Minority Opinions

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Voting Method Opinions

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Perhaps the most unfortunate effect of the impossibility of a perfect voting system is the tendency, among those who care at all, to debate about which method is best.  For some crazy reason, I have researched the issue enough to have opinions of my own.  My views have been swayed, however, by having evaluated several of them from the perspective of an unusual type of election: game design competitions.

In any election, it is important to minimize the effectiveness of tactical voting strategies, so voters are encouraged to vote sincerely.  However, game design competitions are complicated by the additional requirement to work well when most of the voters haven’t played several of the candidate games.  That could be because the rules don’t read well, but lack of time, opponents, and/or equipment also contribute greatly.  It wouldn’t be fair to ruin a game’s chances simply because it was played less than another one.  After all, perhaps everyone who played it had a great time.

On top of that, it’s convenient to have a total ordering, or at least a few good honorable mentions.  A major purpose of the competition is to help people find new games they would most likely enjoy, out of the hundreds or thousands available.  However, not everyone likes every type of game; perhaps the second place entry is more your style than the overall winner, and would be better for you personally.

Finally, the results are hampered by a very small set of voters.  Few people outside of game developers even hear about such competitions.  Of those who do, fewer still have the resources to participate.  Even fewer end up voting.

That means the easiest voting method, plurality, is simply untenable.  Almost nobody knows their favorite out of all the games, so the win could very well go to the one that simply got played the most.  The second place entry fares even worse; with so few voters, it depends too much on knowing each voter’s second-favorite game.

As a step up, approval voting is a workable way to narrow down the list of candidates to something reasonable.  With enough voters, and/or few enough candidates, it could even produce a generally valid result.  As a very simple change from plurality, it could very well be a decent solution to the two-party problem we face in political elections, facing much less opposition than a more complicated ballot process.  However, still penalizes unplayed games too much for competition purposes.

It could be interesting to have each voter rank games on a scale of 1 (or 0) to 10, with the highest average taking the prize.  BoardGameGeek does this on a massive scale; but while doing so, it illustrates a potential problem: Each number on its scale has a verbal description.  How else would I know that my 7 means the same thing as another voter’s 7?  As long as that problem is solved, it means that having played just one candidate game can lead to a meaningful vote, which is a significant improvement over several of the methods here.  For political elections, however, it would probably devolve into approval voting, with strategic voters dishonestly using the extreme ends of the scale.

For a time, I thought the Borda Count method wouldn’t work at all.  The easiest count always gives points to rated candidates, which would again leave unplayed candidates in the dust.  However, there is a zero-sum variant: On each ballot, give each candidate one point for each candidate it beats, but subtract one point for each candidate that beats it.  That leaves the less-played candidates closer to the middle of the pack, unless the more-played candidates are close enough in quality to cancel each other out.

Nevertheless, my gut reaction is to favor a fully ranked method.  Kemeny-Young is probably ideal when it isn’t ambiguous, but nasty to calculate; as an NP-hard problem, it’s solvable by computer, but don’t depend on having the results instantly.  Unfortunately, it lacks a good tie-breaking rule, which makes it distasteful for my purposes.

Instant-runoff voting and Bucklin voting throw away too much information; they could be decent for determining a single winner, but they fail miserably at producing a total ordering.  They also assume that any unranked candidates are losers, just like plurality and approval.

For the most part, that leaves pairwise methods.  By extracting only the information that X is better than Y, we get useful data from any ballot with at least two ranked candidates.  Ranked pairs and beatpath seem to be the current favorites among theorists.  The latter satisfies an extra theoretical criterion, but is slightly harder to calculate, and its champion has been a bit naughty on Wikipedia.  Yes, that’s petty of me, but I reserve the right to make choices based on gut feelings.  I have also seen a river method that claims to be a compromise between the two, but I haven’t yet done the math to see exactly what that means.  Minimax is perhaps simpler to calculate by hand, but has enough weaknesses that I don’t recommend it over those listed above.

Perhaps the best test, though, would be to pit several of the above methods against each other, in real contests, elections, and/or group choices.  How often will the results really be different?

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Written by eswald

31 May 2011 at 10:06 pm

Posted in Entertainment, Politics

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