1, region_surcharge: Optional[Dict] = None, method: Callable = &lt;function bipartition_tree&gt;</em><span class="sig-paren">)</span> &#x2192; gerrychain.partition.partition.Partition<a class="reference internal" href="_modules/gerrychain/proposals/tree_proposals.html#recom"><span class="viewcode-link">[source]</span></a></dt>
 <dd><p>ReCom (short for ReCombination) is a Markov Chain Monte Carlo (MCMC) algorithm
 used for redistricting. At each step of the algorithm, a pair of adjacent districts
 is selected at random and merged into a single district. The region is then split
@@ -3173,7 +3184,7 @@ <h2>Proposals<a class="headerlink" href="#proposals" title="Permalink to this he
 <li><p><strong>epsilon</strong> (<em>float</em>) – The epsilon value for population deviation as a percentage of the
 target population.</p></li>
 <li><p><strong>node_repeats</strong> (<em>int</em><em>, </em><em>optional</em>) – The number of times to repeat the bipartitioning step. Default is 1.</p></li>
-<li><p><strong>weight_dict</strong> (<em>Optional</em><em>[</em><em>Dict</em><em>]</em><em>, </em><em>optional</em>) – The weight dictionary for the graph used for region-aware
+<li><p><strong>region_surcharge</strong> (<em>Optional</em><em>[</em><em>Dict</em><em>]</em><em>, </em><em>optional</em>) – The surcharge dictionary for the graph used for region-aware
 partitioning of the grid. Default is None.</p></li>
 <li><p><strong>method</strong> (<em>Callable</em><em>, </em><em>optional</em>) – The method used for bipartitioning the tree. Default is
 <a class="reference internal" href="api.html#gerrychain.tree.bipartition_tree" title="gerrychain.tree.bipartition_tree"><code class="xref py py-func docutils literal notranslate"><span class="pre">bipartition_tree()</span></code></a>.</p></li>
@@ -3185,10 +3196,6 @@ <h2>Proposals<a class="headerlink" href="#proposals" title="Permalink to this he
 <dt class="field-odd">Return type</dt>
 <dd class="field-odd"><p><a class="reference internal" href="api.html#gerrychain.partition.Partition" title="gerrychain.partition.Partition">Partition</a></p>
 </dd>
-<dt class="field-even">Raises</dt>
-<dd class="field-even"><p><strong>ValueWarning</strong> – Raised when the sum of the weights in the weight dictionary is
-greater than 1.</p>
-</dd>
 </dl>
 </dd></dl>
 
@@ -4483,7 +4490,7 @@ <h2>Updaters<a class="headerlink" href="#updaters" title="Permalink to this head
 
 <dl class="class">
 <dt>
-<em class="property">class </em><code class="sig-prename descclassname">gerrychain.updaters.tally.</code><code class="sig-name descname">DataTally</code><span class="sig-paren">(</span><em class="sig-param">data: Union[Dict, &lt;Mock name='mock.Series' id='140048407164912'&gt;, str], alias: str</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/gerrychain/updaters/tally.html#DataTally"><span class="viewcode-link">[source]</span></a></dt>
+<em class="property">class </em><code class="sig-prename descclassname">gerrychain.updaters.tally.</code><code class="sig-name descname">DataTally</code><span class="sig-paren">(</span><em class="sig-param">data: Union[Dict, &lt;Mock name='mock.Series' id='140565501545008'&gt;, str], alias: str</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/gerrychain/updaters/tally.html#DataTally"><span class="viewcode-link">[source]</span></a></dt>
 <dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
 <p>An updater for tallying numerical data that is not necessarily stored as
 node attributes</p>
diff --git a/genindex.html b/genindex.html
index e36bc6ab..8cab0754 100644
--- a/genindex.html
+++ b/genindex.html
@@ -503,6 +503,8 @@ <h2 id="W">W</h2>
       <li><a href="api.html#gerrychain.graph.graph.Graph.warn_for_islands">warn_for_islands() (gerrychain.graph.graph.Graph method)</a>
 </li>
       <li><a href="api.html#gerrychain.metrics.wasted_votes">wasted_votes() (in module gerrychain.metrics)</a>
+</li>
+      <li><a href="api.html#gerrychain.tree.Cut.weight">weight (gerrychain.tree.Cut attribute)</a>
 </li>
       <li><a href="api.html#gerrychain.updaters.election.ElectionResults.wins">wins() (gerrychain.updaters.election.ElectionResults method)</a>
 </li>
diff --git a/index.html b/index.html
index f3b37b88..73a33fb9 100644
--- a/index.html
+++ b/index.html
@@ -110,6 +110,7 @@ <h3>Supported Python Versions<a class="headerlink" href="#supported-python-versi
 <li><p>Python 3.9</p></li>
 <li><p>Python 3.10</p></li>
 <li><p>Python 3.11</p></li>
+<li><p>Python 3.12</p></li>
 </ul>
 <p>If you do not have one of these versions installed on you machine, we
 recommend that you go to the
@@ -220,7 +221,7 @@ <h3>Setting Up a Virtual Environment<a class="headerlink" href="#setting-up-a-vi
 different Python GIS dependencies, like <code class="docutils literal notranslate"><span class="pre">geopandas</span></code>, <code class="docutils literal notranslate"><span class="pre">pyproj</span></code>,
 <code class="docutils literal notranslate"><span class="pre">fiona</span></code>, and <code class="docutils literal notranslate"><span class="pre">shapely</span></code>. If you run into this issue, try installing
 the dependencies using the
-<a class="reference external" href="https://github.com/mggg/GerryChain/blob/main/docs/geo_settings.txt">geo_settings.txt</a>
+<a class="reference external" href="https://github.com/mggg/GerryChain/raw/main/docs/geo_settings.txt">geo_settings.txt</a>
 file. To do this, run <code class="docutils literal notranslate"><span class="pre">pip</span> <span class="pre">install</span> <span class="pre">-r</span> <span class="pre">geo_settings.txt</span></code> from the
 command line.</p>
 <div class="admonition note">
diff --git a/objects.inv b/objects.inv
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diff --git a/user/data.html b/user/data.html
index 86cf65bf..586e8a5a 100644
--- a/user/data.html
+++ b/user/data.html
@@ -113,7 +113,7 @@ <h1>Good Data Practices<a class="headerlink" href="#good-data-practices" title="
 <div class="section" id="writing-data-to-jsonl">
 <h2>Writing Data to JSONL<a class="headerlink" href="#writing-data-to-jsonl" title="Permalink to this headline">¶</a></h2>
 <div class="center-container">
-  <a href="https://github.com/mggg/GerryChain/blob/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
+  <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
 </div>
 <br style="line-height: 5px;"><p>One of the most common methods for storing data is to write the
 relevant information to a JSONL file. Here is an example with our
@@ -303,128 +303,128 @@ <h2>Pandas DataFrames<a class="headerlink" href="#pandas-dataframes" title="Perm
 <tr class="row-even"><td><p>198</p></td>
 <td><p>11</p></td>
 <td><p>3</p></td>
-<td><p>699433</p></td>
-<td><p>0.831304</p></td>
-<td><p>2162</p></td>
+<td><p>704364</p></td>
+<td><p>0.883639</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-odd"><td><p>199</p></td>
 <td><p>11</p></td>
 <td><p>10</p></td>
-<td><p>700040</p></td>
-<td><p>1.562749</p></td>
-<td><p>2162</p></td>
+<td><p>709547</p></td>
+<td><p>2.228103</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-even"><td><p>200</p></td>
 <td><p>11</p></td>
 <td><p>9</p></td>
-<td><p>702500</p></td>
-<td><p>1.579113</p></td>
-<td><p>2162</p></td>
+<td><p>712201</p></td>
+<td><p>0.801655</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-odd"><td><p>201</p></td>
 <td><p>11</p></td>
 <td><p>5</p></td>
-<td><p>695917</p></td>
-<td><p>3.012263</p></td>
-<td><p>2162</p></td>
+<td><p>699705</p></td>
+<td><p>1.639986</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-even"><td><p>202</p></td>
 <td><p>11</p></td>
 <td><p>15</p></td>
-<td><p>700895</p></td>
-<td><p>1.616416</p></td>
-<td><p>2162</p></td>
+<td><p>706694</p></td>
+<td><p>0.744557</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-odd"><td><p>203</p></td>
 <td><p>11</p></td>
 <td><p>6</p></td>
-<td><p>705782</p></td>
-<td><p>0.239069</p></td>
-<td><p>2162</p></td>
+<td><p>708502</p></td>
+<td><p>0.351298</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-even"><td><p>204</p></td>
 <td><p>11</p></td>
 <td><p>11</p></td>
-<td><p>709813</p></td>
-<td><p>0.357564</p></td>
-<td><p>2162</p></td>
+<td><p>705406</p></td>
+<td><p>0.948691</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-odd"><td><p>205</p></td>
 <td><p>11</p></td>
 <td><p>8</p></td>
-<td><p>705689</p></td>
-<td><p>0.199275</p></td>
-<td><p>2162</p></td>
+<td><p>702576</p></td>
+<td><p>0.109261</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-even"><td><p>206</p></td>
 <td><p>11</p></td>
 <td><p>4</p></td>
 <td><p>705669</p></td>
 <td><p>0.418513</p></td>
-<td><p>2162</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-odd"><td><p>207</p></td>
 <td><p>11</p></td>
 <td><p>18</p></td>
-<td><p>706380</p></td>
-<td><p>0.421818</p></td>
-<td><p>2162</p></td>
+<td><p>705847</p></td>
+<td><p>0.569159</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-even"><td><p>208</p></td>
 <td><p>11</p></td>
 <td><p>12</p></td>
-<td><p>713452</p></td>
-<td><p>0.856847</p></td>
-<td><p>2162</p></td>
+<td><p>695032</p></td>
+<td><p>2.954248</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-odd"><td><p>209</p></td>
 <td><p>11</p></td>
 <td><p>17</p></td>
-<td><p>706041</p></td>
-<td><p>0.622091</p></td>
-<td><p>2162</p></td>
+<td><p>695142</p></td>
+<td><p>0.237470</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-even"><td><p>210</p></td>
 <td><p>11</p></td>
 <td><p>7</p></td>
-<td><p>697675</p></td>
-<td><p>0.329930</p></td>
-<td><p>2162</p></td>
+<td><p>711035</p></td>
+<td><p>0.018885</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-odd"><td><p>211</p></td>
 <td><p>11</p></td>
 <td><p>16</p></td>
-<td><p>716162</p></td>
-<td><p>0.194045</p></td>
-<td><p>2162</p></td>
+<td><p>699557</p></td>
+<td><p>0.283365</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-even"><td><p>212</p></td>
 <td><p>11</p></td>
 <td><p>14</p></td>
-<td><p>704993</p></td>
-<td><p>0.207707</p></td>
-<td><p>2162</p></td>
+<td><p>705526</p></td>
+<td><p>0.060366</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-odd"><td><p>213</p></td>
 <td><p>11</p></td>
 <td><p>13</p></td>
 <td><p>705028</p></td>
 <td><p>0.042608</p></td>
-<td><p>2162</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-even"><td><p>214</p></td>
 <td><p>11</p></td>
 <td><p>2</p></td>
-<td><p>710286</p></td>
-<td><p>0.021872</p></td>
-<td><p>2162</p></td>
+<td><p>705218</p></td>
+<td><p>0.021515</p></td>
+<td><p>2103</p></td>
 </tr>
 <tr class="row-odd"><td><p>215</p></td>
 <td><p>11</p></td>
 <td><p>1</p></td>
-<td><p>699174</p></td>
-<td><p>0.021139</p></td>
-<td><p>2162</p></td>
+<td><p>707880</p></td>
+<td><p>0.221007</p></td>
+<td><p>2103</p></td>
 </tr>
 </tbody>
 </table>
diff --git a/user/geometries.html b/user/geometries.html
index df257619..105491a8 100644
--- a/user/geometries.html
+++ b/user/geometries.html
@@ -118,7 +118,7 @@ <h1>Working With Geometries<a class="headerlink" href="#working-with-geometries"
 <div class="section" id="loading-and-running-a-plan">
 <h2>Loading and Running a Plan<a class="headerlink" href="#loading-and-running-a-plan" title="Permalink to this headline">¶</a></h2>
 <div class="center-container">
-  <a href="https://github.com/mggg/GerryChain/blob/main/docs/_static/MN.zip" class="download-badge" download>Download MN File</a>
+  <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/MN.zip" class="download-badge" download>Download MN File</a>
 </div>
 <br style="line-height: 5px;"><p>For this example, we will make use of a Minnesota GeoJSON file that contains
 the geometries of the state’s precincts (you will need to unzip the above
diff --git a/user/install.html b/user/install.html
index a7f1ce4b..2111531f 100644
--- a/user/install.html
+++ b/user/install.html
@@ -104,6 +104,7 @@ <h2>Supported Python Versions<a class="headerlink" href="#supported-python-versi
 <li><p>Python 3.9</p></li>
 <li><p>Python 3.10</p></li>
 <li><p>Python 3.11</p></li>
+<li><p>Python 3.12</p></li>
 </ul>
 <p>If you do not have one of these versions installed on you machine, we
 recommend that you go to the
@@ -214,7 +215,7 @@ <h2>Setting Up a Virtual Environment<a class="headerlink" href="#setting-up-a-vi
 different Python GIS dependencies, like <code class="docutils literal notranslate"><span class="pre">geopandas</span></code>, <code class="docutils literal notranslate"><span class="pre">pyproj</span></code>,
 <code class="docutils literal notranslate"><span class="pre">fiona</span></code>, and <code class="docutils literal notranslate"><span class="pre">shapely</span></code>. If you run into this issue, try installing
 the dependencies using the
-<a class="reference external" href="https://github.com/mggg/GerryChain/blob/main/docs/geo_settings.txt">geo_settings.txt</a>
+<a class="reference external" href="https://github.com/mggg/GerryChain/raw/main/docs/geo_settings.txt">geo_settings.txt</a>
 file. To do this, run <code class="docutils literal notranslate"><span class="pre">pip</span> <span class="pre">install</span> <span class="pre">-r</span> <span class="pre">geo_settings.txt</span></code> from the
 command line.</p>
 <div class="admonition note">
diff --git a/user/partitions.html b/user/partitions.html
index 7c746192..f3f1e19e 100644
--- a/user/partitions.html
+++ b/user/partitions.html
@@ -101,7 +101,7 @@
   <div class="section" id="working-with-partitions">
 <h1>Working with Partitions<a class="headerlink" href="#working-with-partitions" title="Permalink to this headline">¶</a></h1>
 <div class="center-container">
-  <a href="https://github.com/mggg/GerryChain/blob/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
+  <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
 </div>
 <br style="line-height: 5px;"><p>This document walks you through the most common ways that you might work with a
 GerryChain <code class="docutils literal notranslate"><span class="pre">Partition</span></code> object.</p>
@@ -110,7 +110,7 @@ <h1>Working with Partitions<a class="headerlink" href="#working-with-partitions"
 </pre></div>
 </div>
 <p>We’ll use our
-<a class="reference external" href="https://github.com/mggg/GerryChain/blob/main/docs/_static/PA_VTDs.json">Pennsylvania VTD json</a>
+<a class="reference external" href="https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json">Pennsylvania VTD json</a>
 to create the graph we’ll use in these examples.</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">graph</span> <span class="o">=</span> <span class="n">Graph</span><span class="o">.</span><span class="n">from_json</span><span class="p">(</span><span class="s2">&quot;./PA_VTDs.json&quot;</span><span class="p">)</span>
 </pre></div>
diff --git a/user/quickstart.html b/user/quickstart.html
index 94e9f01a..a7eda79f 100644
--- a/user/quickstart.html
+++ b/user/quickstart.html
@@ -108,7 +108,7 @@ <h2>What you’ll need<a class="headerlink" href="#what-you-ll-need" title="Perm
 <p>Before we can start running Markov chains, you’ll need to:</p>
 <ul class="simple">
 <li><p>Install <code class="docutils literal notranslate"><span class="pre">gerrychain</span></code> from PyPI. See the <a class="reference internal" href="install.html"><span class="doc">installation guide</span></a> for instructions.</p></li>
-<li><p>Download <a class="reference external" href="https://github.com/mggg/GerryChain/blob/main/docs/_static/PA_VTDs.json">this example json of Pennsylvania’s VTDs</a>.</p></li>
+<li><p>Download <a class="reference external" href="https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json">this example json of Pennsylvania’s VTDs</a>.</p></li>
 <li><p>Open your preferred Python environment (e.g. JupyterLab, IPython, or a <code class="docutils literal notranslate"><span class="pre">.py</span></code> file
 in your favorite editor) in the directory containing the <code class="docutils literal notranslate"><span class="pre">PA_VTDs.json</span></code> file
 that you downloaded.</p></li>
@@ -130,7 +130,7 @@ <h2>What you’ll need<a class="headerlink" href="#what-you-ll-need" title="Perm
 <div class="section" id="creating-the-initial-partition">
 <h2>Creating the initial partition<a class="headerlink" href="#creating-the-initial-partition" title="Permalink to this headline">¶</a></h2>
 <div class="center-container">
-  <a href="https://github.com/mggg/GerryChain/blob/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
+  <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
 </div>
 <br style="line-height: 5px;"><p>In order to run a Markov chain, we need an
 adjacency <code class="xref py py-class docutils literal notranslate"><span class="pre">Graph</span></code> of our VTD geometries and
diff --git a/user/recom.html b/user/recom.html
index 64535dcc..3818856d 100644
--- a/user/recom.html
+++ b/user/recom.html
@@ -47,7 +47,10 @@
 <li class="toctree-l1"><a class="reference internal" href="quickstart.html">Getting started with GerryChain</a></li>
 <li class="toctree-l1 current"><a class="current reference internal" href="#">Running a chain with ReCom</a><ul>
 <li class="toctree-l2"><a class="reference internal" href="#a-simple-recom-chain">A Simple Recom Chain</a></li>
-<li class="toctree-l2"><a class="reference internal" href="#region-aware-recom">Region-Aware ReCom</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#region-aware-recom">Region-Aware ReCom</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#how-the-region-aware-implementation-works">How the Region Aware Implementation Works</a></li>
+</ul>
+</li>
 <li class="toctree-l2"><a class="reference internal" href="#what-to-do-if-the-chain-gets-stuck">What to do if the Chain Gets Stuck</a></li>
 <li class="toctree-l2"><a class="reference internal" href="#a-real-world-example">A Real-World Example</a><ul>
 <li class="toctree-l3"><a class="reference internal" href="#imports">Imports</a></li>
@@ -127,7 +130,7 @@ <h1>Running a chain with ReCom<a class="headerlink" href="#running-a-chain-with-
 <div class="section" id="a-simple-recom-chain">
 <h2>A Simple Recom Chain<a class="headerlink" href="#a-simple-recom-chain" title="Permalink to this headline">¶</a></h2>
 <div class="center-container">
-  <a href="https://github.com/mggg/GerryChain/blob/main/docs/_static/gerrymandria.json" class="download-badge" download>
+  <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/gerrymandria.json" class="download-badge" download>
     Download GerryMandria File
   </a>
 </div>
@@ -143,7 +146,7 @@ <h2>A Simple Recom Chain<a class="headerlink" href="#a-simple-recom-chain" title
 
 <span class="c1"># Set the random seed so that the results are reproducible!</span>
 <span class="kn">import</span> <span class="nn">random</span>
-<span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span>
+<span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">2024</span><span class="p">)</span>
 </pre></div>
 </div>
 <p>Now we set up the initial partition:</p>
@@ -182,7 +185,7 @@ <h2>A Simple Recom Chain<a class="headerlink" href="#a-simple-recom-chain" title
     <span class="n">constraints</span><span class="o">=</span><span class="p">[</span><span class="n">contiguous</span><span class="p">],</span>
     <span class="n">accept</span><span class="o">=</span><span class="n">accept</span><span class="o">.</span><span class="n">always_accept</span><span class="p">,</span>
     <span class="n">initial_state</span><span class="o">=</span><span class="n">initial_partition</span><span class="p">,</span>
-    <span class="n">total_steps</span><span class="o">=</span><span class="mi">20</span>
+    <span class="n">total_steps</span><span class="o">=</span><span class="mi">40</span>
 <span class="p">)</span>
 </pre></div>
 </div>
@@ -252,7 +255,7 @@ <h2>Region-Aware ReCom<a class="headerlink" href="#region-aware-recom" title="Pe
 region-aware ReCom chains which create ensembles
 of districting plans that try to keep particular regions of interest together.
 And it only takes one extra line of code: we simply update
-our proposal to include a <code class="docutils literal notranslate"><span class="pre">weight_dict</span></code> which increases the importance of the
+our proposal to include a <code class="docutils literal notranslate"><span class="pre">region_surcharge</span></code> which increases the importance of the
 edges within the municipalities.</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">proposal</span> <span class="o">=</span> <span class="n">partial</span><span class="p">(</span>
     <span class="n">recom</span><span class="p">,</span>
@@ -260,7 +263,7 @@ <h2>Region-Aware ReCom<a class="headerlink" href="#region-aware-recom" title="Pe
     <span class="n">pop_target</span><span class="o">=</span><span class="n">ideal_population</span><span class="p">,</span>
     <span class="n">epsilon</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span>
     <span class="n">node_repeats</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
-    <span class="n">weight_dict</span><span class="o">=</span><span class="p">{</span><span class="s2">&quot;muni&quot;</span><span class="p">:</span> <span class="mf">0.8</span><span class="p">},</span>
+    <span class="n">region_surcharge</span><span class="o">=</span><span class="p">{</span><span class="s2">&quot;muni&quot;</span><span class="p">:</span> <span class="mf">1.0</span><span class="p">},</span>
 <span class="p">)</span>
 </pre></div>
 </div>
@@ -276,14 +279,14 @@ <h2>Region-Aware ReCom<a class="headerlink" href="#region-aware-recom" title="Pe
 and all of the municipalities together in one plan. However, we can try to keep
 the water districts together as much as possible, and then, within those water
 districts, try to be sensitive to the boundaries of the municipalities. Again,
-this only requires for us to edit the <code class="docutils literal notranslate"><span class="pre">weight_dict</span></code> parameter of the proposal</p>
+this only requires for us to edit the <code class="docutils literal notranslate"><span class="pre">region_surcharge</span></code> parameter of the proposal</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">proposal</span> <span class="o">=</span> <span class="n">partial</span><span class="p">(</span>
     <span class="n">recom</span><span class="p">,</span>
     <span class="n">pop_col</span><span class="o">=</span><span class="s2">&quot;TOTPOP&quot;</span><span class="p">,</span>
     <span class="n">pop_target</span><span class="o">=</span><span class="n">ideal_population</span><span class="p">,</span>
     <span class="n">epsilon</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span>
     <span class="n">node_repeats</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span>
-    <span class="n">weight_dict</span><span class="o">=</span><span class="p">{</span><span class="s2">&quot;muni&quot;</span><span class="p">:</span> <span class="mf">0.2</span><span class="p">,</span> <span class="s2">&quot;water&quot;</span><span class="p">:</span> <span class="mf">0.8</span><span class="p">},</span>
+    <span class="n">region_surcharge</span><span class="o">=</span><span class="p">{</span><span class="s2">&quot;muni&quot;</span><span class="p">:</span> <span class="mf">0.2</span><span class="p">,</span> <span class="s2">&quot;water&quot;</span><span class="p">:</span> <span class="mf">0.8</span><span class="p">},</span>
 <span class="p">)</span>
 </pre></div>
 </div>
@@ -298,7 +301,7 @@ <h2>Region-Aware ReCom<a class="headerlink" href="#region-aware-recom" title="Pe
 <span class="p">)</span>
 </pre></div>
 </div>
-<p>Then, we can run the chain and look at the last 20 assignments in the ensemble</p>
+<p>Then, we can run the chain and look at the last 40 assignments in the ensemble</p>
 <a class="reference internal image-reference" href="../_images/gerrymandria_water_muni_ensamble.gif"><img alt="../_images/gerrymandria_water_muni_ensamble.gif" class="align-center" src="../_images/gerrymandria_water_muni_ensamble.gif" style="width: 400px;" /></a>
 <p>Comparing the last map with the municipality and water district maps, we can see
 that the chain has done a pretty good job of keeping the water districts together
@@ -306,36 +309,73 @@ <h2>Region-Aware ReCom<a class="headerlink" href="#region-aware-recom" title="Pe
 <div class="figure align-center" id="id1">
 <a class="reference internal image-reference" href="../_images/gerrymandria_water_and_muni_aware.png"><img alt="../_images/gerrymandria_water_and_muni_aware.png" src="../_images/gerrymandria_water_and_muni_aware.png" style="width: 400px;" /></a>
 <p class="caption"><span class="caption-text">The last map in the ensemble from the 10000 step region-aware ReCom chain with
-weights of 0.2 for the municipalities and 0.8 for the water districts.</span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p>
+surcharges of 0.2 for the municipalities and 0.8 for the water districts.</span><a class="headerlink" href="#id1" title="Permalink to this image">¶</a></p>
 </div>
 <div style="display: flex; justify-content: space-around;">
     <figure style="text-align: center;">
-        <img src="../_images/gerrymandria_cities.png" style="width: 100%;">
+        <img src="../../_images/gerrymandria_cities.png" style="width: 100%;">
         <figcaption><em>Municipalities of Gerrymandria</em></figcaption>
     </figure>
     <figure style="text-align: center;">
-        <img src="../_images/gerrymandria_water.png" style="width: 100%;">
+        <img src="../../_images/gerrymandria_water.png" style="width: 100%;">
         <figcaption><em>Water Districts of GerryMandria</em><figcaption>
     </figure>
-</div><div class="admonition attention" id="weight-dict-warning">
-<p class="admonition-title">Attention</p>
-<p>The <code class="docutils literal notranslate"><span class="pre">weight_dict</span></code> parameter is a dictionary that assigns a weight to each
-edge within a particular region that is determined by the keys of the dictionary.
-In the event that multiple regions are specified, the weights are added together,
-and if the weights add to more than 1, then the following warning will be printed
-to the user:</p>
-<div class="highlight-console notranslate"><div class="highlight"><pre><span></span><span class="go">ValueWarning:</span>
-<span class="go">The sum of the weights in the weight dictionary is greater than 1.</span>
-<span class="go">Please consider normalizing the weights.</span>
+</div><div class="section" id="how-the-region-aware-implementation-works">
+<h3>How the Region Aware Implementation Works<a class="headerlink" href="#how-the-region-aware-implementation-works" title="Permalink to this headline">¶</a></h3>
+<p>When working with region-aware ReCom chains, it is worth knowing how the spanning tree
+of the dual graph is being split. Weights from the interval <span class="math notranslate nohighlight">\([0,1]\)</span> are randomly
+assigned to the edges of the graph and then the surcharges are applied to the edges in
+the graph that span different regions specified by the <code class="docutils literal notranslate"><span class="pre">region_surcharge</span></code> dictionary.
+So if we have <code class="docutils literal notranslate"><span class="pre">region_surcharge={&quot;muni&quot;:</span> <span class="pre">0.2,</span> <span class="pre">&quot;water&quot;:</span> <span class="pre">0.8}</span></code>, then the edges that
+span different municipalities will be upweighted by 0.2 and the edges that span different
+water districts will be upweighted by 0.8. We then draw a minimum spanning tree using
+by greedily selecting the lowest-weight edges via Kruskal’s algorithm. The surcharges on
+the edges helps ensure that the algorithm picks the edges interior to the region
+before it picks the edges that bridge different regions.</p>
+<p>This makes it very likely that each region is largely contained in a connected subtree
+attached to a bridge node. Thus, when we make a cut, the regions attached to the
+bridge node are more likely to be (mostly) preserved in the subtree on either side
+of the cut.</p>
+<p>In the implementation of <code class="xref py py-meth docutils literal notranslate"><span class="pre">biparition_tree()</span></code> we further bias this
+choice by deterministically cutting bridge edges first (when possible). In the event that
+multiple types of regions are specified, the surcharges are added together, and edges are
+selected first by the number of types of regions that they span, and then by the
+surcharge added to those weights. So, if we have a region surcharge dictionary of
+<code class="docutils literal notranslate"><span class="pre">{&quot;a&quot;:</span> <span class="pre">1,</span> <span class="pre">&quot;b&quot;:</span> <span class="pre">4,</span> <span class="pre">&quot;c&quot;:</span> <span class="pre">2}</span></code> then we we look for edges according to the order</p>
+<ul class="simple">
+<li><p>(“a”, “b”, “c”)</p></li>
+<li><p>(“b”, “c”)</p></li>
+<li><p>(“a”, “b”)</p></li>
+<li><p>(“a”, “c”)</p></li>
+<li><p>(“b”)</p></li>
+<li><p>(“c”)</p></li>
+<li><p>(“a”)</p></li>
+<li><p>random</p></li>
+</ul>
+<p>where the tuples indicate that a desired cut edge bridges both types of region in
+the tuple. In the event that this is not the desired behaviour, then the user can simply
+alter the <code class="docutils literal notranslate"><span class="pre">cut_choice</span></code> function in the constraints to be different. So, if the user
+would prefer the cut edge to be a random edge with no deference to bridge edges,
+then they might use <code class="docutils literal notranslate"><span class="pre">random.choice()</span></code> in the following way:</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">proposal</span> <span class="o">=</span> <span class="n">partial</span><span class="p">(</span>
+    <span class="n">recom</span><span class="p">,</span>
+    <span class="n">pop_col</span><span class="o">=</span><span class="s2">&quot;TOTPOP&quot;</span><span class="p">,</span>
+    <span class="n">pop_target</span><span class="o">=</span><span class="n">ideal_population</span><span class="p">,</span>
+    <span class="n">epsilon</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span>
+    <span class="n">node_repeats</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
+    <span class="n">region_surcharge</span><span class="o">=</span><span class="p">{</span>
+        <span class="s2">&quot;muni&quot;</span><span class="p">:</span> <span class="mf">2.0</span><span class="p">,</span>
+        <span class="s2">&quot;water_dist&quot;</span><span class="p">:</span> <span class="mf">2.0</span>
+    <span class="p">},</span>
+    <span class="n">method</span> <span class="o">=</span> <span class="n">partial</span><span class="p">(</span>
+        <span class="n">bipartition_tree</span><span class="p">,</span>
+        <span class="n">cut_choice</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">,</span>
+    <span class="p">)</span>
+<span class="p">)</span>
 </pre></div>
 </div>
-<p>It is generally inadvisable to set the weight of a region to 1 or more. When
-using <a class="reference internal" href="../api.html#gerrychain.proposals.recom" title="gerrychain.proposals.recom"><code class="xref py py-meth docutils literal notranslate"><span class="pre">recom()</span></code></a> with a <code class="docutils literal notranslate"><span class="pre">weight_dict</span></code>, the proposal
-will try to draw a minimum spanning tree using Kruskal’s algorithm where,
-the weights are in the range <span class="math notranslate nohighlight">\([0,1]\)</span>, then the weights from the weight
-dictionary are added to them. In the event that
-many edges within the tree have a weight above 1, then it can sometimes
-cause the biparitioning step to stall.</p>
+<p><strong>Note</strong>: When <code class="docutils literal notranslate"><span class="pre">region_surcharge</span></code> is not specified, <code class="docutils literal notranslate"><span class="pre">bipartition_tree</span></code> will behave as if
+<code class="docutils literal notranslate"><span class="pre">cut_choice</span></code> is set to <code class="docutils literal notranslate"><span class="pre">random.choice</span></code>.</p>
 </div>
 </div>
 <div class="section" id="what-to-do-if-the-chain-gets-stuck">
@@ -353,7 +393,7 @@ <h2>What to do if the Chain Gets Stuck<a class="headerlink" href="#what-to-do-if
 <span class="kn">from</span> <span class="nn">gerrychain.constraints</span> <span class="kn">import</span> <span class="n">contiguous</span>
 <span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">partial</span>
 <span class="kn">import</span> <span class="nn">random</span>
-<span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span>
+<span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
 
 <span class="n">graph</span> <span class="o">=</span> <span class="n">Graph</span><span class="o">.</span><span class="n">from_json</span><span class="p">(</span><span class="s2">&quot;./gerrymandria.json&quot;</span><span class="p">)</span>
 
@@ -376,7 +416,14 @@ <h2>What to do if the Chain Gets Stuck<a class="headerlink" href="#what-to-do-if
     <span class="n">pop_target</span><span class="o">=</span><span class="n">ideal_population</span><span class="p">,</span>
     <span class="n">epsilon</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span>
     <span class="n">node_repeats</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
-    <span class="n">weight_dict</span><span class="o">=</span><span class="p">{</span><span class="s2">&quot;muni&quot;</span><span class="p">:</span> <span class="mf">1.0</span><span class="p">,</span> <span class="s2">&quot;water_dist&quot;</span><span class="p">:</span> <span class="mf">1.0</span><span class="p">},</span>
+    <span class="n">region_surcharge</span><span class="o">=</span><span class="p">{</span>
+        <span class="s2">&quot;muni&quot;</span><span class="p">:</span> <span class="mf">2.0</span><span class="p">,</span>
+        <span class="s2">&quot;water_dist&quot;</span><span class="p">:</span> <span class="mf">2.0</span>
+    <span class="p">},</span>
+    <span class="n">method</span> <span class="o">=</span> <span class="n">partial</span><span class="p">(</span>
+        <span class="n">bipartition_tree</span><span class="p">,</span>
+        <span class="n">max_attempts</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
+    <span class="p">)</span>
 <span class="p">)</span>
 
 <span class="n">recom_chain</span> <span class="o">=</span> <span class="n">MarkovChain</span><span class="p">(</span>
@@ -384,22 +431,18 @@ <h2>What to do if the Chain Gets Stuck<a class="headerlink" href="#what-to-do-if
     <span class="n">constraints</span><span class="o">=</span><span class="p">[</span><span class="n">contiguous</span><span class="p">],</span>
     <span class="n">accept</span><span class="o">=</span><span class="n">accept</span><span class="o">.</span><span class="n">always_accept</span><span class="p">,</span>
     <span class="n">initial_state</span><span class="o">=</span><span class="n">initial_partition</span><span class="p">,</span>
-    <span class="n">total_steps</span><span class="o">=</span><span class="mi">20</span>
+    <span class="n">total_steps</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span>
 <span class="p">)</span>
 
 <span class="n">assignment_list</span> <span class="o">=</span> <span class="p">[]</span>
 
 <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">item</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">recom_chain</span><span class="p">):</span>
     <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Finished step {i + 1}/{len(recom_chain)}&quot;</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s2">&quot;</span><span class="se">\r</span><span class="s2">&quot;</span><span class="p">)</span>
-    <span class="n">assignment_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">item</span><span class="o">.</span><span class="n">assignment</span><span class="p">)</span>
+    <span class="n">assignment_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">item</span><span class="o">.</span><span class="n">assignment</span><span class="p">))</span>
 </pre></div>
 </div>
 <p>This will output the following sequence of warnings and errors</p>
-<div class="highlight-console notranslate"><div class="highlight"><pre><span></span><span class="go">ValueWarning:</span>
-<span class="go">The sum of the weights in the weight dictionary is greater than 1.</span>
-<span class="go">Please consider normalizing the weights.</span>
-
-<span class="go">BipartitionWarning:</span>
+<div class="highlight-console notranslate"><div class="highlight"><pre><span></span><span class="go">BipartitionWarning:</span>
 <span class="go">Failed to find a balanced cut after 50 attempts.</span>
 <span class="go">If possible, consider enabling pair reselection within your</span>
 <span class="go">MarkovChain proposal method to allow the algorithm to select</span>
@@ -412,12 +455,6 @@ <h2>What to do if the Chain Gets Stuck<a class="headerlink" href="#what-to-do-if
 to rerun the part of the script that sets the random seed to 42.
 Let’s break down what is happening in each of these:</p>
 <ul>
-  <li><strong>ValueWarning</strong>
-    This is just telling us that we have made an ill-advised
-    choice of weights for our regions. See <a href="#weight-dict-warning">the above warning</a>
-    for more information.
-  </li>
-  <br style="line-height: 5px;">
   <li><strong>BipartitionWarning</strong>
     This is telling us that somewhere along the way,
     we picked a pair of districts that were difficult to bipartition underneath
@@ -452,13 +489,20 @@ <h2>What to do if the Chain Gets Stuck<a class="headerlink" href="#what-to-do-if
     <span class="n">pop_target</span><span class="o">=</span><span class="n">ideal_population</span><span class="p">,</span>
     <span class="n">epsilon</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span>
     <span class="n">node_repeats</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
-    <span class="n">weight_dict</span><span class="o">=</span><span class="p">{</span><span class="s2">&quot;muni&quot;</span><span class="p">:</span> <span class="mf">1.0</span><span class="p">,</span> <span class="s2">&quot;water_dist&quot;</span><span class="p">:</span> <span class="mf">1.0</span><span class="p">},</span>
+    <span class="n">region_surcharge</span><span class="o">=</span><span class="p">{</span>
+        <span class="s2">&quot;muni&quot;</span><span class="p">:</span> <span class="mf">1.0</span><span class="p">,</span>
+        <span class="s2">&quot;water_dist&quot;</span><span class="p">:</span> <span class="mf">1.0</span>
+    <span class="p">},</span>
 <span class="p">)</span>
 </pre></div>
 </div>
 <p>Running this code, we can see that we get stuck once again, so this was not the fix.
 Let’s try to enable reselection instead:</p>
-<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">method</span> <span class="o">=</span> <span class="n">partial</span><span class="p">(</span><span class="n">bipartition_tree</span><span class="p">,</span> <span class="n">allow_pair_reselection</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">method</span> <span class="o">=</span> <span class="n">partial</span><span class="p">(</span>
+    <span class="n">bipartition_tree</span><span class="p">,</span>
+    <span class="n">max_attempts</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
+    <span class="n">allow_pair_reselection</span><span class="o">=</span><span class="kc">True</span>
+<span class="p">)</span>
 
 <span class="n">proposal</span> <span class="o">=</span> <span class="n">partial</span><span class="p">(</span>
     <span class="n">recom</span><span class="p">,</span>
@@ -466,7 +510,10 @@ <h2>What to do if the Chain Gets Stuck<a class="headerlink" href="#what-to-do-if
     <span class="n">pop_target</span><span class="o">=</span><span class="n">ideal_population</span><span class="p">,</span>
     <span class="n">epsilon</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span>
     <span class="n">node_repeats</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
-    <span class="n">weight_dict</span><span class="o">=</span><span class="p">{</span><span class="s2">&quot;muni&quot;</span><span class="p">:</span> <span class="mf">1.0</span><span class="p">,</span> <span class="s2">&quot;water_dist&quot;</span><span class="p">:</span> <span class="mf">1.0</span><span class="p">},</span>
+    <span class="n">region_surcharge</span><span class="o">=</span><span class="p">{</span>
+        <span class="s2">&quot;muni&quot;</span><span class="p">:</span> <span class="mf">1.0</span><span class="p">,</span>
+        <span class="s2">&quot;water_dist&quot;</span><span class="p">:</span> <span class="mf">1.0</span>
+    <span class="p">},</span>
     <span class="n">method</span><span class="o">=</span><span class="n">method</span>
 <span class="p">)</span>
 </pre></div>
@@ -494,7 +541,7 @@ <h3>Imports<a class="headerlink" href="#imports" title="Permalink to this headli
 <div class="section" id="setting-up-the-initial-districting-plan">
 <h3>Setting up the initial districting plan<a class="headerlink" href="#setting-up-the-initial-districting-plan" title="Permalink to this headline">¶</a></h3>
 <div class="center-container">
-  <a href="https://github.com/mggg/GerryChain/blob/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
+  <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
 </div>
 <br style="line-height: 5px;"><p>We’ll create our graph using the example Pennsylvania json file.</p>
 <div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">graph</span> <span class="o">=</span> <span class="n">Graph</span><span class="o">.</span><span class="n">from_json</span><span class="p">(</span><span class="s2">&quot;./PA_VTDs.json&quot;</span><span class="p">)</span>