In my last post (13 Dec 2011) I wrote:
A better method would (instead of "acquiescing majorities") use the set I just defined in my last post. *If there is a solid coalition of candidates S (as measured by the number of ballots on which those candidates are strictly voted above all others) that is bigger than the sum of all its rival solid coalitions (i.e. those that contain some candidate not in S), then those candidates not in the smallest such S are disqualified. Elect the most top-rated qualified candidate.*
That method I suggested wouldn't meet the FBC (it has now occurred to me), so I suspend my "..better method.." claim.
In my other EM post the same day, I wrote:
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.
Thinking about it a bit more I now doubt that the last sentence is true, but still I think it wouldn't be as bad for that purpose as the usual "Mutual Majority set".
Chris Benham ---- Election-Methods mailing list - see http://electorama.com/em for list info
