Extend a Dashboard with visualizers which apply different voting rule algorythms

[JaneSjs]

Consider extending a dashboard with the following visualizers:

Option 1: Multiwinner voting with approved ballots

• Wiki:
  https://en.wikipedia.org/wiki/Multiwinner_voting
  https://en.wikipedia.org/wiki/Multiwinner_approval_voting

• Multi-Winner Voting with Approval Preferences

Example 1
Classic examples are elections for a (small) committee or creating a shortlist._

Example 2

Multiwinner voting example as motivation for more diverse voting rules

Suppose your company wants to invite all employees to a cinema show. However, the cinema would be too crowded to host all of the staff members at once. Thus, the organizer plans to split the event into two evenings. Now they want to find suitable dates with the goal of having as many employees as possible join for at least one evening.

Traditional approval voting (AV) would ask each person to approve the dates on which they are available, and the two dates with the highest individual approval rates would win.
AV in this setup can result in two dates where the same set of people - representing, e.g., only 40% of the whole staff - are available. Hence, the second evening does not benefit anyone because it does not increase the percentage of employees who can join the cinema show.

However, there are alternative algorithms called "multiwinner voting rules" or "committee voting rules" which try to find results with higher representation, i.e., which satisfy more voters. Examples are "Proportional Approval Voting (PAV)" or "Chamberlin-Courant (CC)." The input is still a simple survey in which every voter states which alternatives they approve, i.e., in our example, on which evenings they are available.

The CC rule would maximize the number of staff members who can join for at least one evening. The PAV rule provides a small extra bonus if more employees are available on both evenings, but not as much as the AV rule does. Finally, the AV rule degenerates in the sense that it treats two voters who each have time on exactly one evening and one person who has time on both dates completely equally.

In our example, the CC rule might find two dates where up to 80% of the staff members can go to at least one cinema show. Hence, CC can potentially double the percentage of happy people in this setting.

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Option 2: Kemeny-Young Method

Wiki: A matrix which summarizes the pairwise comparison counts
to allow the voters to submit rankings of candidates and getting back an aggregated ranking, e.g. using the well-known Kemeny rule.

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Check the original inquiry for more examples: T12055 - Feature Request / PR willingness: Multiwinner voting.