[EM] Approval equivalent to Condorcet-random :-)

[MIKE OSSIPOFF]

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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