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Tuesday 2011-05-03

voting

The leaflets put out by the "No2AV" campaign consist almost entirely of outright lies. I'm not talking about mere spin and fuzziness; they say one thing after another that is simply, demonstrably, not true, and that they surely must know are not true. These people are not interested in truth.

One of the more credible-sounding claims they make is this one: AV gives more votes to supporters of minority parties. (Of course they make this claim in a way that is plainly calculated to make you think it amounts to "AV gives lots of power to the BNP". That'll be why the BNP oppose it. But I digress.)

That claim is, of course, false. I've seen it made by at least one extremely intelligent person, so let me show why it's false.

AV is basically equivalent to a series of simpler elections: one with the whole field, then another in which the least popular candidate is removed, then another in which the newly least popular candidate is removed, and so on until someone has all the votes. (AV differs from this in that voters have to decide ahead of time which candidates they prefer to which; hence the alternative name of "instant runoff voting".)

In each of these elections, every voter gets exactly one vote. What's different about the supporters of minority parties is that in some of the elections their less-preferred votes are counted instead of their first-preference votes. This is not an advantage.

Here's a hypothetical election. Three candidates: Left, Right and Crazy. Five voters. Two prefer Left, then Right, then Crazy. Two prefer Right, then Left, then Crazy. One prefers Crazy, then Right, then Left.

So, Crazy gets eliminated and then his second-place vote for Right is counted in the next round (alongside the first-place votes of the other voters). Right wins.

The Right party, although they happen to win this one, are very upset: the Crazy supporter got his second-place vote counted. How very unfair. Very well, gentlemen, we'll count your supporters' second-place votes instead of their first-place votes, shall we? Result: Left wins by a landslide.

Much, much more detailed analysis of the arguments by Tim Gowers: one, two, three. (If you're short on time or patience, read the last one.)

In some situations AV can give really crazy results: see Ka-Ping Yee's simulations and Warren Smith's examples of comprehensively pathological AV results and spoiler effects that may make AV as prone to two-party domination as FPTP.

For the avoidance of doubt, despite those ugly phenomena I think AV is clearly a better system than FPTP.