[EM] Majority Criterion, actually Mutual Majority Criterion (MMC)

[MIKE OSSIPOFF]

Bart wrote:

In an earlier post, I didn't pay close enough attention to the
definition for this criterion:

James Green-Armytage wrote:
>
>majority criterion: If a majority of the voters prefers all of the members
>of a given set of candidates over all candidates outside that set, and
>they vote sincerely, then the winning candidate should come from that set.


This isn't what I generally think of as "majority criterion."  Most
places I have encountered the term, it refers to a requirement that the
candidate with a majority of first preferences must win.  Nurmi calls it
the "majority winner criterion".

I reply:

Yes, the criterion in the paragraph before last is the Mutual Majority 
Criterion (MMC). I wrote it, based on a votes-only version of it written by 
Bruce Anderson. With my version, Plurality & Approval fail the criterion for 
the reason why we'd expect them to. When it's written votes-only, Plurality 
passes, unless we require or pretend that rank-balloting is used.

You continued:

James's majority criterion looks more like the "Condorcet condition" or
smith set.

I reply:

Smith Criterion compliance implies MMC compliance. Of course the Smith 
Criterion is a generalization of the Condorcet Criterion.

You continued:

Who named it the majority criterion?

I replyi:

I wrote it and named it the Mutual Majority Critrerioin. Bruce had called it 
the Generalized Majority Criterion, but I didn't consider it general enough 
to merit that name, because MMC is about a fortuitous special case, a mutual 
majority. (Fortuitous for the more fortunate voters, that is).

You continued:

This sounds like
Woodall's terminology

I reply:

I'm going to pretend that I didn't hear that  :-)

Mike Ossipoff

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