nice post. a couple comments.
On Jan 3, 2005, at 8:19 AM, MIKE OSSIPOFF wrote:
[snip]
Another person told me that, though Nader is more honest than Kerry, and offers better policies than Kerry, that person would vote only for kerry in Approval. Due to a mistaken impression of how Approval works? Maybe. Or maybe due to the completely misguided progressive anger at Nader for allegedly spoiling the corrupt Democrat. This may sound surprising, but many progressives confuse stratgegy with candidate merit, and will telll you that Nader is less desirable--and when asked why, can only give you the alleged strategic reasons for not voting Nader. But somehow they begin to perceive that as a matter of candidate merit rather than strategy. "But isn't Nader egotistical" (because takes votes from the corrupt media-anointed candidates)? "He's whacko" (Further questioning reveals that he's whacko because he runs though he isn't viable, not because of his policies).
On confusing "strategy" vs "candidate merit", I remember there being many polls from early 2004 saying that Kerry's most important and desirable quality was his "electability", a strategy issue.
[snip]
Smith mentioned Bayesian regret. I've heard of it, but not heard it defined. If I read his definition correctly, it's the SU (social utility) of the SU maximizer minus the SU of the winner. Is that right? One way to minimize it is to prevent high SU candidates from running. Another way is to maximize SU of the winner. Smith says that CR does best at that. But that would only be true under sincere voting, and under the special conditions where the CW doesn't maximize SU.
That's what I keep wanting to understand also. I like talking about maximizing social utility. What I learned in probability class about "Bayes rule" keeps confusing me when I "Bayesian regret". The probability of regret based on the probability of some candidate and {mumble mumble}?
A potential difference could be along the lines of, instead of maximizing social utility, minimize the square of voter disapproval, so that no one is terribly unhappy with the result. Following that goal would lead to different results.
[snip]
Smith wrote:
6.BAYESIAN REGRET (FOR STATISTICS NERDS):
Approval voting does quite badly (measured by Bayesian Regret)
compared to many other more expressive voting systems such
as Borda and Black, when there are 4 or more candidates and we have honest voters.
I reply:
He means nonstrategizing voters. Strategizing isn't dishonest. Borda isn't going to give us nonstrategic voting. It can't be counted on in any method other than maybe Condorcet.
But if voters are divided between strategy and sincere rating, maybe CR will do better than Approval by SU, if the Approval strategy is based on incorrect information. I don't expect CR to do better than Condorcet by SU under actual conditions.
My simulations found something similar, except under conditions of error (counting error, candidate lies, voter confusion). Under such conditions Approval degrades less rapidly than Borda. I didn't test Black. These where honest/non-strategic voters.
Brian Olson http://bolson.org/
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