[EM] Majority Criterion

[Bart Ingles]

In my 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".

James's majority criterion looks more like the "Condorcet condition" or
smith set.  Who named it the majority criterion?  This sounds like
Woodall's terminology, or maybe the authors of the recent SciAm
article.  That said, I most of my post seems to work with either
definition (except fot the direct references to first-choice majority,
of course).


Eric Gore wrote:
> 
> Now, if you can present an example where the Condorcet winner, with a 
> reasonable interpretation of the ballots, did not win, you may have a 
> good discussion on your hands.

Nurmi gives this example (credited to Fishburn):

1  a>b>c>d>e
1  b>c>e>d>a
1  e>a>b>c>d
1  a>b>d>e>c
1  b>d>c>a>e

Condorcet winner:  a

    1st/2nd/3rd/4th/5th ranks
   ---------------------------
a   2/1/0/1/1
b   2/2/1/0/0

This is a case where the Borda (and possibly Approval) winner really
does sound more plausible than the CW based on ranks alone.

Bart