At 12:04 PM 9/23/2008, you wrote:
Do you or does anyone know if this muti-seat IRV method that splits votes of voters to their second choice candidates after some winning candidates receive the threshold amount of votes, exhibits non-monotonicity or not like the normal IRV method does? If so, is there an example posted somewhere?
Imagine a two-winner election using STV. The vote-splitting method doesn't matter because a scenario can be constructed where there is no vote splitting. If one candidate wins with an exact quota of first-place votes, those ballots are set aside and are not counted any more, because all those voters got their representative. Now the remaining ballots are used to elect a representative for the *rest* of the voters.
And this is simply an IRV election. So you can use any IRV non-monotonicity example. If I'm correct, votes for the already-chosen candidate, found on these remaining ballots once elimination starts, will be disregarded and the next-lower choice awarded the votes, pending victory or elimination.
STV is, as I've said many times, quite a good method, and it gets better the more candidates elected, *if* the electorate is well-informed and can coherently rank many candidates. Asset Voting finesses this problem, by essentially allowing voters to use their favorite candidate as a trusted proxy.
Asset has other implications, though. It makes it possible for there to be a standing "electoral college," consisting of public voters (all those who received votes in the secret ballot portion of the election), and this could even become a form of "almost-direct" democracy. But it starts as a simple fix for the ballot exhaustion problem that plagues IRV and to a lesser extent STV.
The complexities of vote transfers are, in my opinion, justified by better representation. Very fair methods exist. I dislike random reassignment, but the mathematical methods, simplified to 1/1000 vote, seem fine to me. What does Cambridge, Massachusetts, do? (They've been using STV for a very long time.)
(In Asset Voting, I'd use *exact* quotas, probably the Hare quota, -- votes/seats -- and exact fractional transfers, though they would presumably be rounded to some reasonable accuracy, sufficient to make a change of result from roundoff error very unlikely.)
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