[EM] suggested improvement on Mutual Majority criterion/set

[C.Benham]

Back in December 2008  I criticised  Marcus Schulze's  "beatpath  
Generalized Majority Criterion"  (which says in effect that if any 
candidate X has a majority-strength beatpath to candidate Y then Y can't 
win unless Y has a majority-strength beatpath back to X)  in part 
because the concept is vulnerable to Mon-add-Plump. That is, extra 
ballots that plump for candidate A can cause A to fall out of the set of 
candidates that  the criterion specifies are qualified to win.

Then it was pointed out to me that to some extent the Mutual Majority 
(aka Majority for Solid Coalitions) criterion has the same problem. A 
candidate X can be in the set of candidates that are qualified to win 
and then some extra ballots that plump for X are added and then the set 
of candidates the criterion specifies are qualified to win expands to 
include one or more new candidates. X doesn't actually fall out of the 
set (as with beatpath GMC), but nonetheless according to the criterion 
X's case has been weakened by the new ballots that plump for X.

I propose a replacement for Mutual Majority which addresses this problem 
and also unites it with Majority Favourite.

Preliminary definitions:

A "solid coalition" of candidates of size N is a set S of (one or more) 
candidates that on N number of ballots have all been voted strictly 
above all outside-S candidates.

Any given solid coalition A's  "rival solid coalitions" are only those 
that contain a candidate not in A.

Statement of criterion:

*If one exists, the winner must come from the smallest  solid coalition 
of candidates that is bigger than the sum of all its rivals.*

[end criterion definition]

This wording could perhaps be polished, and I haven't yet thought of a 
name for this criterion and resulting set. (Any suggestions?)

It might be possible to use the set as part of  an ok voting method.


Chris Benham