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

Chris Benham chrisbenham at bigpond.com
Wed Jun 8 21:37:27 PDT 2005

```Kevin,
Regarding the Plurality criterion, I wrote:

> That of course should have been:
> The "pairwise version" says that  X must not win if  there are more
> voters that rank Y above all the other candidates than there are
> voters that rank X over *any*  candidate.

You responded:

>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).

>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?

>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?

Chris  Benham

>
>

```