[EM] Best-Single Method-MJ

Juho Laatu juho.laatu at gmail.com
Thu Jun 27 23:59:10 PDT 2019

Yes, it is useful to discuss both strategic and sincere performance of different election methods. I tend to divide the targets of single winner methods from this point of view in two categories, cardinal and ordinal/ranked methods. The former typically aim at providing best sum of utilities. The latter ones are more majority oriented.

In the utility oriented category it is typical to aim at maximal sum of utilities, but it would be also possible to try to lift the lowest utilities as high as possible. In practice this would probably not mean making the absolutely lowest utility higher (to please the most unsatisfied voter) but to achieve a distribution of utilities that emphasises lifting the lower half of utilities among the voters.

In the majority oriented methods most people on this list like the Condorcet criterion. This approach can be characterised as seeking a good compromise. Other approaches, like that of IRV, put more emphasis on the number of first preferences in the votes. There is also a difference between trying to find the ideal winner vs trying to establish a total social order among the candidates. The results may be different, depending on how you define the ideal winner or the ideal social order.

When determining the ideal winner in ranked methods, one could concentrate on the number of other candidates that would beat the potential winner in a pairwise comparison, or the strengths of those defeats, or the worst defeat, or closeness of being an ideal winner, or maybe even chains of defeats to other candidates. The arguments here could be related to how well the chosen winner would be able to do his job in the competitive situation he finds himself in after he has been elected. I.e. how much and what kind of opposition there could be working against him.

It is good if the results can be easily understood. People tend to like natural looking things, like the elimination approach of IRV. People may also like the idea of forcing the cyclic group opinions to a more natural looking linear order of candidates. One should be careful about when one is talking about something that looks good vs something where the end result actually is good (according to the chosen criteria).

Different societies may have different needs in different elections. There is no ideal single winner method that would be best in all situations. Ideal winner can be defined in a different way e.g. in sports and in politics.

One could thus try to seek a winner that has the best sum of utilities, that is best for the median or average voter, most liked by those with strong opinions, most acceptable to majority, least hated by all, most efficient according to experts (this could mean indirect elections where elected experts elect the final winner). Most often we assume the one-man-one-vote principle, but that need not be the case always. We may plan the method for large or small elections, or large or small number of candidates. Sometimes easy and effortless voting is a key target, to guarantee high level of participation in the election, or to allow frequent and effortless voting. Easy understandability may mean also ability to see afterwards why the winner won, and what the opinions of different districts were, and how they summed up, or how close to victory the other candidates were. In political elections we typically like methods that can hide the opinions of individual voters.

In non-competitive elections we have lots of alternative approaches to select from. In competitive elections our choices are more limited since we need to take also the strategic vulnerabilities into account. The definition of ideal winner may actually already include some assumptions about what kind of a winner would be ideal in a competitive world (e.g. one that could work efficiently also when the opposition does not support his work).


> From: Toby Pereira

> With all the discussion of different single-winner methods and the criteria they pass and fail, I'm interested to know what you think the "ideal" method should hope to achieve. For example, some people might want to maximise utility summed across the voters. Others might want to find the candidate that is closest to the "median voter". For others it might be more about obeying some sort of majority criterion (e.g. Condorcet). Etc.
> Personally, the measure that makes most sense to me is to maximise utility. But this doesn't automatically mean score voting (where a score could simply be seen as a utility rating of a candidate), at least in part because strategies that voters adopt might reduce its effectiveness. Obviously a voting method also needs to be simple enough to understand (in terms of voting and understanding how the winner is calculated), and it might be that different types of election suit different methods.
> Toby

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