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

Kevin Venzke stepjak at yahoo.fr
Mon Dec 31 15:56:05 PST 2007

```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?

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).

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

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