Mark – my words
No voter in AV gets more than one vote, nor is any voter’s vote more infuential than any other. This has been established in legal precedent in the USA.
There is no question of multiple bites of the cherry. All voters’ votes are counted in each round of the AV runoff (unless all candidates they indicated a preference for have been eliminated). If your single first-preference vote turns out to have been for the winning candidate, your vote has nevertheless been counted exactly the same number of times as that of a voter whose preferred candidates have been successively eliminated. And who knows, his final preference may have been the same as your first, and been the one vote that pushed that candidate over the winning line!
Consider a BNP supporter whose second preference is UKIP, and third preference is Conservative. When the BNP candidate is eliminated, this voter becomes to all intents and purposes a UKIP voter, indistinguishable from someone who voted UKIP as their first preference. When the UKIP candidate is eliminated, our voter is supporting the Conservative party. His vote is no less valid because his desire for minority representation has been thwarted.
Some people get very exercised about lower-preference votes being somehow less worthy than first-preference ones. But in this country we’ve never been in the least bit concerned to examine how enthusiastically a voter’s single vote is awarded to a candidate under FPTP. I would venture to suggest that any given individual’s level of committment to his FPTP vote could be any of: highly positive; cynical, opportunist & tactical; a chore, undertaken out of a sense of duty; a coerced act; an act of despair; and much else besides.
Allowing voters to express any or all of these sentiments on a single ballot paper, from which ultimately only a single vote will count in the eventual result, seems to me to be self-evidently a superior and more empowering form of democracy.