Is AV ‘unfair’?

There is a referendum coming up here on whether to opt for a new electoral system. The proposed new system is the so called ‘Alternative Vote’ (AV) system (used in lower house elections in Australia, though the UK version will not require voters to express further preferences than first), where voters register not a single vote for a candidate, but rank candidates in preference order. If no candidate gets an outright majority of first preferences, the least first-preferred candidate is eliminated, and the second-preferences of their voters distributed to the remaining candidates; this elimination and redistribution is repeated if no candidate then achieves a majority of preferences.

The campaign has been pretty torpid so far, but with the date of the referendum looming, it’s becoming a bit more lively. Something which has interested me is the claim by the ‘No to AV’ campaign that AV is ‘unfair’:

The winner should be the candidate that comes first, but under AV the candidate who comes second or third can actually be elected. That’s why it is used by just three countries in the world – Fiji, Australia and Papua New Guinea. Voters should decide who the best candidate is, not the voting system. We can’t afford to let the politicians off the hook by introducing a loser’s charter. (‘Why vote No?’)

As an argument in favour of the claim of ‘unfairness’, this is obviously pretty weak. Probably we shouldn’t expect more from a political campaigning group. (And presumably the pro-AV side is just as bad.) But still it’s pretty embarrassing. I mean: surely ‘the winner should be the candidate that comes first’ is just a tautology. The real problem they seem to have is that ‘the candidate who comes first’ could refer to someone different if AV were in place than if first-past-the-post were in place. But that simply begs the question; suppose AV were in place, and candidate X wins, while candidate Y gets the most first preferences and comes in second. Would the FTTP people wish to say ‘The winner should be the candidate who comes in second, but under AV the candidate who comes in first can actually be elected’? Surely not—but their apparent assumption that the ‘winner’ of an election is somehow a fact fixed independently of the voting system in place is bizarre.

The aim of an electoral system is to elect a representative for a group of people. Different electoral systems embody different conceptions of what adequate conditions for representativeness are. There is no obvious sense in which getting the most number of people to most prefer you is sufficient for representativeness, as the behaviour of FPTP systems in many party political systems would show, where extremism may be rewarded. It isn’t much more obvious that AV is representative, but by incorporating further preferences when they matter (noting that the second preferences of those who most prefer the eventual winner never need to matter, since they get their first preference satisfied), it does seem to incorporate more information about the group to be represented.

There are lots of ways of incorporating information about preferences. No system will be perfect, as Arrow’s theorem seems to show (unless we have a metric on preferences). We could have a system which assigns points to candidates depending on rank, and the candidate with the most points wins (known as the Borda count, I now discover). We could have a system which only cares about most-preferred (FPTP). Etc. But quite how any of systems is ‘unfair’ is mysterious to me. I can see why FPTP might be unrepresentative, and perhaps unfair to those groups of people who end up being represented by someone who is not the consensus choice. I can see why AV might be more plausibly consensual than FPTP. But I don’t see at all a rationale for calling AV unfair, unless it is due to the sophistry I discussed above.

UPDATE (21 April): I notice that Tim Gowers has a post on a similar theme, though at much greater length, where he makes some similar points as well as many others. He makes the nice point that it is sometimes in the interests of voters not to vote for their most preferred candidate under a FPTP system, if one is convinced that one’s second choice candidate has both a need of votes and has some realistic prospect of being elected.

Gowers also makes explicit the connection between AV and multiple round elections (one reason AV is sometimes called ‘instant runoff’). Of course in genuine multiple round elections, one can change one’s votes from round to round (and this might even be rational—no obvious reason why one’s preferences among a collection of options must be preserved when one of those options is removed). The fact that lower-ranked preferences for those who first-prefer unpopular candidates come into play earlier is pretty obviously bad news for those voters in a multiple round election (it’s just evidence that what they most want, they won’t get). Quite why it’s supposed to be good for those voters to not get their most preferred option, according to the ‘No to AV’ campaign (who misleading characterise it as those voters getting ‘more votes’), is never made clear—and how could it be?

Anyway, head over there for his sensible commentary.

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