[EM] MMT repaired. MTAOC simplified. Alternative definition of voting x over y.

[MIKE OSSIPOFF]

It's natural to look for a method based on the Mutual Majority Criterion (MMC). I posted one about a week ago. It wasn't written right.

In this post, I propose a different wording of MMT. It's only slightly different from my initial wording, modified to meet FBC. This new wording
is now what I mean by MMT:

MMT:

For any set of candidates who are all voted equal to or over everyone outside that set, by each member of the same majority of voters,
the winner must come from that set.

If there is such a set, the winner is the most top-rated member of that set. If there is not such a set then the winner is just the most
top-rated candidate in the election.

[end of MMT definition]

MMT is a very briefly-worded method that meets the criteria that I want, and seems to avoid the (not-valid) criticisms of
MMPO and MDDTR.

MTAOC simplification:

I feel that, for most people, the option to mark some of one's top-rated candidates as "coalition-sufficient" is too much of
a complication. Just one too many complication can be enough to put someone off, and cause hir to dismiss the method as
too complicated.

Additionally, if you are top-rating some compromise candidates, it's for a good reason. It's important to you to elect them instead
of someone who is unacceptable. Therefore, there is little if any reason to expect that someone wouldn't want all of hir
top-rated candidates to be available for coalition. So then, in this revised MTAOC, all of a voter's top-rated candidates are
"coalition-sufficient", and so there is no need for the distinction that I've called "coalition-sufficient".

So, in both places in the pseudocode where "if sufficient(b,x) = "yes" " appears, it should be replaced by:

"if top(b,x) = "yes".

Likewise, where "coalition-sufficient" appears in the comments, and in the initial description of the 3 program sections, it
should be replaced by "top-rated".

Alternative definition of voting x over y:

You're voting x over y is switching the names of x and y on your ballot could change the winner from x to y, but
could not change the winner from y to x.

[end of alternative definition of voting x over y]

This avoids the "probably" or the phrase "consistent with more configurations of other voters' ballots". It's simpler and
neater. Either definition would do.

Of course by this #2 definition, in IRV you never really know whether you're voting x over y or y over x.

No problem.

My criteria still apply to IRV. A criterion-failure-example-writer can always make up a monotonic example for hir
failure example.

Mike Ossipoff



 		 	   		  
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