A Description of Different Multiwinner Voting Systems for the General Public

This post is primarily for the benefit of Laurel and Hardy Fan Club members who are deciding which of these voting systems to use to elect four new admins. However, I am making this post even more generally available for the benefit of the general public, because it was hard for me to find a central location on the web that gave general public descriptions of these voting systems. Even on Wikipedia, descriptions of some multiwinner voting systems are lacking. This document is meant to help fill some of that current gap for the general public, while directing interested readers to more detailed discussions on these voting systems. I try not to discuss the pros and cons of the systems, and try to focus on the details of the procedures themselves, insofar as they are amenable to general consumption. There exist other places to discuss the pros and cons and the technical details, and I hope the links provided allow the reader to pursue those matters if they so wish.

Assume there are c number of candidates running for s numbers of seats. The following describes how different voting systems work assuming there are a fixed number of open seats. Some of these voting systems would be different if the number of open seats were variable.

Minisum Voting Procedure
Each voter is given a list of the c candidates. The voter marks each candidate to which she consents to. This means a given voter could consent to any number of candidates (i.e. none, one, some, or all). Whichever s candidates receive the most consents win the election. For example, if there are 4 seats available, then the four candidates that receive the most consents win.

For more details on this procedure, please read chapter 5 of Mathematics and Democracy. If that book is inaccessible, the 2nd best, though imperfect, existing text is here.

Minimax Voting Procedure
Each voter is given a list of the c candidates. The voter marks each candidate to which she consents to. This means a given voter could consent to any number of candidates (i.e. none, one, some, or all). Thus, the ballot for the minimax procedure is the same as the minisum procedure. The difference is in how it is tallied.

In the tallying process, after each voter submits her ballot, each given ballot is re-weighted based on its proximity to other ballots. The tallying procedure then chooses the set of s candidates that minimizes the maximum hamming distance to the voters' ballots.

For more details on this procedure, please read chapter 5 of Mathematics and Democracy. If that book is inaccessible, the 2nd best, though imperfect, existing text is here.

Plurality Voting
Under this procedure, each voter marks the single candidate she believes is best. The s candidates that are marked by the greatest number of voters win the election. For example, if there are four open seats, then the four candidates with the most marks win.

For more details on this procedure, please click here.

Reweighted Range Voting
Under this method, voters are asked to grade each candidate on a given scale (e.g. from 1 to 10, where only whole numbers are admissible grades). In the first round, the candidate with the highest average grade is elected. In the second round, roughly speaking, ballots are reweighted and averages are recalculated and a second winner is chosen. This process continues until all seats have been filled.

For more details on how this procedure works, please click here.

Single Transferable Vote with Hagenbach-Bischoff Quota
Under this procedure, each voter rank orders all candidates from their favorite to least favorite. Any candidate that meets the quota, is given a seat. If a candidate does not meet the quota, but some other candidate does, and there are still seats available, then votes are transferred from the winning candidates to losing candidates, until s number of candidates meet the quota.

To learn more about this system, please click here.


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