Mike,
I was a bit confused about this for a while, because your definition of
MMT doesn't make clear that a majority candidate set may contain only
one candidate.
Given that this uses 3-slot ballots, isn't it just (interpreting any
above-Bottom rating as approval) Majority Approval//Top Ratings?
*If no candidate is majority-approved elect the most top-rated
candidate. Otherwise elect the most top-rated majority-approved candidate.*
But of course that fails Later-no-Harm, because it could be that if some
voters vote A truncate then no candidate will have majority approval and
A wins but if they vote AB then B will have majority approval and the
win will change to B.
Chris Benham
Mike Ossipoff wrote (5 Dec 2011):
Mutual-Majority-Top (MMT):
A set of candidates who are each rated above bottom by each member of the
same majority of the voters is a majority candidate set.
If there are one or more majority candidate sets, then the winner is the
most top-rated candidate who is in a majority candidate set.
If there are no majority candidate sets, then the winner is the most
top-rated candidate.
[end of MMT definition]
The previous definition didn't allow for the fact that there can be
overlapping
majorities of the voters.
MMT has the properties that I want (FBC, LNHa, ABE-non-failure, 3P), and
avoids the
not-really-valid criticisms of Mono-Add-Plump failure and electing
C in Kevin's MMPO bad-example.
That also seems to be true of Forest's FBC/ABE-passing method, which seems
to act quite similarly to MMT.
MTAOC too, with the added advantage of optional unconditional middle-rating
support for a lesser-evil.
We're always seeking better methods, and I'd like to find out if there's
a simple wording
that would allow voters in MMT to have the option of giving
unconditional middle-rating
support. But if I find that, I won't make it a replacement for the
current MMT. I'll give
it a different name.
Likewise, it would be interesting if MTAOC, or something like it, could
be written with
a complete description in a short paragraph (though there's nothing
wrong with
its full definition being a computer program, while having a brief
verbal description).
Those two goals probably amount to about the same thing.
Mike Ossipoff
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