econ_models.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "import squigglepy as sq\n",
    "from squigglepy.numbers import K, M, B\n",
    "import numpy as np\n",
    "import copy\n",
    "import general_equations as ge\n",
    "\n",
    "SIMULATIONS = 10*M\n",
    "\n",
    "\n",
    "def dalys_per_1000_by_reducing_risk_mixture_model(models_dict, weights_dict, power):\n",
    "    p_success, risk, bp_per_billion_if_success, times_credit_if_success = ge.create_variables(models_dict, weights_dict)\n",
    "    dalys_risk_weighted = ge.one_model_dalys_per_1000_by_reducing_risk(risk, power, p_success, bp_per_billion_if_success, times_credit_if_success)\n",
    "\n",
    "    return dalys_risk_weighted\n",
    "\n",
    "def find_percentile_of_value(value, array_of_values):\n",
    "    prop_under =  sum(array_of_values < value)/len(array_of_values)\n",
    "    return prop_under\n",
    "\n",
    "def print_outputs(dalys_per_1000_unweighted, risk_function, interpretation_function, const):\n",
    "    dalys_per_1000_ghd = ge.dalys_per_1000_ghd_intervention()\n",
    "\n",
    "    ev_ghd_dalys_per_1000 = np.mean(dalys_per_1000_ghd)\n",
    "    ev_dalys_per_1000 = np.mean(dalys_per_1000_unweighted)\n",
    "    print(\"Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: {}\".format(ev_dalys_per_1000))\n",
    "    print(\"Standard deviation DALYs/$1000 for no risk-aversion: {}\".format(np.std(dalys_per_1000_unweighted)))\n",
    "\n",
    "    print(\"Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: {}\".format(ev_ghd_dalys_per_1000))\n",
    "    print(\"Standard deviation DALYs/$1000 for no risk-aversion: {}\".format(np.std(dalys_per_1000_ghd)))\n",
    "\n",
    "    rw_dalys_per_1000 = risk_function(dalys_per_1000_unweighted, const)\n",
    "    rw_ghd_dalys_per_1000 = risk_function(dalys_per_1000_ghd, const)\n",
    "\n",
    "    ev_rw_dalys_per_1000 = np.mean(rw_dalys_per_1000)\n",
    "    ev_rw_ghd_dalys_per_1000 = np.mean(rw_ghd_dalys_per_1000)\n",
    "\n",
    "    print(\"Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = {}: {}\".format(const, ev_rw_dalys_per_1000))\n",
    "\n",
    "    print(\"GHD Risk-Weighted DALYs/$1000, shape = {}: {}\".format(const, ev_rw_ghd_dalys_per_1000))\n",
    "\n",
    "    if ev_rw_dalys_per_1000 > ev_rw_ghd_dalys_per_1000: \n",
    "        print(\"X-risk reduction is better than GHD in terms of Risk-weighted expected value\")\n",
    "    elif ev_rw_dalys_per_1000 < ev_rw_ghd_dalys_per_1000:\n",
    "        print(\"GHD is better than X-risk reduction in terms of Risk-weighted expected value\")\n",
    "    else:\n",
    "        print(\"X-risk reduction and GHD are equally good in terms of Risk-weighted expected value\")\n",
    "\n",
    "    p_needed = interpretation_function(const)\n",
    "    return ev_rw_dalys_per_1000, ev_rw_ghd_dalys_per_1000, p_needed\n",
    "\n",
    "def get_percentiles_to_make_equal_to_ghd(dalys_per_1000_unweighted, risk_function, interpretation_function, c=0):\n",
    "    dalys_per_1000_ghd = ge.dalys_per_1000_ghd_intervention()\n",
    "    ev_ghd_dalys_per_1000 = np.mean(dalys_per_1000_ghd)\n",
    "    print(\"Mean DALYs per $1000 if you choose GHD: \", ev_ghd_dalys_per_1000)\n",
    "    prop_under = find_percentile_of_value(ev_ghd_dalys_per_1000, dalys_per_1000_unweighted)\n",
    "    print(\"If you choose X-risk, there's a {} chance of saving fewer lives than the mean GHD spending\".format(ge.get_pct(prop_under)))\n",
    "\n",
    "    ev_rw_dalys_per_1000, ev_rw_ghd_dalys_per_1000, p_needed = print_outputs(dalys_per_1000_unweighted, risk_function, interpretation_function, c)\n",
    "    return ev_rw_dalys_per_1000, ev_rw_ghd_dalys_per_1000, p_needed\n",
    "    "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Population Times the Present We Can Take Credit For if we Solve X-risk\n",
    "low_pop_credit = sq.lognorm(10, 1000)\n",
    "high_pop_credit = sq.lognorm(47.5, 40000)\n",
    "pop_weights = [0.9, 0.1]\n",
    "pop_models = [low_pop_credit, high_pop_credit]\n",
    "\n",
    "## Probability of Success\n",
    "p_success = sq.lognorm(0.4,0.8, lclip=0.01, rclip=0.99)\n",
    "p_success_models = [p_success]\n",
    "p_success_weights = [1]\n",
    "\n",
    "## Risk\n",
    "risk = sq.lognorm(0.1, 0.25, lclip=0.01, rclip=0.5)\n",
    "risk_models = [risk]\n",
    "risk_weights = [1]\n",
    "\n",
    "## Basis Points Per Billion If Success\n",
    "bp_model1 = sq.lognorm(0.001, 0.001)\n",
    "bp_model2= sq.lognorm(0.001, 2.2)\n",
    "bp_model1n = sq.uniform(-0.0005, -0.00005)\n",
    "bp_model2n= sq.norm(-.5, -0.0005)\n",
    "\n",
    "bp_models = [bp_model1, bp_model2, bp_model1n, bp_model2n]\n",
    "bp_per_billion_weights = [0.9/2, 0.1/2, 0.95/2, 0.05/2]\n",
    "\n",
    "models = {'p_success': p_success_models, 'risk': risk_models, \n",
    "        'bp_per_billion_if_success': bp_models, 'times_credit_if_success': pop_models}\n",
    "\n",
    "weights = {'p_success': p_success_weights, 'risk': risk_weights, \n",
    "           'bp_per_billion_if_success': bp_per_billion_weights, 'times_credit_if_success': pop_weights}\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CRRA Utility Function"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def crra_interpretation(const):\n",
    "    if const == 1:\n",
    "        p_needed = np.log(100)/np.log(10*K)\n",
    "    else:\n",
    "        p_needed = (100**(1-const)-1**(1-const))/((10*K)**(1-const)-1**(1-const))\n",
    "\n",
    "    return p_needed\n",
    "\n",
    "def crra_risk_aversion(dalys, c=0):\n",
    "    dalys2 = copy.deepcopy(dalys)\n",
    "    if 0 < c < 1:\n",
    "        for idx, value in enumerate(dalys):\n",
    "            if value > 0:\n",
    "                dalys2[idx] = (value**(1-c)-1)/(1-c)\n",
    "            elif value < 0:\n",
    "                dalys2[idx] = -((-1*value)**(1-c)-1)/(1-c)\n",
    "            else:\n",
    "                dalys2[idx] = 0\n",
    "    elif c == 1: \n",
    "        for idx, value in enumerate(dalys):\n",
    "            if value > 0:\n",
    "                dalys2[idx] = np.log(value)\n",
    "            elif value < 0:\n",
    "                dalys2[idx]  = -np.log(-1*value)\n",
    "            else:\n",
    "                dalys2[idx] = 0\n",
    "\n",
    "    elif c == 0:\n",
    "        dalys2 = dalys\n",
    "    return np.array(dalys2)\n",
    "\n",
    "def multiple_crra_risk_aversion(models, weights):\n",
    "    coefficients = [0, 0.01, 0.05, 0.1, 0.2, 0.3, 0.35, 0.38, 0.4, 0.42, 0.43, 0.44, 0.45, 0.5, 0.6, 0.7, 0.8, 0.9, 1]\n",
    "    dalys_per_1000_unweighted = dalys_per_1000_by_reducing_risk_mixture_model(models, weights, 1)\n",
    "    for c in coefficients:\n",
    "        print(\"-------------------------------------------------------------------\")\n",
    "        if c == 0:\n",
    "            print(\"Coefficient of Relative Risk Aversion: c = {} (No Risk Aversion)\".format(c))\n",
    "        else:\n",
    "            print(\"Coefficient of Relative Risk Aversion: c = {}\".format(c))\n",
    "        ev_rw_dalys_per_1000, ev_rw_ghd_dalys_per_1000, p_needed = get_percentiles_to_make_equal_to_ghd(dalys_per_1000_unweighted, crra_risk_aversion, crra_interpretation, c)\n",
    "        print(\"This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a {} chance of getting $10K and {} chance of getting $1\".format(ge.get_pct(p_needed), ge.get_pct(1-p_needed)))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### CRRA Utility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 4/4 [00:00<00:00, 26.86it/s]\n",
      "100%|██████████| 1000000/1000000 [00:01<00:00, 890715.02it/s]\n",
      "100%|██████████| 2/2 [00:00<00:00, 21.40it/s]\n",
      "100%|██████████| 1000000/1000000 [00:01<00:00, 972040.45it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0 (No Risk Aversion)\n",
      "Mean DALYs per $1000 if you choose GHD:  15.359686885705129\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.366743805158453\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.685464417557634\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0: 3271.343896327515\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0: 15.366743805158453\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 0.99% chance of getting $10K and 99.01% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.01\n",
      "Mean DALYs per $1000 if you choose GHD:  15.36520637358624\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.363880457138947\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.69024834843495\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.01: 2707.073267824957\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.01: 14.084066256196149\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 1.04% chance of getting $10K and 98.96% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.05\n",
      "Mean DALYs per $1000 if you choose GHD:  15.357913721528387\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.363801083052044\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.684430061350697\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.05: 1281.97139822167\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.05: 13.025095298926749\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 1.24% chance of getting $10K and 98.76% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.360649069926886\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.37067826567354\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.689779339357416\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.1: 516.8672773165083\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.1: 11.832112741996406\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 1.56% chance of getting $10K and 98.44% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.2\n",
      "Mean DALYs per $1000 if you choose GHD:  15.36560139684905\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.364395953264813\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.683956449529354\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.2: 94.26475089987277\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.2: 9.791691114430671\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 2.45% chance of getting $10K and 97.55% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.3\n",
      "Mean DALYs per $1000 if you choose GHD:  15.365158392897008\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.356461010806859\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.679864410547428\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.3: 21.240956781933644\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.3: 8.148987744260626\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 3.83% chance of getting $10K and 96.17% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.35\n",
      "Mean DALYs per $1000 if you choose GHD:  15.368765231001264\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.357650301469059\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.676390388889962\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.35: 11.151648768644435\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.35: 7.452708470003101\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 4.77% chance of getting $10K and 95.23% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.38\n",
      "Mean DALYs per $1000 if you choose GHD:  15.356756752625309\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.359395552626623\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.682053572892322\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.38: 7.8531052690458\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.38: 7.068997450576928\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 5.44% chance of getting $10K and 94.56% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.4\n",
      "Mean DALYs per $1000 if you choose GHD:  15.363107576531792\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.359767535411999\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.687063263840333\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.4: 6.31250089209324\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.4: 6.825943132841658\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 5.94% chance of getting $10K and 94.06% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.42\n",
      "Mean DALYs per $1000 if you choose GHD:  15.364333318054092\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.367314095818314\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.6818887210748565\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.42: 5.137385350909389\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.42: 6.595469908713709\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 6.47% chance of getting $10K and 93.53% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.43\n",
      "Mean DALYs per $1000 if you choose GHD:  15.365294776465344\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.363572245607442\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.676800013647654\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.43: 4.656100252820104\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.43: 6.481394931903921\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 6.76% chance of getting $10K and 93.24% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.44\n",
      "Mean DALYs per $1000 if you choose GHD:  15.37225544423404\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.366202171276264\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.68835905933555\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.44: 4.232841956922671\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.44: 6.371272143681508\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 7.05% chance of getting $10K and 92.95% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.45\n",
      "Mean DALYs per $1000 if you choose GHD:  15.360508113046395\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.368728486680359\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.688726931784863\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.45: 3.859755821909016\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.45: 6.263558775378342\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 7.36% chance of getting $10K and 92.64% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.5\n",
      "Mean DALYs per $1000 if you choose GHD:  15.35718870469849\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.36375025165357\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.679447016414112\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.5: 2.543147545204196\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.5: 5.752846089906998\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 9.09% chance of getting $10K and 90.91% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.6\n",
      "Mean DALYs per $1000 if you choose GHD:  15.366742807465517\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.373052778374904\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.691837766317952\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.6: 1.34403721700456\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.6: 4.879129223985427\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 13.68% chance of getting $10K and 86.32% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.7\n",
      "Mean DALYs per $1000 if you choose GHD:  15.361971422151067\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.370530305350483\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.6904589005600945\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.7: 0.8679536370552292\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.7: 4.162612310432144\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 20.08% chance of getting $10K and 79.92% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.8\n",
      "Mean DALYs per $1000 if you choose GHD:  15.361431962119008\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.364072721413022\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.681470762383208\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.8: 0.6398855475485898\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.8: 3.574060974646421\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 28.47% chance of getting $10K and 71.53% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 0.9\n",
      "Mean DALYs per $1000 if you choose GHD:  15.361983354196743\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.368754845812559\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.686193383374934\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 0.9: 0.5142178358608278\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 0.9: 3.0896154169504695\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 38.69% chance of getting $10K and 61.31% chance of getting $1\n",
      "-------------------------------------------------------------------\n",
      "Coefficient of Relative Risk Aversion: c = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.370666816530216\n",
      "If you choose X-risk, there's a 90.40% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 3271.343896327515\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 2327984.609815226\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.369057990699888\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.690955742052268\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = 1: 0.4385387361887909\n",
      "GHD Risk-Weighted DALYs/$1000, shape = 1: 2.687842352568409\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion is like being indifferent to choosing to take $100 with certainty or a 50.00% chance of getting $10K and 50.00% chance of getting $1\n"
     ]
    }
   ],
   "source": [
    "multiple_crra_risk_aversion(models, weights)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prospect Theory Method"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prospect_theory_utility(dalys, cs): \n",
    "    a, b, l = cs\n",
    "    dalys2 = copy.deepcopy(dalys)\n",
    "    for idx, value in enumerate(dalys):\n",
    "        if value > 0:\n",
    "            dalys2[idx] = (value)**a\n",
    "        else:\n",
    "            dalys2[idx] = -l*(-1*value)**b\n",
    "\n",
    "    return np.array(dalys2)\n",
    "\n",
    "def prospect_theory_utility_estimates(models, weights, coefficients, loss_aversion):\n",
    "    c_tuples = [(a, a, l) for a in coefficients for l in loss_aversion]\n",
    "    dalys_per_1000_unweighted = dalys_per_1000_by_reducing_risk_mixture_model(models, weights, 1)\n",
    "    for cs in c_tuples:\n",
    "        a, b, l = cs\n",
    "        print(\"-------------------------------------------------------------------\")\n",
    "        print(\"Coefficients of Prospect Theory: a = {}, b = {}, l = {}\".format(a, b, l))\n",
    "        rw_ev_dalys_per_1000, rw_ghd_ev_dalys_per_1000, p_needed = get_percentiles_to_make_equal_to_ghd(dalys_per_1000_unweighted, prospect_theory_utility, prospect_theory_indifference, cs)\n",
    "        print(\"This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus {} chance of getting $10K versus nothing\".format(ge.get_pct(p_needed)))\n",
    "\n",
    "def prospect_theory_indifference(cs):\n",
    "    a, b, l = cs\n",
    "    p = (l*100**b)/(l*100**b+9900**a)\n",
    "    return p \n",
    "\n",
    "coefficients = [0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.62, 0.63, 0.64, 0.65, 0.675, 0.7, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.8, 0.82, 0.85, 0.88, 0.9, 1]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loss Aversion Not Allowed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 4/4 [00:00<00:00, 33.90it/s]\n",
      "100%|██████████| 1000000/1000000 [00:00<00:00, 1177506.15it/s]\n",
      "100%|██████████| 2/2 [00:00<00:00, 30.80it/s]\n",
      "100%|██████████| 1000000/1000000 [00:00<00:00, 1245095.68it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.01, b = 0.01, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.363555339505739\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.36715017959696\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.685277966867611\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.01, 0.01, 1): 0.00496388375084389\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.01, 0.01, 1): 1.027246688077532\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 48.85% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.05, b = 0.05, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.370110983829766\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.360825134554243\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.683259212791631\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.05, 0.05, 1): 0.0240103270283383\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.05, 0.05, 1): 1.1439434494127754\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 44.28% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.1, b = 0.1, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.364066697375765\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.367040379454869\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.6872889968058065\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.1, 0.1, 1): 0.051646841821545865\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.1, 0.1, 1): 1.3089452067273506\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 38.71% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.2, b = 0.2, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.359271993467802\n",
      "If you choose X-risk, there's a 90.41% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.364388208948215\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.684704331119244\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.2, 0.2, 1): 0.12744305312868726\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.2, 0.2, 1): 1.7148065500278853\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 28.52% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.3, b = 0.3, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.361772230829752\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.364086667369884\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.683794759773356\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.3, 0.3, 1): 0.2578627891819626\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.3, 0.3, 1): 2.2485410676289783\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 20.12% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.4, b = 0.4, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.358279854391794\n",
      "If you choose X-risk, there's a 90.41% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.364704154605397\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.689180748366258\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.4, 0.4, 1): 0.5278416691399446\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.4, 0.4, 1): 2.9509962189999843\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 13.73% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.5, b = 0.5, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.361108592712226\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.363901483055297\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.68667688530412\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.5, 0.5, 1): 1.2176494401472409\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.5, 0.5, 1): 3.8763376458314367\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 9.13% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.6, b = 0.6, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.36076864240194\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.353058055934131\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.675986263292993\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.6, 0.6, 1): 3.3709701659962823\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.6, 0.6, 1): 5.094392043667799\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 5.97% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.62, b = 0.62, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.358981908500063\n",
      "If you choose X-risk, there's a 90.41% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.369705063463943\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.687347849856395\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.62, 0.62, 1): 4.229854151877639\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.62, 0.62, 1): 5.384984733277668\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 5.47% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.63, b = 0.63, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.362845232274017\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.373878270770339\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.687154100828667\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.63, 0.63, 1): 4.751407636528539\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.63, 0.63, 1): 5.535726259261841\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 5.24% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.64, b = 0.64, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.37222416130101\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.359808721762112\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.686630742125413\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.64, 0.64, 1): 5.346949936197153\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.64, 0.64, 1): 5.686330276215095\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 5.02% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.65, b = 0.65, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.361337508301913\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.367497579435975\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.687577299017484\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.65, 0.65, 1): 6.027807438295774\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.65, 0.65, 1): 5.846504541747844\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 4.80% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.675, b = 0.675, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.364069717963607\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.367239869678466\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.688376287825003\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.675, 0.675, 1): 8.194705477644854\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.675, 0.675, 1): 6.261985428939391\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 4.30% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.7, b = 0.7, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.368630455151392\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.369144280073208\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.688839665042076\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.7, 0.7, 1): 11.253305652146244\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.7, 0.7, 1): 6.7080660185945815\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 3.85% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.72, b = 0.72, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.366369789768491\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.365712427581629\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.683357476569078\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.72, 0.72, 1): 14.601583156258858\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.72, 0.72, 1): 7.086480042504212\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 3.53% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.73, b = 0.73, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.36283524010112\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.363039780074036\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.677908065811559\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.73, 0.73, 1): 16.667630528064343\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.73, 0.73, 1): 7.283372264927014\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 3.38% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.74, b = 0.74, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.3646042380958\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.360990482570468\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.682830747176242\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.74, 0.74, 1): 19.05145537335667\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.74, 0.74, 1): 7.485779872315869\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 3.23% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.75, b = 0.75, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.368321178769268\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.361973630733752\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.680599370351732\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.75, 0.75, 1): 21.804264428427462\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.75, 0.75, 1): 7.695238009237124\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 3.09% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.76, b = 0.76, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.363130740820331\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.36818729627351\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.688150504028596\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.76, 0.76, 1): 24.98576854395166\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.76, 0.76, 1): 7.912416722466356\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 2.95% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.77, b = 0.77, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.36435803813101\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.37094203216621\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.68897468735889\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.77, 0.77, 1): 28.665626552792954\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.77, 0.77, 1): 8.134645290759364\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 2.82% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.8, b = 0.8, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.370058532385816\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.368150619076854\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.684727069015701\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.8, 0.8, 1): 43.57879298223411\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.8, 0.8, 1): 8.835072724651571\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 2.47% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.82, b = 0.82, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.371321429203014\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.3630495090768\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.675164920516566\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.82, 0.82, 1): 57.91454234795621\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.82, 0.82, 1): 9.334076376199283\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 2.26% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.85, b = 0.85, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.369981002955148\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.356361812681737\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.67795525940235\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.85, 0.85, 1): 89.3445506584385\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.85, 0.85, 1): 10.136503357988321\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 1.97% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.88, b = 0.88, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.358035418270644\n",
      "If you choose X-risk, there's a 90.41% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.365500057730557\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.683074717635002\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.88, 0.88, 1): 138.86580711249783\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.88, 0.88, 1): 11.01855452129209\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 1.72% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.9, b = 0.9, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.36046023414143\n",
      "If you choose X-risk, there's a 90.42% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.37020711090331\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.696345930475759\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.9, 0.9, 1): 187.02582434093742\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.9, 0.9, 1): 11.648469396741545\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 1.57% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 1, b = 1, l = 1\n",
      "Mean DALYs per $1000 if you choose GHD:  15.358931889092553\n",
      "If you choose X-risk, there's a 90.41% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 860.1238457312088\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 122305.43675789665\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.360900545120298\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.689609126427072\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (1, 1, 1): 860.1238457312088\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (1, 1, 1): 15.360900545120298\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 1.00% chance of getting $10K versus nothing\n"
     ]
    }
   ],
   "source": [
    "loss_aversion=[1]\n",
    "prospect_theory_utility_estimates(models, weights, coefficients, loss_aversion)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loss Aversion Allowed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 4/4 [00:00<00:00, 31.57it/s]\n",
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      "100%|██████████| 2/2 [00:00<00:00, 23.42it/s]\n",
      "100%|██████████| 1000000/1000000 [00:00<00:00, 1168485.06it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.01, b = 0.01, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.36465298558977\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.363422409357783\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.6813789646123976\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.01, 0.01, 2.25): -0.35849021165747463\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.01, 0.01, 2.25): 1.027244894132698\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 68.24% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.05, b = 0.05, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.372896208186644\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.365050358234836\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.690279385519783\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.05, 0.05, 2.25): -0.3536742808932603\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.05, 0.05, 2.25): 1.1439523273555883\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 64.13% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.1, b = 0.1, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.366333794295976\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.364929759812474\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.69059661878357\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.1, 0.1, 2.25): -0.35028436664757184\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.1, 0.1, 2.25): 1.3089178202720375\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 58.70% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.2, b = 0.2, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.366476639494218\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.372118376193628\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.699139244314178\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.2, 0.2, 2.25): -0.3555885636480933\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.2, 0.2, 2.25): 1.71492752650001\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 47.30% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.3, b = 0.3, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.360227814856973\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.361405592530502\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.683920411086205\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.3, 0.3, 2.25): -0.38796816388745897\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.3, 0.3, 2.25): 2.2484049009193825\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 36.18% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.4, b = 0.4, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.363674187116382\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.372344888003564\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.687584324332739\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.4, 0.4, 2.25): -0.4705175363072933\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.4, 0.4, 2.25): 2.951606140185134\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 26.36% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.5, b = 0.5, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.356122759487072\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.366667490063293\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.682481220376581\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.5, 0.5, 2.25): -0.6241023487607045\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.5, 0.5, 2.25): 3.8767532065578663\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 18.44% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.6, b = 0.6, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.363807064836257\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.370374001958362\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.690997628717325\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.6, 0.6, 2.25): -0.7165426893906035\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.6, 0.6, 2.25): 5.097655766084926\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 12.50% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.62, b = 0.62, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.355055201078168\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.36742140462533\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.691680306697242\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.62, 0.62, 2.25): -0.665224523300368\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.62, 0.62, 2.25): 5.384378941094613\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 11.53% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.63, b = 0.63, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.371063175909214\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.357514121111683\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.693191338455019\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.63, 0.63, 2.25): -0.6184084218214769\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.63, 0.63, 2.25): 5.531788543676072\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 11.07% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.64, b = 0.64, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.367273501078511\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.368725324433104\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.687194294127901\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.64, 0.64, 2.25): -0.552863530341561\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.64, 0.64, 2.25): 5.688490999781035\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 10.62% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.65, b = 0.65, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.358949623873439\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.361483675457967\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.680881191379153\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.65, 0.65, 2.25): -0.46421757928846114\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.65, 0.65, 2.25): 5.845144641018539\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 10.19% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.675, b = 0.675, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.363807944818234\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.368245343208363\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.685110894562617\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.675, 0.675, 2.25): -0.10428913435763719\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.675, 0.675, 2.25): 6.262358497973115\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 9.19% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.7, b = 0.7, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.372282043598076\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.367148857709715\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.679585406549839\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.7, 0.7, 2.25): 0.5519701209258765\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.7, 0.7, 2.25): 6.7076203990037655\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 8.27% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.72, b = 0.72, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.362040729448056\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.369404676041329\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.681063749842658\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.72, 0.72, 2.25): 1.4102486535471388\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.72, 0.72, 2.25): 7.08774758225649\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 7.60% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.73, b = 0.73, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.357792036697358\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.361438609009776\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.684805133506789\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.73, 0.73, 2.25): 1.9951836654114985\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.73, 0.73, 2.25): 7.282644052757146\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 7.29% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.74, b = 0.74, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.368185884189806\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.356449844204215\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.68381797051363\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.74, 0.74, 2.25): 2.7127998888111855\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.74, 0.74, 2.25): 7.4841118616781275\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 6.98% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.75, b = 0.75, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.367120521108005\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.36883988456714\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.687312008082004\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.75, 0.75, 2.25): 3.5900471894880766\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.75, 0.75, 2.25): 7.697676780244809\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 6.69% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.76, b = 0.76, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.363589034771032\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.365458690807728\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.686127000462939\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.76, 0.76, 2.25): 4.659138072763252\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.76, 0.76, 2.25): 7.9114027774242315\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 6.41% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.77, b = 0.77, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.359471848970836\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.363774324835692\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.683003504858843\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.77, 0.77, 2.25): 5.958561446537443\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.77, 0.77, 2.25): 8.131780108428453\n",
      "GHD is better than X-risk reduction in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 6.14% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.8, b = 0.8, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.36592875047399\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.367621535948158\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.689010304844424\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.8, 0.8, 2.25): 11.744907839538607\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.8, 0.8, 2.25): 8.834755055181617\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 5.39% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.82, b = 0.82, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.375422836420615\n",
      "If you choose X-risk, there's a 90.39% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.362386262317425\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.68279742635147\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.82, 0.82, 2.25): 17.870568828341888\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.82, 0.82, 2.25): 9.333585874133849\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 4.94% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.85, b = 0.85, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.361053347058602\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.356681278517652\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.683057145809907\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.85, 0.85, 2.25): 32.54732615069273\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.85, 0.85, 2.25): 10.136559675079228\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 4.33% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.88, b = 0.88, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.369351800983537\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.366542880257152\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.685369353377099\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.88, 0.88, 2.25): 57.88722646312578\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.88, 0.88, 2.25): 11.01915644162288\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 3.80% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 0.9, b = 0.9, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.357632052278245\n",
      "If you choose X-risk, there's a 90.38% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.362466862368931\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.67973148094043\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (0.9, 0.9, 2.25): 84.22198407600557\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (0.9, 0.9, 2.25): 11.643402966085914\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 3.47% chance of getting $10K versus nothing\n",
      "-------------------------------------------------------------------\n",
      "Coefficients of Prospect Theory: a = 1, b = 1, l = 2.25\n",
      "Mean DALYs per $1000 if you choose GHD:  15.377818661019678\n",
      "If you choose X-risk, there's a 90.39% chance of saving fewer lives than the mean GHD spending\n",
      "Expected Value DALYs/$1000 if you choose X-risk, No risk-aversion: 809.2915473179779\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 178064.54237286892\n",
      "Expected Value DALYs/$1000 if you choose GHD, No risk-aversion: 15.36784715324867\n",
      "Standard deviation DALYs/$1000 for no risk-aversion: 4.68822620988797\n",
      "Risk-Weighted EV DALYs/$1000 if you choose X-risk, shape = (1, 1, 2.25): 518.4230881421719\n",
      "GHD Risk-Weighted DALYs/$1000, shape = (1, 1, 2.25): 15.36784715324867\n",
      "X-risk reduction is better than GHD in terms of Risk-weighted expected value\n",
      "This level of risk aversion and loss aversion is like being indifferent between choosing to take $100 with certainty versus 2.22% chance of getting $10K versus nothing\n"
     ]
    }
   ],
   "source": [
    "loss_aversion=[2.25]\n",
    "prospect_theory_utility_estimates(models, weights, coefficients, loss_aversion)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sensitivity Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1st Order] Sensitivity analysis for DALYs per $1000 spending on LT\n",
      "LT DALYs per $1000 Sensitivity Analysis\n",
      "probability_success : 0.013 +/- 0.024\n",
      "bp_per_billion_if_success : 0.221 +/- 0.034\n",
      "times_credit_if_success : 0.114 +/- 0.03\n",
      "---------------------------------------------------------------------------\n",
      "[Total] Sensitivity analysis for DALYs per $1000 spending on LT\n",
      "LT DALYs per $1000 Sensitivity Analysis\n",
      "probability_success : 0.514 +/- 0.031\n",
      "bp_per_billion_if_success : 0.852 +/- 0.034\n",
      "times_credit_if_success : 0.741 +/- 0.031\n",
      "---------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "import sensitivity_analysis\n",
    "\n",
    "sensitivity_analysis.lt_dalys_per_1000_sensitivity()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tests\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "test_crra_close_when_equal (__main__.TestFunctions) ... ok\n",
      "test_crra_interpretation (__main__.TestFunctions) ... ok\n",
      "100%|██████████| 4/4 [00:00<00:00,  5.73it/s]Functions) ... \n",
      "100%|██████████| 1000000/1000000 [00:03<00:00, 285758.38it/s]\n",
      "100%|██████████| 2/2 [00:00<00:00,  8.63it/s]\n",
      "100%|██████████| 1000000/1000000 [00:02<00:00, 444580.83it/s]\n",
      "ok\n",
      "test_prospect_interpretation (__main__.TestFunctions) ... ok\n",
      "test_prospect_theory_close_when_equal (__main__.TestFunctions) ... ok\n",
      "100%|██████████| 4/4 [00:00<00:00, 15.45it/s]TestFunctions) ... \n",
      "100%|██████████| 1000000/1000000 [00:02<00:00, 454197.00it/s]\n",
      "100%|██████████| 2/2 [00:00<00:00, 14.19it/s]\n",
      "100%|██████████| 1000000/1000000 [00:02<00:00, 450578.49it/s]\n",
      "ok\n",
      "\n",
      "----------------------------------------------------------------------\n",
      "Ran 6 tests in 260.652s\n",
      "\n",
      "OK\n"
     ]
    }
   ],
   "source": [
    "\n",
    "import unittest\n",
    "import os\n",
    "\n",
    "class TestFunctions(unittest.TestCase):\n",
    "\n",
    "    def test_value_gained_by_reducing_risk(self):\n",
    "        pass_test = True\n",
    "\n",
    "        p_success, risk, bp_per_billion_if_success, times_credit_if_success = ge.create_variables(models, weights)\n",
    "        value_of_status_quo = ge.years_healthy_per_year()*ge.lifespan_person()*ge.world_population()*times_credit_if_success\n",
    "        power = 1\n",
    "\n",
    "        did_succeed = ge.generate_success_bernoullis(p_success)\n",
    "        \n",
    "        x_risk_reduction = did_succeed*bp_per_billion_if_success*ge.one_basis_point()*1*K/(1*B)\n",
    "\n",
    "        value_gained = ge.value_gained_by_reducing_x_risk(risk, x_risk_reduction, value_of_status_quo, power)\n",
    "        expected_value_gained = x_risk_reduction*value_of_status_quo\n",
    "        \n",
    "        if np.median(value_gained) < 0.9*np.median(expected_value_gained) or np.median(value_gained) > 1.1*np.median(expected_value_gained):\n",
    "            pass_test = False\n",
    "            print(\"x-risk reduced: {}, value status quo: {}\".format(x_risk_reduction, value_of_status_quo))\n",
    "            print(\"Expected value gained: \", expected_value_gained)\n",
    "            print(\"Got value gained: \", value_gained)\n",
    "\n",
    "        self.assertTrue(pass_test)\n",
    "\n",
    "    def test_dalys_when_p_success_zero(self):\n",
    "        pass_test = True\n",
    "        p_success, risk, bp_per_billion_if_success, times_credit_if_success = ge.create_variables(models, weights)\n",
    "        p_success = np.zeros(SIMULATIONS)\n",
    "\n",
    "        dalys = ge.one_model_dalys_per_1000_by_reducing_risk(risk, 1, p_success, bp_per_billion_if_success, times_credit_if_success)\n",
    "\n",
    "        if dalys.all() != 0:\n",
    "            pass_test = False\n",
    "            print(\"DALYs when p_success is zero: \", dalys)\n",
    "\n",
    "        self.assertTrue(pass_test)\n",
    "\n",
    "    def test_crra_close_when_equal(self):\n",
    "        pass_test = True\n",
    "        outside = 0\n",
    "        count = 0\n",
    "        outside_c = []\n",
    "        for c in coefficients:\n",
    "            dalys_per_1000_lt = ge.dalys_per_1000_ghd_intervention()\n",
    "\n",
    "            dalys_per_1000_ghd = ge.dalys_per_1000_ghd_intervention()\n",
    "\n",
    "            ev_ghd_dalys_per_1000 = np.mean(dalys_per_1000_ghd)\n",
    "            ev_dalys_per_1000 = np.mean(dalys_per_1000_lt)\n",
    "\n",
    "            rw_dalys_per_1000 = crra_risk_aversion(dalys_per_1000_lt, c)\n",
    "            rw_ghd_dalys_per_1000 = crra_risk_aversion(dalys_per_1000_ghd, c)\n",
    "\n",
    "            ev_rw_dalys_per_1000 = np.mean(rw_dalys_per_1000)\n",
    "            ev_rw_ghd_dalys_per_1000 = np.mean(rw_ghd_dalys_per_1000)\n",
    "\n",
    "            count += 2\n",
    "            if ev_rw_dalys_per_1000 < 0.9*ev_rw_ghd_dalys_per_1000 or ev_rw_dalys_per_1000 > 1.1*ev_rw_ghd_dalys_per_1000:\n",
    "                outside += 1\n",
    "                outside_c.append(c)\n",
    "            if ev_dalys_per_1000 < 0.9*ev_ghd_dalys_per_1000 or ev_dalys_per_1000 > 1.1*ev_ghd_dalys_per_1000:\n",
    "                outside += 1\n",
    "                outside_c.append(c)\n",
    "        if outside/count > 0.2:\n",
    "            pass_test = False\n",
    "            print(\"Outside 20% of the time\")\n",
    "        \n",
    "        self.assertTrue(pass_test)\n",
    "\n",
    "    def test_prospect_theory_close_when_equal(self):\n",
    "        pass_test = True\n",
    "        outside = 0\n",
    "        count = 0\n",
    "        outside_c = []\n",
    "        loss_aversion = [1, 2.25]\n",
    "        for c in coefficients:\n",
    "            for l in loss_aversion:\n",
    "                cs = [c, c, l]\n",
    "                dalys_per_1000_lt = ge.dalys_per_1000_ghd_intervention()\n",
    "\n",
    "                dalys_per_1000_ghd = ge.dalys_per_1000_ghd_intervention()\n",
    "\n",
    "                ev_ghd_dalys_per_1000 = np.mean(dalys_per_1000_ghd)\n",
    "                ev_dalys_per_1000 = np.mean(dalys_per_1000_lt)\n",
    "\n",
    "                rw_dalys_per_1000 = prospect_theory_utility(dalys_per_1000_lt, cs)\n",
    "                rw_ghd_dalys_per_1000 = prospect_theory_utility(dalys_per_1000_ghd, cs)\n",
    "\n",
    "                ev_rw_dalys_per_1000 = np.mean(rw_dalys_per_1000)\n",
    "                ev_rw_ghd_dalys_per_1000 = np.mean(rw_ghd_dalys_per_1000)\n",
    "\n",
    "                count += 2\n",
    "                if ev_rw_dalys_per_1000 < 0.9*ev_rw_ghd_dalys_per_1000 or ev_rw_dalys_per_1000 > 1.1*ev_rw_ghd_dalys_per_1000:\n",
    "                    outside += 1\n",
    "                    outside_c.append(c)\n",
    "                if ev_dalys_per_1000 < 0.9*ev_ghd_dalys_per_1000 or ev_dalys_per_1000 > 1.1*ev_ghd_dalys_per_1000:\n",
    "                    outside += 1\n",
    "                    outside_c.append(c)\n",
    "        if outside/count > 0.2:\n",
    "            pass_test = False\n",
    "            print(\"Outside 20% of the time\")\n",
    "        \n",
    "        self.assertTrue(pass_test)\n",
    "\n",
    "    def test_prospect_interpretation(self):\n",
    "        pass_test = False\n",
    "        for l in [1, 2.25]:\n",
    "            for a in coefficients:\n",
    "                p_10k = l*100**a/(l*100**a+9900**a)\n",
    "                u_10k = 9900**a\n",
    "                u_0 = -1*l*100**a\n",
    "\n",
    "                u_100 = p_10k*u_10k + (1-p_10k)*u_0\n",
    "\n",
    "                if round(u_100,2) !=0:\n",
    "                    pass_test = False\n",
    "                    print(\"Back calculated probability wrong\")\n",
    "                    print(u_100)\n",
    "                p = prospect_theory_indifference([a, a, l])\n",
    "\n",
    "                u_100_2 = p*u_10k + (1-p)*u_0\n",
    "                if round(u_100_2,2) != 0:\n",
    "                    pass_test = False\n",
    "                    print(\"Calculated probability wrong\")\n",
    "            \n",
    "                if round(p,2) != round(p_10k,2):\n",
    "                    pass_test = False\n",
    "                    print(\"Probabilities not equal\")\n",
    "\n",
    "    def test_crra_interpretation(self):\n",
    "        pass_test = False\n",
    "        for c in coefficients:\n",
    "            if c != 1:\n",
    "                p_10k = ((100)**(1-c)-1**(1-c))/((10*K)**(1-c)-1**(1-c))\n",
    "                u_10k = ((10*K)**(1-c)-1)/(1-c)\n",
    "                u_1 = ((1)**(1-c)-1)/(1-c)\n",
    "\n",
    "                u_100 = p_10k*u_10k + (1-p_10k)*u_1\n",
    "\n",
    "                if round(u_100) != round((100**(1-c)-1)/(1-c)):\n",
    "                    pass_test = False\n",
    "                    print(\"Back calculated probability wrong\")\n",
    "                    print(c)\n",
    "                    print(u_100)\n",
    "                    print(\"Supposed to be: {}\".format((100**(1-c)-1)/(1-c)))\n",
    "                p = crra_interpretation(c)\n",
    "\n",
    "                u_100_2 = p*u_10k + (1-p)*u_1\n",
    "                if round(u_100_2) != round(u_100):\n",
    "                    pass_test = False\n",
    "                    print(\"Calculated probability wrong\")\n",
    "            \n",
    "                if round(p,2) != round(p_10k,2):\n",
    "                    pass_test = False\n",
    "                    print(\"Probabilities not equal\")\n",
    "            else: \n",
    "                p_10k = np.log(100)/np.log(10*K)\n",
    "\n",
    "                u_10k = np.log(10*K)\n",
    "                u_1 = np.log(1)\n",
    "                u_100 = p_10k*u_10k + (1-p_10k)*u_1\n",
    "\n",
    "                if round(u_100) != round(np.log(100)):\n",
    "                    pass_test = False\n",
    "                    print(\"Back calculated utility wrong\")\n",
    "                    print(c)\n",
    "                    print(\"Calculated: {}\".format(u_100))\n",
    "                    print(\"Supposed to be: {}\".format(np.log(100)))\n",
    "                p = crra_interpretation(c)\n",
    "\n",
    "                u_100_2 = p*u_10k + (1-p)*u_1\n",
    "                if round(u_100_2) != round(u_100):\n",
    "                    pass_test = False\n",
    "                    print(\"Calculated probability wrong\")\n",
    "            \n",
    "                if round(p,2) != round(p_10k,2):\n",
    "                    pass_test = False\n",
    "                    print(c)\n",
    "                    print(\"Probabilities not equal\")\n",
    "                    print(p)\n",
    "                    print(p_10k)\n",
    "\n",
    "\n",
    "res = unittest.main(argv=[''], verbosity=3, exit=False)"
   ]
  }
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