Yee Paper on Visualizing Voting Methods

Just a quickie (I know, I haven't posted that Egypt piece I promised; turns out, just because you don't know a lot about a foreign country's politics, doesn't mean they're simple) and not something that's new if you've been following us closely, but Ka-Ping Yee has a nice, simple, short paper based on his previous work, titled "Disadvantages of Transferable Vote Systems". This one is restricted to just plurality, IRV, and approval, and comes out strongly for approval. Also, the pictures look pretty sweet, so check it out.

Clowns to the Left of Me, Jokers to the Right

I have a game for you. Get one hundred things--pennies, toothpicks, whatever--and set them up in a line, from left to right. This is our voting populace in simplified, one-dimensional form. Each "voter" has just one simple rule to decide how to vote: vote for whichever one candidate stands closest to them (yes, we're using plurality voting; and if there's a tie for closest, each gets a half vote). Now, grab another thing--a pencil, a button, it doesn't matter--and place it on the line, between two voters, so that 17 voters are to the left of it. This new thing is one of our "candidates", Libram McLeftyson. Nearly five out of six voters think he's too liberal. Grab another candidate, and place it, mirror-like, so that 17 voters are to the right of it, and in equal measure to her competitor, nearly five out of six voters think Constance O'Righterly is too conservative.

Now, here's how you win the game: place a third candidate between any two voters (except right on top of one of the existing candidates) such that they win the election. Go on, try it; I'll wait while you count your things.

Give up yet? You should, because the challenge is impossible. No matter where you put your third candidate, it is impossible to make it so they win; even putting them right in the center won't do it. As an added bonus, you'll find that whichever of the other two candidates you put them closer to, also loses. And if I move them from inside the 17 marks to precisely the 25 marks, you can't even come in second. I can even put them at the 49 marks, practically next to each other, and there's still nowhere you can go where you can win.

More and more Americans are agitating for a "third party", most without even realizing that there are already dozens of active third parties to choose from. But they don't win. They can't win. And this is without even acknowledging the effects of tactical voting, this is with honest voters! In this simulation, the only ones voting for the big-two are the ones who honestly believe them to be the uniquely best option available.

The existence of a multitude of third parties hasn't change this. Screaming that we need even more third parties won't change this. You cannot win this game. The only way you can win, is if you change the rules.

And the rules that would give third parties a chance to win are approval voting and score voting.

A Majority of a Majority is a Minority

Consider an election in a swing district; one that is very nearly evenly split between voters who generally prefer Democrats over Republican and voters who generally prefer Republicans over Democrats. Consider also that, in nearly all districts, voters can vote in a primary election, but in only one of the two primaries. Unless the primaries are complete blowouts, the winner of the election can not possibly be the favorite of a majority of voters. Rather, they will be the favorite of a majority of the majority, which could be as little as 25%+1 of the voters—or less if there are more than two candidates in the primary!

Score voting is occasionally attacked because it fails the "majority criterion", which states that, if a candidate is the first-choice of a majority of the voters, that candidate should win the election. I'll provide a simple example: three candidates, A, B, and C. Three voters, two of which vote A=9, B=5, C=0, and one who votes A=0, B=9, C=9. A majority of the voters (two out of three) prefer A over B, but B wins the election, with an average score of 6.33 versus A's score of 6.00. Score voting fails the majority criteria. (This might not be a bad thing, but that's a post for another day...)

But consider this in context of the first paragraph's example: plurality elections are known to fail spectacularly when there are more than two strong candidates, which is why the system of party primaries developed. But this has the side effect of squeezing the middle out of the pool of candidates. While it's true that many primary voters will take into consideration a candidate's chances of winning the general election, the voters are still by and large trying to choose a candidate who is preferable only to the majority of the party members; then, the hope is that the party members will be a majority of the electorate. However, we must remember that this candidate was the first-preference of only a majority of a majority. And since that's the case, is it even meaningful to say that plurality elections (preceded by primaries) choose a "majority winner"?

If you were to put all the candidates from both parties' primaries up at once, how often would more than half of all the voters indicate a single one of those candidates as their favorite? Not very often! Surely, if there were such a candidate, they would win any subsequent plurality election, but when we say that plurality elects a "majority winner", we are usually not talking about such a candidate, even if the system we use obscures this fact from us.

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.