[EM] Three variations of GMAT and MMT

[MIKE OSSIPOFF]

MTGMAT:

This is just GMAT with an initial search for a majority-top-ratings winner.

Majority-Top-Greatest-Mutual-Approval-Top (MTGMAT):

If one or more candidates have top ratings from a majority of the voters,
then the winner is the one of those with the most top-ratings.

Otherwise do GMAT.

[end of MTGMAT definition]

I don't know if this is better than GMAT. It might be.

MMMT:

This is just MMT with an initial search for a majority-top winner.

That initial majority-top search is superfluous, because, if there are
one or more candidates with top ratings from a majority, then the MMT
winner will be one of those anyway.

So I don't suggest MMMT.

GMMT:

This differs from MMT by looking for the mutual majority set whose members are
rated above bottom by the most voters, and then electing the most top-rated winner
in that set.

It might be better than MMT. It loses most or all of MMT's brief-definition
advantage over GMAT.

Greatest Mutual Majority top (GMMT):

A mutual majority set is a set of candidates who are all rated above bottom by the
same majority of the voters--where, for each ballot in that majority of voters,
the set includes at least one top-rated candidate on that ballot.

The winning mutual majority set is the one with the most voters rating all of its
members above bottom.

The winner is the most top-rated candidate in the winning mutual majority set.

[end of GMMT definition]

Mike Ossipoff