I neglected to mention:
With Approval, if a party is at the voter-median position, it's the only party that can win at Myerson-Weber equilibrium.
That's why I say that Approval will quickly home in on the vote-median, and then stay there.
Why is that good? For one thing, the voter median candidate is the CW and the social utility maximizer. And it's been shown that, in general, the CW tends to be the social utulity maximizer. Greatest good for greatest number. So that's an argument for Condorcet too.
Why does social utility (SU) matter?:
Say we're talking about elections at some time in the future. We don't know what the candidate lineup will be, what kind of an examples the elections will be, or where you'll be in those examples.
Your espectation in those future elections is no better than the SU that can be expected of the winners. No better than the SU quality of the voting system that will be used in those future elections. So propose methods that do well by SU.
I consider the majority defensive strategy criteria, and the goal of getting rid of the lesser-of-2-evils problem, important too. But the methods that do well by those criteria are the ones that well at SU because of going to the voter-median, the CW.
Mike Ossipoff
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