[EM] Re: [Condorcet] Copeland's criteria

Kevin Venzke stepjak at yahoo.fr
Mon Sep 12 13:09:55 PDT 2005


--- Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> At 06:44 PM 9/11/2005, Kevin Venzke wrote:
> >I thought about this a bit. Consider this election:
> >
> >49 A
> >24 B>E
> >27 C>D>B>E
> >
> >C has 3 wins, and is the only Copeland winner.
> Let's look at this. C is not just the Copeland winner, C is the 
> Condorcet winner, 

C is not the Condorcet winner. There is no Condorcet winner. Schulze(wv),
Tideman(wv), River, Minmax(wv), and e.g. DMC all pick B. Condorcet//Approval
or Smith//Approval return a BE tie. (I am assuming implicit approval.)

>because in all the pairwise elections, A has 49 
> votes, and *all the other candidates* have 51 votes, because all the 
> other candidates' voters ranked A last by truncating.

If truncating a candidate means you're counted in favor of any candidate
above that candidate, then the only candidate who does not have >=51 of
the votes against him is B.

But I don't know what method you are using, which is counted in this way.
It sounds like you're using Mike Ossipoff's "power truncation" option.

> Eliminate A, 
> and C obviously has more votes than B.
> So exactly who would Mr. Venzke have win this election? Looks to me 
> like the electorate is (1) polarized very badly, and no election 
> method is going to produce really good results with such an 
> electorate, and (2) A majority of voters preferred "anybody but A."

I disagree with (1) and (2).
(1): Most serious methods satisfy the plurality criterion, according to
which C and D cannot be elected. The only way to keep their supporters from 
regretting the way they voted is to "see past" the C and D preferences and 
elect B.

(2): The 24 B>E voters didn't vote "anybody but A." They voted "anybody but
A, C, or D." The A voters voted "anybody but B, C, D, or E." So it's also true
that a majority of voters preferred "anybody but C" and "anybody but D."
The only candidates of whom it cannot be said that a majority didn't vote
"anybody but them" are B and E.

> If it is not A, then who should it be? Obviously, C.

No, B. Why do you prefer that C win?

Kevin Venzke


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