Date: Mon, 14 Mar 2005 22:03:25 -0800 From: Russ Paielli <[EMAIL PROTECTED]> Subject: Re: [EM] About random election methods
Russ wrote to Andrew:
Andrew,
I think voters will reject any method that isn't deterministic. Barring actual numerical ties, why should the selection of the winner depend in any way on some random event? Yes, randomness may help thwart strategy, but so what? Of course strategy is useless if we toss dice to determine the winner. That's just my opinion, of course.
Regards, Russ
Forest replies:
I think that you are right that the general public will reject randomness not needed for tie breaking.
But what constitutes a tie?
Suppose that (pairwise) candidate A beats B who beats C who beats A, and that Condorcet gives the win to A because the weakest defeat (by some measure) is the C beats A defeat.
Then C can say, "Sure my victory over A wasn't as strong as A's victory over B, but my victory was over a strong candidate (the putative winner) whereas A's victory was only over a loser."
Who is the real winner in rock, paper, scissors?
Right or wrong, many people consider majority beat cycles as "Condorcet ties."
Personally, I believe that approval information can resolve these "ties" most of the time.
But there are cases where there is still enough ambiguity to consider the result a "tie" even when there is a CW.
Consider (sincere utilities in parenthesis):
55 A(100), B(99), C(0) 45 B(100), C(50), A(0)
Candidate A wins in any Condorcet election. But in a zero information approval election B wins, and the A supporters will not have much to complain about.
Examples like these lead me to believe that when the Approval Winner is not the Condorcet Winner, both should have a claim to some of the probability.
The approval winner can say, "My win was based on stronger, higher priority preferences."
The Condorcet winner can say, "But my win was based on more complete information."
The AW replies, "But that information was probably contaminated by insincere order reversals."
And so there is an impasse, a sort of tie.
Random ballot to pick between the CW and the AW is a far cry from the random candidate image conjured up by "tossing dice to determine the winner."
You said, "Randomness may help thwart strategy, but so what?"
If strategy is not thwarted, then the result of the deterministic method is garbage, no matter how nice it might work in a zero info environment.
Ironically, in many cases a good random method has a much greater probability of electing the sincere CW than any deterministic Condorcet efficient method.
Forest
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