Thursday, April 15, 2010

Betrayal and Clones

Why do I call this blog The Least of All Evils? It's a play on a well-known phrase that seems to come up a lot around election time every year. Many voters—and perhaps you've been one of these voters—have found themselves standing in the election booth, looking at a Democrat and a Republican, and also perhaps some other third choice, and said to themselves "I really like this third option; but I know they haven't being polling great, and I really hate the Democrat (or the Republican), so in order to prevent the worst candidate from winning, perhaps it's best if I vote for the lesser of two evils." And so either voters take such a tactical position—and third-party candidates become self-fulfilled prophecies of failure—or voters stick to their honest views—and third-party candidates become spoilers.

Making the tactical choice is an example of favorite betrayal, which is hands-down the most common type of strategic voting, and is probably the most damaging as well, so it shouldn't be surprising if a student of voting theory might try to design a voting system to combat it. (And yet, the Wikipedia article for the favorite betrayal criterion has been deleted.) This is the crux of my problem with instant runoff voting: that it cannot guarantee immunity to favorite betrayal and, more so, that it markets itself by lying that it can.

A Brief Digression

Let me change gears for a moment and talk about primaries again. I said before that the sole reason for political parties to exist is to hold primaries, in which they try to determine which of several similarly-minded candidates would best serve their members while still wining the election. What if a party were to consider two completely identical candidates, and they found themselves tied for first-place in their party's primary, could the party run both candidates? Of course not! At best, everyone will vote for the same candidate and any effort spent on the other will be wasted, and at worst the votes will be split perfectly equally, and the party will have done nothing but increase the share of votes they need to win from half to two-thirds. Having this sort of problem crop up in a voting system is called susceptibility to cloning. (I should note that there are voting systems, such as the Borda count, that have the opposite problem, where a party's best strategy is run as many similar candidates as possible; this is sometimes called "teaming", but we'll refer to both collectively as "cloning" here.)

Now, why have I brought up cloning? Because there is an interesting piece of mathematical work [PDF] that shows that no voting system based on ranked order ballots (which is the kind of ballots used in instant runoff voting) can be immune to both favorite betrayal and to cloning. So given the choice between a voting system that prevents the worst type of tactical voting, and one that can protect elections from the Star Wars Clone Army, instant runoff supporters have decided that the science fiction ravings of George Lucas are a bigger threat.

Accidentally On Purpose

Now, back to favorite betrayal, and how instant runoff supporters lie that they can fix it. Here's their claim (from's "How Instant Runoff Voting Works"):

IRV allows all voters to vote for their favorite candidate, while avoiding the fear of helping elect their least favorite candidate.

Now, this is simply not true; I can provide simple examples illustrating it, and point to real-life elections where it was not the case. If it's so obvious, why the lie? Perhaps it's not intentional; perhaps they are simple confusing favorite betrayal with independence of clones?

To fall for this lie, you only need to make one unstated, seemingly-intuitive, but regrettably false, assumption: that everyone's true favorite is functionally a clone of another candidate. Allow me to sketch an example. Lets assume there's a Republican, a Democrat, and a Green running in an election. If you assume that every Democrat-first voter has the Green candidate as their second choice, and every Green-first voter has the Democratic candidate as their second choice—which seems to be close-enough to true that it shouldn't really effect the outcome of the election—then instant-runoff voting performs flawlessly! That's because you've treated the Green and the Democrat as clones; you could just as easily had two identical Democrats running in the election, and the voters would have acted the same way. But the problem is this: it only takes one, single, solitary voter to throw the election into a situation where a large number of voters will find that they have accidentally elected their least-preferred candidate, which they could have avoided if they'd strategically betrayed their favorite and voted their second-favorite first, just like so many voters do today under plurality. This is because instant runoff is immune clones, but is not immune to favorite betrayal. And all it takes is one Democrat who likes the Republicans better than the Greens (someone like Al Gore, to name one example.)

A Whole Lot of Work, For Nothing

Because of its susceptibility to favorite betrayal, instant runoff voting will ultimately result in the same two-party-dominated system as we have under plurality; the proof is in the Australian House of Representatives, which has used instant runoff for decades and is as two-party-dominated as the U.S. House of Representatives. (Note that the Liberal and National parties are universally considered to be the same party, to the point that they don't run candidates in the same elections unless Labor isn't running.)

A better answer is approval voting and score voting. Approval voting and score voting are immune to both cloning and to favorite betrayal. They do what no other voting system can, because they don't use rank order ballots, which means they are the only systems which can actually help third parties, and the only system which can help us escape from two-party politics. If you are a third-party supporter, or if you are simply fed up with feeling you are forced to pick the lesser of two evils, then your number-one political priority should be to enact approval or score voting. Even if all politicians are scum, you should at least have your choice among The Least of All Evils.

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