This isn’t an attempt to plug AV, nor to speculate on what would happen under it, but just to knock down the notion that it’s fiendishly complex.
(Update 26/4: I'm getting quite a bit of Google traffic to this post, which is nice, but I should say that this video featuring Dan Snow is a much better explanation of the difference between AV and FPTP. It's not neutral, but I'm sure you're smart enough to separate out the 'how it works' from the 'why it's good'.)
How to vote
Anne, Bob, Claire, Doug and Eve all want you to vote for them. So who do you like the most? Pick one (Bob, say) and put a ‘1’ next to their name: that’s your first choice. Then, pick which of the rest of them you’d like the most if Bob were out of the race (Eve, say) and put a ‘2’ next to their name. Then, pick which of the rest you’d like the most if Bob and Eve were out of the race – and so on.
You can go all the way and put ‘1’, ‘2’, ‘3’, ‘4’ and ‘5’ next to each name, or you can stop at the point where you don’t have a view on which of the rest is best. You can just put ‘1’ and leave at it that, if you don’t care for the rest of them at all. Then you’re done.
How to count the votes to see who wins
We put all the votes that mark Anne as the first choice in a pile. And then the ones for Bob and Claire and so on. If one of them has more than half the votes, they win.
If not, then the one placed last (say it’s Bob) gets knocked out and we move to round two. Round two, at root, asks: ‘Who do you like the most out of Anne, Claire, Doug and Eve?’
We look at all the votes from Bob’s pile to see who’s the next choice on each. If you marked Bob ‘1’ and left it at that, then you’ve said you have no view on the rest of them, so your vote gets put to the side. If you marked, say, Eve ‘2’, your vote goes on her pile. We move all the Bob votes that do have a ‘2’ marked to the piles for Anne, Claire, Doug or Eve. The votes these four had from round one still count this time, of course: those who cast them still have the same first choice in a race with no Bob.
And if one of them has more than half the votes, they win.
If not, we do the same thing: say Anne is last this time. She gets knocked out and for round three the votes in her pile get moved to Claire’s, Doug’s and Eve’s piles, as marked. And if one of these three has more than half the votes, they win. If not, we knock out the one placed last and go to round four, in the same way. When we get to the point where one of them has more than half the votes, they win. And that’s that.
(Number three in an extremely occasional series.)