I suspect most people will have already cast their vote before reading this, but figured it was worth putting out there anyway, if only to show how I think.
I'm voting Yes to AV.
Democracy - which we like to believe that we have here in the UK - relies upon the will of the people. The people often don't really know what they want, and only get to express their will every 4 years, but what the hell - we'll accept this idea that the will of the people determines who governs us.
But we don't look at the will of the country overall - that sounds far too much like PR, and would mean that the BNP and UKIP would get seats. No - we look at it on a constituency basis. In each constituency, the people are asked who they want to rule, and they collectively decide.
Now, we're accepting here that the people have a collective will, and that it can be measured. Then what we want to do is measure it as accurately as possible, in order to represent them as accurately as possible.
Consider an election with only two people running. We'll call them A and B. Now, suppose that A gets more votes that B. We know that the people would rather have A running things than B. Under FPTP and AV, the result is the same as there are only two candidates.
Now, consider what happens if a third candidate is introduced (and we'll call them C, just to keep it simple). As this is a thought exercise, let's suppose also that C is not very well liked and will get less votes than either A or B, but will get some votes. If C has policies that are closer to As than Bs, then more of the A voters will change from A to C. In this way, it's possible for B to win under FPTP, thanks to the extra candidate - despite the fact that we know the voters prefer A to B. Under AV, C would be eliminated and the votes redistributed to the people's second choice, leaving us with the A vs B situation again.
Another way of thinking about it would be to consider a seat under our current system. In the last election, the constituency that I'm in (Croydon Central) returned a conservative. The Conservative had 19,657 votes, and the next best was Labour with 16,688. For the sake of brevity, I'm disregarding everyone else except those who voted for these two (not least because we have no way of knowing where the second choice votes would have gone). Imagine if noone changed their opinion of which party to vote for, and the election were run again, but the conservatives (for some reason - miscommunication perhaps?) ran two candidates. They'd get about 10,000 votes each, but the Labour candidate would still have 16,688, and Labour would win with twice the majority that the Conservatives currently have, despite the people still preferring the Conservatives overall. With AV, the 10,000 votes each would most likely have the other conservative candidate as the second choice, so as soon as whichever one gets least votes is removed, the other wins, and the collective will of the people is once more triumphant.
That's why I'm voting Yes.
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