[Election-Methods] RE : Smith + mono-add-top?

Diego Santos diego.renato at gmail.com
Mon Dec 31 16:57:00 PST 2007

2007/12/31, Kevin Venzke <stepjak at yahoo.fr>:
> Hi Diego,
> --- Diego Santos <diego.renato at gmail.com> a écrit:
> > Definition: "Some candidate X is a potential winner if, for all Y that
> > beats
> > X, the margin of Y against X is lesser than the greatest margin of
> > another
> > candidate against Y". The winner is the Condorcet winner among potential
> > winners".
> >
> > This method meets mono-add-top and I think also Smith, because always
> > Minimax(margins) and Smith//Minimax(margins) winners are potential,
> > although
> > Markus said that no known method passes both criteria
> Am I correct that in the following scenario:
> 49 A
> 24 B
> 27 C>B
> Your method selects A and B as "potential winners" and elects B?

Yes, you are right.

Specifically: A's loss to B is weaker than B's loss to C. B's loss to C is
> weaker than C's loss to A. Only C's loss to A is stronger than A's loss to
> B. Then, the CW between A and B is B. B is not a potential winner of
> either
> Minmax(margins) or Smith//Minmax(margins).

I not said the "final" winner of my method is the same of Minimax(margins)
or Smith//Minimax(margins), but that s/he is in "potetial winner set"
(Santos Set?), in this case, A.

Mono-add-top is a very difficult criterion to satisfy if the method only
> regards pairwise contests. When you add an A>B>C>D ballot there is no
> record in the matrix that the top preference on this ballot was A. You
> need
> a way to ensure that if A wins, A remains the winner no matter what other
> information is on the new ballot. I can barely think how to do this, let
> alone how to do it when Smith compliance is also needed.
> Kevin Venzke

In your example, I don't see any way that B > A > C, B > C > A or B > A = C
ballots can cause other candidate different from B to be CW.
Diego Santos
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