But one objection that I'd never really held with was the idea that AV is complicated. All the voter has to do, so they say, is write down the numbers 1 to 9 (or whatever) in order of preference. It's simple - in much the same way that solving a Sudoku is simple (or indeed that playing the flute is simple, according to Monty Python).
But the more I think about it, the more complicated it gets. Problems can occur in many areas, but the one I'd like to focus on is the phenomenon of the second choice marginal.
Let's consider an imaginary constituency with just Tory, Liberal and Labour candidates (or one in which other, less popular candidates have already been knocked out in earlier rounds of AV). I use real party names rather than abstractions such as A, B and C not to express any party bias, but because it's easier to follow and easier to decide whether such a scenario could really happen. Suppose the first choice votes are roughly:
'Roughly?' I hear you bellow. 'Surely we must be accurate here.' Well, yes and no. If this were a First Past the Post election, then those kind of round numbers are quite clear enough to show that Labour wins. Of course, even under FPTP we have marginals if the two leading candidates are close, and then accuracy matters, but under AV we also have the possibility of this kind of second choice marginal (or, indeed, third, fourth of fifth choice) where precise counting even for second place really matters.
More marginals? Isn't that one of the key aims of AV; to force parties to genuinely campaign in more seats, rather than just focussing on the few marginals that matter so much under FPTP? True enough, but you might find that what they're campaigning for isn't quite what you'd expected.
Under AV the winning candidate needs to get more than half the votes cast, so in this case the winning post is 17,500. (Odd, isn't it, that it's AV that actually has the fixed finishing post, and so-called First Past the Post that doesn't?) No one here has 17,500, so we have to consider those second choice votes.
We can ignore the Labour second choices, because they're never going to be counted, though they'll probably be mostly for the Liberals. The Tory second choices are likely to be mostly Liberal too. Admittedly there may be a lot of support from Tories for, say, UKIP, but we're assuming they've been eliminated by now. At this stage, a Tory's second choice can only be Labour or Liberal (or nothing, but that's another story).
As for the Liberal voters, let's assume they spilt 50-50 amongst Tory and Labour. In reality, there might well be more of a bias towards Labour, but it doesn't much matter. With Labour only needing around 2,500 to win, the Liberal spilt could be up to 75% pro Tory, and the mathematics would still be much the same.
So, we had Liberals and Tories on about 10,000 each. Time to be specific. Let's suppose that the Liberal got 10,005 and the Tory 10,000. The Tory drops out and his second choice votes get allocated. We've assumed they're mostly Liberal and very few Labour, and so it seems reasonable that the Liberals will pick up the extra 7,500 they need and will win. This is exactly the sort of result that AV is supposed to achieve. The Liberals come second in the first round, but win on the second round.
But just suppose it goes the other way. Suppose it's the Tory who gets 10,005 and the Liberal 10,000. Then the Liberal drops out and his second choice votes get reallocated. We've assumed it's a 50-50 spilt, so Labour gets 5,000 more votes and wins. Just read that again:
The Tory is more popular than the Liberal and therefore Labour wins.
And on top of that, the difference is the matter of just a few votes. Under FPTP a few votes will matter in a marginal, but at least there a vote for Labour will help Labour, a vote for the Liberals will help the Liberals. Here it's the swing between Tories and Liberals that determines a result between the Liberals and Labour.
So what's a Tory voter to do? In this particular constituency, they know that their favoured candidate has no chance of winning, so the next best option is for the Liberal to win. But if they vote Tory first and Liberal second, that actually increases the chance of Labour winning, by pushing out the Liberal on the first round and thereby getting his second choices counted. It's a better bet for the Tory to vote Liberal first and Tory second, so that the Tory drops out and his second choice votes go to the Liberal. It's classic tactical voting; if you're a Tory afraid of Labour, vote Liberal.
In fact, it's better than tactical voting under FPTP. Not only does the Tory vote for the Liberal mean one more vote for the Liberals; if it makes the Tory candidate drop to third, it means thousands more votes for the Liberal as all those second choices get counted.
And it's not just Tories who can vote tactically. Remember the set up: Liberal second place is good for the Liberals; a Tory second place is good for Labour. So why don't a few hundred Labour supporters tactically vote Tory? It costs a few hundred votes, but if it pushes the Liberals into third and reaps a few thousand Labour votes it's a worthwhile reward.
In both styles of tactical voting, there is a powerful psephological lever in operation. Switching a small number of votes away from your first choice party can actually liberate a huge number in favour of the result you want. It may take a fair deal of voter management from the political parties, but guess what? - they're good at that.
And what about recounts? Let's go back to that scenario where the Tory gets 10,005 and the Liberal 10,000. That means Labour wins. The Liberal isn't happy and there's only five votes in it, so it's worth asking for a recount. But the thing is, the Tory (with Nick Berry's Every Loser Wins ringing in his ears) isn't happy with it either - because Labour wins. So both the winning and the losing candidate (in the second and third place play-off) will be asking for a recount. At least under FPTP it tends to be the loser who wants a recount and the winner who doesn't. It puts the returning officer in a difficult position of perhaps having to act against the requests of both candidates.
And will those candidates have enough information to decide whether a recount is worthwhile. With different second choice voting patterns, it's quite possible that the Labour candidate would win regardless of who comes second. Would the Tory and Liberal candidates know that before deciding whether it's worth bickering over the few votes that determine second and third place?
Of course, we've been looking at a specific example which won't occur everywhere. But with 650 constituencies, this sort of thing could crop up more than once, along with other permutations that aren't even dreamt of here.
Putting the numbers 1 to 9 nine in order has never been more of a challenge.