## A complicated game

Some thoughts on AV, mostly cut and pasted (it’s late) from comments on other people’s blogs.

First, the mechanics. AV is basically the Single Transferable Vote, but in a single-member constituency. STV gives a seat to every candidate who can muster a ‘quota’ of votes, where a quota is defined as (1/n+1)+1 vote, n being the number of seats in the constituency. In other words, in a three-member seat the three people who can each claim more than a 1/4 of the votes cast get elected (there can’t be more than 3, for obvious reasons.

Now, in AV there is by definition only one seat per constituency, so the quota is 1/2 of all votes cast plus one vote. So the maximum number of voters whose preferences can have no influence at all on the outcome is 50% minus one vote. This potentially leaves a lot of voters out in the cold.

Under the Simple Preference system we’ve got now, the ‘quota’ can only be guaranteed to be as high as 50% if there are only two candidates. In multi-party contests, the winning plurality may be arbitrarily small. Except, actually, not that arbitrarily small. In practice, approximately 10,000 MPs have been elected in the 17 General Elections held since 1945; out of those MPs, only 30 have had less than 33.3% of the vote (source: Wikipedia). Most of those were close to 1/3; the winning plurality has been below 30% 7 times – 1 SNP, 1 DUP, 2 Tory and 3 Lib Dem(!).

So the representation deficit that AV offers to put right is, at worst, the difference between an MP representing 33% of the voters and an MP representing 50% of the voters, with the gap generally being much smaller. And what’s the practical effect of assembling a 50% vote from first and lower preferences instead of going off first preferences? There are two possibilities, represented by these two scenarios.

Scenario 1:

33% vote Left, all with Centre as second preference (L1, C2)
18% vote C1, L2
13% vote Centre, with Right as second preference (C1, R2)
24% vote R1, C2
12% vote Neo-Nazi, with Right as second preference (N1, R2)

First round: N eliminated; 36% R, 33% L, 31% C
Second round: C eliminated: 49% R, 51% L. Left candidate duly elected.

In this scenario 51% of voters are happy – the 33% of the voters who put the L candidate first plus the 18% who put them second; therefore only 49% of the voters are unhappy. Result. But the outcome would have been exactly the same under SP, the only difference being that those 18% of voters have had to explicitly state that they preferred L to R instead of just thinking it to themselves.

Scenario 2:

33% vote L1, C2
16% vote C1, L2
15% vote C1, R2
24% vote R1, C2
12% vote N1, R2

First round: N eliminated; 36% R, 33% L, 31% C
Second round: C eliminated: 51% R, 49% L. Right candidate duly elected.

All that’s changed is the split within the Centre voters, and even that hasn’t changed by much (18/13 to 16/15 – the majority is still C/L rather than C/R). But because the split is slightly different, the happy (represented) 51% now consists of the 24% of the voters whose first preferences went to the Right party, together with the neo-Nazi voters and the minority of Centre voters who preferred Right to Left. It’s not at all clear to me that the fact that 27% of voters for smaller parties lean more to right than to left should be given enough weight to overturn the verdict expressed by first preferences. (According to this paper, in any case, the first scenario would apply most of the time: a full simulation based on survey data found that only 43 of 650 seats would have changed hands if the 2010 election had been held under AV.)

The problem with AV is the way that preferences are counted, and aren’t counted. Under STV, the surplus votes for any candidate who has met the quota are redistributed to second preference parties, in proportion to the overall split of second preferences. Under AV there are no surplus votes – elected is elected, and only one elected candidate is required – so second preferences are weighted differently according to what’s happened to the first preference vote. Some voters’ second preferences are decisive; others’ are never counted. And which party is in which category cannot be predicted. Another scenario:

35% vote Labour 1, Green 2
30% vote Tory 1, Lib Dem 2
14% vote Lib Dem 1, Tory 2
6% vote Lib Dem 1, Green 2
10% vote Green 1, Labour 2
5% vote BNP 1, Tory 2

BNP 1st prefs transfer to the Tories, Green 1st prefs transfer to Labour, some Lib Dem 1st prefs transfer to the Tories and others are wasted because the Green has already been eliminated.

Final score:
Labour 45% (35% 1st pref + 10% transfer from Green)
Tory 49% (30% 1st pref + 19% transfers from Lib Dem and BNP)
The Tory is therefore elected.

But look what happens if we add up the first and second preferences:

Labour: 35% (1) + 10% (2) = 45%
Tory: 30% (1) + 19% (2) = 49%
Lib Dem: 20% (1) + 30% (2) = 50%
Green: 10% (1) + 41% (2) = 51%
BNP: 5% (1) = 5%

On a simple addition of first and second preferences, the Green would actually come top. Even a weighted addition of preferences – what’s known as a Borda count – puts Labour ahead of the Tories, although the Lib Dems and Greens stay in third and fourth place. If those Labour second preferences shouldn’t be counted against their first preferences, why should the Lib Dems’? Big differences in the way votes are counted could rest on very small – and unforeseeable – differences in vote totals.

On the CT thread on AV, I have also argued that (a) AV favours, nay produces, bi-polar contests; (b) AV in Britain would chiefly benefit the third party, the Lib Dems; and (c) that I support PR, which would also benefit the Lib Dems. It looks as if at least one of these statements ought to be incorrect, but I think they’re all valid. The key is to focus on individual constituencies. Up and down the country, the Liberal Democrats consistently campaign on the position that “\$X can’t win here”, X being the Tories in Labour seats and Labour in Tory seats. Their interest in three-party politics is strictly tactical; their ideal is to turn every constituency into a “two-horse race” (a phrase that appears in Lib Dem literature almost as often as those bar charts), one of them being the Lib Dems. AV is well suited to producing this result. More generally, AV’s preference-aggregating procedure, and the single-member constituencies which make it necessary, will tend to favour parties whose programmes are bland, opportunistic or both. A minority party with a consistent and distinctive programme will have less chance of getting an MP elected under AV than even under SP; AV structurally favours a smaller number of contenders aggregating a wider range of preferences. I am perhaps biased by my long-established tendency to vote for small left-wing parties: I tend to look at it from the standpoint of a minor party trying to get into the system, and it seems clear to me that the barriers to entry are higher under AV. Indeed, some advocates of AV number among its advantages the fact that it puts smaller parties in a position to exert pressure on larger parties without getting representation in their own right (the two contenders in Australia’s lower house each appear to have a slew of preference-trading satellites); others argue that AV would be a good thing because it would makes the major parties seek votes in the centre ground, making it less likely that they will be dominated by their extreme wings. (These things can’t both be true, but it’s interesting that neither of them has any role for smaller parties with independent representation.)

I also believe that getting AV would damage the movement for electoral reform worse than failing to get it: if AV passes, AV’s supporters and beneficiaries will be happy anyway, the supporters of FPTP will regroup to fight for single-member constituencies, and there’ll be no public appetite for messing around with the electoral system again. Anyone pushing for PR after AV had passed would be told, at best, that the system needed time to bed in before we thought about changing it again; at worst, we’d simply be told that we’d asked for electoral reform and we’d got electoral reform. In addition, I believe that the Coalition would be destabilised far more effectively by failing to get AV (and lighting a fuse under Nick Clegg) than by getting AV (and annoying Tory backwoodsmen, whose main role in life is to be sat on by their leadership); I also think that getting AV would be highly conducive to the perpetuation of a Lib Dem/Tory coalition after the next election. However, I accept that all these points are arguable.

So on balance, no, my position really isn’t one of “pretend that you have reasons other than ‘I hate Nick Clegg’ for your otherwise unjustifiable political position”. My position is one of supporting PR and opposing AV, because I think even our current system is preferable. That’s why I’ll be voting No, and I encourage anyone who thinks likewise to do the same.