"I'm the Greatest!"

Sports metaphors are always popular when discussing politics. But is an election more like a boxing match, or a foot race? To answer that question, let me ask some more questions: Who do you think is the fastest runner in the world, and who do you think is the best boxer in the world? And how would you know?

In a foot race, the number of contestants is limited only by the width of the track; actually, since everyone runs against the same clock, even that isn't necessarily a restriction. And so there's no question who the fastest runner in the world is.

But boxing is different. If you put Muhammad Ali, George Foreman, and Joe Frasier together in the same ring at the height of their careers, which one would have won? And could you even be sure that the last man standing was the best boxer, and not, for instance, that #2 and #3 didn't just gang up on the "real" world heavyweight champion?

Sadly, elections seem more like boxing matches. Any third challenger either is forced out and not allowed into the ring (via ballot access laws), or drags down a better winner (by being a spoiler). But a little over 200 years ago (or perhaps quite a bit earlier) an improvement was discovered by the Marquis de Condorcet: if there are more than two candidates, have each of them compete, in effect, one-on-one; the truly best one will always beat any other challenger.

(This is done be examining every ballot for its expressed opinion on each pair of candidates; every ballot that list A above B, is a point for A over B. Rankings for any other candidates are inconsequential in the A versus B determination. Then we compare A versus C, and then B versus C, and so on, until we've examined every ballot while considering every pair of candidates.)

There's only one little problem: such a "beats all" or "Condorcet winner" doesn't always exist. Just like Foreman beat Frasier, and Frasier beat Ali, but Ali beat Foreman, so it can go when counting votes. This may not seem obvious, but it's true! Consider:

• 40%: A > B > C
• 35%: B > C > A
• 25%: C > A > B

65% of these voters prefer A over B, and 75% prefer B over C... but 60% prefer C over A! (For this to happen, there would have to be more than a single topic over which voters consider the options. It couldn't just be "right versus left," for instance, but left versus right on "social issues" and "fiscal issues" would be enough to trigger this problem.) When a Condorcet voting method is used then, it's important to have a method to break these "Condorcet cycles," a sort of circular-tie-breaker. Over the years, different tie-breakers have been proposed and used, but they all run into one problem or another, especially when voters begin to act tactically; potentially even electing the worst possible candidate.

How can we improve on this? We can make elections more like a foot race. The problems that other election methods have, they have because they ask the voters to explicitly rank the candidates relative to each other; they ask "who would win in a fight?" But if we instead make the seemingly-minor change of rating every candidate against an independent scale--in other words, have them all race against the clock, so that they are ranked against each other only implicitly--then we discover some surprising things.

For one, we'd find that we can allow many more contestants to run simultaneously, without "spoiling" the election; any supporter of third-party or independent candidates should be excited by that. Of course, there would still be some interaction among candidates; I might rate a candidate lower not because I think they are worse, but because I think it will help my favored candidate win. That's tactical voting. So rather than a 100 meter dash, perhaps a marathon, where all the runners bunch together and pace each other (i.e., run faster or slower because of the presence of the other runners), is a better analogy. (Although we should point out that not even the 100 meter dash is immune to pacing effects.)

Although tactical voting is still present, what we find is that it is a much less significant factor in determining the outcome. The truly surprising thing though is that, when we allow our models to account for tactical voting, we discover that these rating-based methods--such as approval voting and score voting--are more likely to elect the honest Condorcet winner than any actual, rankings-based, Condorcet voting method! (Scroll down to the first chart; Condorcet methods are highlighted in blue; score voting is equivalent to range voting.)

Condorcet's insight is a powerful tool for evaluating election methods. And even though he only considered it in the context of ranked ballots, in practice, the most reliable way to achieve it is through rated ballots; through approval voting and score voting.

Award Season

I've been trying to come up with some sort of clear conclusion to draw about the Academy Awards vs. IMDB's Top 250, but I keep running into the problem that I don't know half the movies on both lists, and when I try to generalize anything from conclusions based on what I do know, I run into this wall of uncertainty (another reason that I was hoping for comments, but oh well.) But, before I give it all a rest, I'd like to talk about another award-slash-voting-system: science fiction's Hugo Awards.

According to their description, the Hugo Awards (like the Academy Awards) uses a two-step process; nominations and final voting. The nomination process for the Hugo's uses approval voting (good on them!) but with a limit of five titles on each persons ballot (oh well, no one's perfect) with the top five being nominated. The final voting step is instant-runoff (uh oh!) with one important exception.

In addition to the nominees, Hugo voters are allowed to rank "no award" anywhere on their ballot. After determining the IRV winner by the normal method, the potential winner is compared pairwise to "no award" (obviously, if "no award" was the IRV winner, there is no award). In other words, for each ballot it is determined whether that ballot ranks the potential winner higher or "no award" higher, irrespective of the rankings of all other nominees. If more ballots prefer "no award" than prefer the potential winner, then there is no award.

This "special case" highlights one of the more damning aspects of instant runoff: it does not, despite its advocate's claims, always pick a majority-preferred candidate, but rather, sometimes, one of the other candidates is preferred over the "winner" by a majority of voters. (This, among other issues, happened in Burlington, Vermont's most recent mayoral election.)

These sorts of pairwise comparissons—looking at a more-than-two way race as a series of one-on-one contests—is the heart of another ranked-order voting method (or rather, a family of such methods) called Condorcet's method; and as ranked-order methods go, based on Bayesian regret, Condorcet is better than IRV (not a tall order since IRV is the second-worst method, only ahead of plurality). If the Hugo awards are so fearful of "no award" getting an unfair pairwise chance against the IRV winner, I wonder why they don't use an entirely pairwise method; surely there must be some overlap with judges of a science-fiction contest (geeks) and open-source programmers (more geeks), and the programmers use Condorcet for their elections.

Of course, I recommend that both of them move to score voting; however, the approval-based nomination step is a great idea for the initial round of a two-step process (although on average the approval votes alone would likely get a better result than the final IRV round, barring the fact that the two-round process gives everyone a chance to go read any nominees they missed before the decisive round.)

Finally: I try to keep my personal views on any actual issues out of my writing here, and focus only on the process by which groups can make more-democratic decisions. But if Anathem doesn't win Best Novel, I will riot in the streets.