The AV referendum and rationality

I know ‘Politics is the mind-killer’ and I’m prepared for downvotes here, but thought this would be worth pointing out.
In the UK at the moment we’re preparing for a referendum, on May 5, on whether to switch our voting system for General Elections from First Past The Post (FPTP) to the Alternative Vote (AV). I see this not as a question of politics (the fact that it crosses normal party lines tends to suggest I’m right) but as a question of information theory and cybernetics. Once it’s seen in that light, the answer becomes obvious.
Unfortunately, the only real coverage this has received in the media has been along group identity lines. Both sides claim the Nazis would benefit from a vote for the other side, and other than that the No campaign’s line has been pretty much “There’s a black man in this leaflet but not this other one, therefore the Yes campaign are racist!” or “Nick Clegg likes AV and you don’t like Nick Clegg, therefore you don’t like AV!”
Meanwhile the Yes campaign has been little better, its main campaign consisting of “MPs don’t like AV and you don’t like MPs, so vote Yes!” and “Stephen Fry likes AV, and you like Stephen Fry, so vote Yes!”

It would be quite understandable, with debate like that, if the average British LessWronger were to think that the matter was just a matter of normal mammalian status politics, on a par with the riots last year over whether to call something a ‘graduate tax’ or ‘tuition fees’. But in this case, there is a substantial difference, and an obvious rational choice.

Assuming, for the moment, that we’re agreed that representative democracy of some form is a reasonable system of government, one of the main advantages of that system is that it has to be somewhat responsive to the citizenry—voters put information into the system at election time, and that information determines the makeup of the government.

Assuming we think that a good thing, we want to maximise the amount of information each voter can put into the system. The more information put in, the more accurately the government can respond to the will of the people.

Now, with First Past The Post, the system is that in each constituency, the candidate with the largest number of votes gets elected, and all the candidate cares about is his/​her majority over the candidate with the next-largest number of votes. This means that in all but a very small number of cases, the only votes that ‘count’ in any important sense are those for the first and second-placed candidate. That means each voter gets to influence the government at a bitrate of one bit every five years. Not great.

With AV, on the other hand, voters rank candidates, and then the candidate with the lowest number of first preferences gets knocked out and their votes redistributed to the voters’ second preferences. This process is repeated until one candidate has over 50% of expressed preferences.

This *vastly* increases your ability to put information into the system. In my constituency, for example, last time there were eight candidates. Assuming I used all my preferences (and I would, to ensure the Christian Party were firmly at the bottom) that would give me 8! different possible rankings—roughly sixteen bits of information I could put into the system, rather than one.

Clearly, the rational thing to do in this case is to vote yes, to increase the effectiveness of the democratic system. Unless I’m missing something, in which case I’m sure the comments will say...