Hunting The Muse

Vote Systems Review

Election season has me in a voting sciences mood again.

Really fascinating that I am seeing more articles on the Borda Count recently, which some experts says is the only voting method WORSE than our current plurality (most votes win) system.

In Borda Count, you rank candidates. If there are five candidates, your top choice gets five points, second choice gets four points, etc. If everyone votes rationally, it works okay, but there's a big chance for strategic voting as well. Say your rational choice for three candidates, are: A, B, C. But A and B are in a tight race, and C is a longshot. To maximize A's chances, strategically it's better to rank your votes: A, C, B. You've artificially increased the gap between A and B and given A a better chance to win. This is a voting system that asks you to vote against your preference in order to vote your preference.

That's unfair. What do I mean by unfair? Turns out there is an academic definition of unfair in the voting world. Fair voting means that voting your actual preference order should never, never, never, mean that it increases the chances of candidates winning in an order other than your own.

See, there was this guy named Kenneth Arrow. And he proved that for any election of more than two candidates, it is impossible to have a fully fair election. Just flat out impossible. Isn't that depressing?

You think Instant Runoff Voting is the answer? IRV was very popular last election because it eliminates the spoiler effect. This is the other voting method written up in these articles. IRV means that you rank your candidates. Count all the 1st place votes. If no one gets over 50%, take away the lowest vote-getting first-placer, then refigure. Repeat until someone wins. It sounds cool - Nader's votes go to Gore, Gore wins - but there are a lot of demonstrations out there that show how it's possible that ranking someone low will increase their chances of winning and vice versa. And how if there's a competitive three-way race, very strange results can happen. Really weird things can happen with Instant Runoff Voting.

Back to Arrow. It turns out that there is ONE voting method that is extremely, extremely, extremely close to fully fair. And that is Condorcet voting. Here's how it works. Basically, the only truly fair vote is when it's between only two candidates. Everyone votes, winner takes all. Easy. But that's not choice - how do you do that with more candidates? Well, you rank your candidates, and look at it as a bunch of one on one candidates. Rank: A, B, C. That means that A->B, A->C, and B->C. Say someone else ranks B, C, A. That means that B->C, C->A, and B->A. Then you total them all together. A->B: 1. A->C: 1. B->C: 2. etc.

It turns out there is a very solid way of figuring out who wins the election in this method, and if one arguably flawed requirement of Arrow's Theorem is relaxed just a little bit, then it fits all of his criteria for fair voting. Most importantly, there is no need for strategic voting.

Of course, this whole subject only fits for people that actually want their preferences known. What happens when people don't? Like tonight - I know that many people are voting for Measure 23 not because they hope it will pass, but because they are sure it won't, but want it to only fail by a little bit so a better revised version will come out next election. Boy, is that asking for trouble. :) I ended up abstaining from voting on this particular measure (sort of unintentionally, but I think in hindsight that was the best way to go). Posted by Curt at November 5, 2002 02:17 AM