The difference between counting votes and votes counting

The No campaign in the referendum is saying that one of the problems with AV is that if you vote for a minority party, your vote could be 'counted more than once' - the implication being that voters for mainstream parties are at some kind of disadvantage.

Here's how they put it on their website:

"Under AV, people are asked to rank candidates in order of preference. When the votes are counted, if the person coming first doesn't have 50% of the vote, the votes of the lowest ranked candidates are recycled until someone gets over the winning margin.

In this way it allows people who vote for the minor, fringe parties to have their votes counted several times, while those voting for mainstream parties can have their voted counted just once. AV is the opposite of one person, one vote. In fact, if you support a less popular party, you are more likely to have your vote counted multiple times."

The point was endorsed by David Cameron in an article he wrote for the London Standard last week:

"When they say: "AV will make every vote count", tell them it won't. It will actually make some people's votes - especially those who vote for extremist parties - get counted more than others.

They'll get two, three, four, perhaps even five bites of the cherry when many others only get one."

Hmm. It certainly sounds unfair.

But there's a sleight of hand about the maths here.

What will actually happen in an AV recount when no party gets more than half the votes is that people who voted for the smallest party will have their votes reallocated (if they chose to express a preference for more than one candidate.)

So their second preference votes will now go to one of the bigger parties.

But of course that doesn't give voters for smaller parties "another bite of the cherry" compared to the rest - because the votes of those who chose the bigger parties will also be added up again to make a new set of totals. Now whether they are physically "counted again" is not important: presumably the pile of votes for the leading parties stays the same and so doesn't need recounting.

But even if the first choice votes are not counted again, they will count, just as much as the new ones added to the pile.

If you're really looking for someone who's disadvantaged by the system, you could say it's the voters for the smaller parties because in the count that determines the result, they are only represented by their second or even third choices.

And incidentally, shouldn't we abandon the term 'first past the post' - since the main distinction between the two systems is that there isn't a post to pass under the current system, but there is (50 per cent) for the AV system? But the phrase has become so strongly associated with the current system that it is actually used to describe it in the Referendum question.