[EM] Choice among the MM-preferred set. MM//Woodall and MM//Benham

[Michael Ossipoff]

Here I'm talking only about methods for the Green scenario.

For a 1-dimensional political spectrum, I sometimes speak of these
sets of voters: The CW-preferrers, and the two "wings", consisting of
the voters to the two sides of the CW-preferrers. The CW-preferrers
plus either wing adds up to a majority. The wing containing the
CW-preferrers' 2nd choice, I call the "favored wing". The other wing,
I call the "non-MM wing".

I abbreviate mutual majority as "MM", and refer to the candidates that
an MM prefer to all the others as an MM-preferred set.

IRV meets the Mutual Majority Criterion (MMC), meaning that if a MM
vote sincerely, then the winner must come from their preferred set.

I suggest that choosing from the innermost MM-preferred set is the
important thing. IRV, the Condorcet hybrids, and Approval-IRV (IRV
with equal rankings, abbreviated AIRV), do that. Because  IRV and the
hybrids automatically avoid the chicken dilemma, and AIRV does so
among the MM, that means that there's no disincentive to sincere
ranking among those chicken-dilemma-protected voters, and the
rank-balloting ideal is available.

The hybrids additionally elect a voted CW, and some of them, such as
Woodall or Benham, choose from the voted Smith set.

Riker spoke of the fact that people can always find a way to elect the
CW. Maybe the non-MM voters will top-rank the CW. Or maybe the
CW-preferrers will help the non-MM voters replace IRV with Benham or
Woodall.

As mentioned, the CW-preferrers, plus either wing, add up to a
majority. If the method is IRV, and the CW-preferrers don't like their
CW favorite being eliminated, then they can side with the non-MM wing,
in a majority vote to replace IRV with a more Condorcet-efficient
method, such as a hybrid, or AIRV.

That would be fine, if they did--or if they didn't.  And they might not.

The CW is a member of the innermost MM-preferred set, but it isn't an
importantly desirable member. After all, what makes hir the CW? The
fact that the non-MM voters prefer hir to the rest of the MM-preferred
set. The CW could say:

"I should win, because, among the MM-preferred sett,  I'm closer to
the group of voters (the non-MM voters) whose policies are the last
choice of all of us" :-)

For example, suppose that one of the progressive partys' candidates is
the CW.  ...because the other progressives prefer hir to the
Republocrats, and the Republocrats prefer hir to the other progressive
candidates. But how important is it to let the Republocrats choose
which progressive should win? Why shouldn't that choice be made among
the mutual majority?  I mean, would it make any sense for the
Republicans to choose the Democrat nominee?

IRV excludes the non-MM voters from the choice among the MM-preferred set.

There's nothing wrong with that.

But, if the CW isn't necessarily an importantly desirable choice among
the MM-preferred set, maybe IRV's choice among them can sometimes be a
bit arbitrary. I'm not saying that's bad. But could it be improved on?

Why not use a Condorcet or Smith complying method to choose among the
innermost MM-preferred set?

For instance, use a Condorcet-IRV hybrid to choose among the innermost
MM-preferred set.

For instance, that could be MM//Benham or MM//Woodall.

Michael Ossipoff