An anti-AV canard

Following on from my post in May, ripping up a couple of pro-AV canards (link), I think it's only fair to rip up at least one anti-AV canard, repeated by Robert McIlveen at the Spectator Coffee House blog (src). He writes:

AV’s solution – recycling votes until someone does get 50 percent acquiescence – treats third preferences (I dislike him slightly less than her) the same as first preferences (I really want this person to be my MP).

No, it doesn't. People's ballots are counted the same number of times (assuming they don't get exhausted) regardless. Watch.

Say we have an election which ends up going to six rounds of counting. If someone puts the winner down as a first preference, then their first preference ballot counts in the winner's favour six times, once at each stage. If someone else selects the loser at each stage, then their ballot counts at each stage for the loser. We might put it like this: the first person has one vote counted six times; the second person has six votes counted once. In total, both have had their ballot counted six times.

And in order for your first preference to be counted alongside a third preference, you must have been through at least three rounds of counting: in other words, your first preference vote has counted at least three times, and the other person's third preference has counted fewer times, perhaps only once. It is equal and sensible, whichever way you cut it.