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

[Kevin Venzke]

Hi Diego,

--- Diego Santos <diego.renato at gmail.com> a écrit :
> 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.

Ok, but this is only an argument that selecting from the Santos set isn't
incompatible with either Smith or Mono-add-top. It doesn't argue that all
three are compatible.

> 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.
> 
> 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.

In this example it may not be possible. However, do you see that when you
add a ballot such as A>B>C>D, you are adding many pairwise votes into the
pairwise matrix, that can affect whether various candidates make it into
the Santos set?

I will try to find an example for you.

Kevin Venzke


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