Mon 13 Mar 2017 1:03AM

Relaxed Majority Criterion

MF Mark Frohnmayer Public Seen by 22

The majority criterion states that "if one candidate is preferred by a majority (more than 50%) of voters, then that candidate must win." This criterion is used to dismiss Score and Approval voting, which don't pass the majority criterion, as running contrary to our basic notions of democracy. Further, this MC failure is hypothesized to encourage factional bullet voting, because a majority offering any support at all to another candidate can cause the majority's preferred choice to lose.

SRV also does not satisfy the majority criterion, but in a much less "severe" way than Approval and Score -- the majority has to offer support to two additional candidates in order for the majority's top choice to lose. This suggests a new criterion that makes more realistic sense for evaluating voting methods that balance competing criteria.

The Relaxed Majority Criterion:

A voting system passes the RMC if a majority faction of voters can express maximum support to a first choice, and a non-zero "maximum support - 1" to a second choice, and guarantee that their first choice wins.

IRV and SRV pass RMC, Score and Approval do not.


Sara Wolf Wed 15 Mar 2017 12:28AM

This is an interesting topic. It ties in well with the debate over tyranny-of-the-majority vs later-no-harm criteria or as I've been calling them, Later-No-Harm vs. Compromise Acceptance Criteria. (Criteria names should ideally describe the desired effect.) Doesn't IRV as is pass Later-No-Harm/Majority Criteria as those terms are normally used?

A point that I have been thinking but haven't brought up is how the idea of "majority" changes if no candidate is actually the 1st choice of a majority.
* Is 3nd choice support as strong as 2rd choice support and so on?
* Is some support from a majority of people enough to say that that winner had a majority?
* What if multiple candidates have some level of support from a majority of people but neither has a majority of 1st choices? How do you decide which majority is stronger overall? Strength of support or number of supporters.

Ideally there would be another word to describe these kinds of majorities which are not as strong as the conventional definition. In IRV the kind of majority that is promised is one of these lesser "majorities" if one exists and really that's a plurality, just like in a general election with Plurality voting when nobody gets a full 50%+. A real majority of voters only actually prefers the winner in what are considered landslide wins.

Broadest plurality describes the winner with the most supporters. Is this the same as Condorcet winner?

Most enthusiastic plurality winner describes the candidate with strongest support, say the highest average support. This would be the Score Voting winner in most cases.

As I understand it SRV and Voter Satisfaction Efficiency sort of split the difference and take these both into account. IRV also takes a somewhat compromise position here, but strikes a different balance. Stronger support and broader support are both important and a balance is ideal, but how to determine what is best?

Currently we are using Condorcet to examine IRV winners, because it works well with rankings, which is the info we have, even though we admit that that's not ALWAYS the actual best winner. We are determining that Burlington was decisive enough that we don't need to split hairs to determine if it was a spoiler or not. To better measure IRV winners I think some sort of score would be a good lens to look through in addition to finding the Condorcet winner. Assign 1st choices with 5 points. 2nd Choices with 4 points, 3rd Choices with 3 points and 4th choices with 2 points. Others would get a 0. Then total up the scores and see who won. Obviously this isn't as accurate as if voters had actually picked their own scores, but I'd be really interested to see how a Burlington recount would turn out by this method. And we have the relevant info to do it!