Kevin Venzke stepjak at yahoo.fr
Wed Sep 21 13:38:15 PDT 2005


--- Jobst Heitzig <heitzig-j at web.de> a écrit :
> You wrote:
> > I don't believe DMC satisfies SFC:
> > 
> > 49 A
> > 24 B>A
> > 27 C>B
> > 
> > It's possible to place the DMC approval cutoffs so that B has the lowest
> > approval, and A wins.
> > 
> > I believe this would be a violation of SFC, since more than half of the
> > voters prefer B to A, but no majority prefers anyone to B. That is, B is
> > clearly preferred to A, and no one is clearly preferred to B.
> Why do you say no-one was clearly preferred to B? C beats B, so B is not the CW...
> I thought SFC only talks about situations with a CW??

Sorry, I could have been clearer. I say B is "clearly preferred" to A
because, no matter how indifference between A and B is resolved (if there
were any), A can't pairwise beat B. But it is possible to complete
indifferent rankings so that B beats everyone.

SFC talks about situations with a *sincere* CW. It says if there is a
sincere CW, and more than half of the voters rank the CW over candidate
B, and no one uses order reversal, then the winner can't be B.

> > I'd say the purpose of SFC is to protect the B>A voters from giving the
> > election to A. (That's assuming B wins and not C.)
> In DMC, those who prefer B to A can easily do so, they only need to place their approval cutoff
> between B and A:
> 24 B>>A
> 27 C>B
> In this way, B doubly defeats A, so A cannot win.

Unfortunately, I don't believe SFC is worded as "the majority must have a
way of voting..." The point is that this majority needn't do anything special.

Kevin Venzke


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