# [EM] Plurality criterion (Oops! X/Y mix-up)

Kevin Venzke stepjak at yahoo.fr
Thu Jun 9 13:02:54 PDT 2005

```Chris,

--- Chris Benham <chrisbenham at bigpond.com> a écrit :
> >I should say first of all that I didn't realize you *were* describing a
> >pairwise version, which is why I responded as though you were paraphrasing
> >Woodall. I'm really not sure what "rank Y above all the other candidates"
> >means if not first preferences, though.
> >
> It wasn't meant to mean anything else, but thinking about it, I suppose
> that can't be read just from the pairwise matrix. Ok, for a "pairwise
> approximation" of the Plurality criterion
> try "X must not win if  Y's lowest score in any pairwise comparison is
> greater than X's greatest score in any pairwise comparison" ("score"
> here referring to gross number of votes).

> You instead suggested this:
>
> >if the greatest number of votes against X in some contest exceeds the
> >greatest number for X in some contest, then X mustn't win.
> >
>
> > Shouldn't  the second of  your three "X"s  be  a  Y?  Otherwise, in
> > the  49A, 24B, 27C>B  example both A and C would be barred by it.
>
> You replied:
>
> >The "pairwise" version that I know of doesn't use a Y, and both A and C
> >are actually barred by it.
> >
> That seems to be something much stronger, an interesting combination of
> Plurality and MD. Have you thought of using it as the front part of a
> method?

Yes, I used it in the method I suggested in the message "an attempt at a
method satisfying FBC and SDSC."

I also tried using it repeatedly until one candidate remains. But I believe
this fails clone independence and monotonicity.

> >This criterion is probably known by a different name...
> >
> I doubt that its really "known" at all, because you only recently
> invented it. Do you want to give it a name?

Not really. I call it "pairwise Plurality," a stronger form of "pairwise
Minimal Defense" (i.e., a candidate with a majority loss and no majority win
can't be elected).

Kevin Venzke

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