Russ said:
If that is true, then it seems to me that Approval may be roughly equivalent to Condorcet with random selection of the winner from the Smith set. Do you agree with that?
I comment:
First of all, the Smith set that Russ is presumably referring to is the smallest set of candidates such that each candidate in that set pairwise-beats each candidates outside that set. But the "Smith set" that Approval converges to is what is called the sincere Smith set, the set of candidates who are all publicly preferred to every candidate outside that set--where X is publicly preferred to Y if more voters prefer X to Y than vice-versa.
Russ�s confusion about that elementary difference shows that he doesn�t understand the material that he copied into his own website. That distinction was clearly made there, in the articles of mine that Russ had there. You can easily undestand why Russ�s website was an embarrassment, with the sloppiness and befuddlement exhibited in Russ�s Smith-set confusion, and his sloppified rewordings.
Very obviously, the fact that Approval, when voters vote in their best interest based on information from previous elections, converges to the Smith set does not imply that Approval is equivalent to Condorcet (by which Russ presumably means pairwis-count) with random selection from the Smith set. For instance, just to cite a few differences by criteria that Russ had copied to his own website, Approval meets FBC & WDSC, while pairwise-count//random meets neither.
Russ desesves credit for trying very hard to sound as if he�s doing some original investigations of voting systems. Sometimes he discovers things that have been known for a long time, things which have been previously explained to him. Sometimes he discovers things that are very obviously not true.
Russ�s pretetentious posing and continual ignorant pronouncements suggest that instead of calling someone else an intellectual midget, perhaps it would be better if Russ would try not be be one. Unless, of course, he can�t help it.
Russ continued:
So the bottom line is that, even in the simplest, most idealized case, Approval Voting can be unstable.
I comment:
I guess that, by "unstable", Russ means that when there�s no CW, Approval can fail to converge to a single outcome. Apparently Russ�s earlier astounding discovery is still being announced.
In such cases, the
ultimate winner would essentially be a random function of when the election happened to be held. A sort of random lottery. And many voters would regret their decision.
I comment:
As I�ve often said here, with a few reasonable approximations, Approval maximizes the number of voters who are pleasantly surprised by the outcome--the number of voters for whom the outcome is better than their perceived expectation before the election. The fact that, with Approval, voters can regret their decision, is one of the most widely-known things about Approval, but thanks to Russ for discovering it.
Any voting system for which you can't say the same (like plurality) is easily manipulated and leads to multiple equilibria, some of which may not elect an existing Condorcet winner. If you find
I assume you mean that plurality can be manipulated by throwing in spoilers (e.g., Nader or Perot).
I comment:
That wasn�t what Rob said. I�m not saying this for Russ�s benefit, but, as I was saying earlier, with Plurality, almost any 2 parties can keep winning at MW equilibrium. The voters are told that a certain 2 parties are "the 2 choices", and that no one else is viable. Voters, believing that, vote for whichever of "the 2 choices" they prefer to the other, even if they dislike both. Then, guess what, no one else gets any significant number of votes, "confirming" what the voters were told, that only the candidates of those 2 parties are viable, and that those 2 parties are indeed "the 2 choices".
Mike Ossipoff
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