[EM] Chris: MMT criterion compliances.

[C.Benham]

Mike,

> ...now it's a matter of whether MMT2 meets FBC and Mono-Add-Plump.


> MMT2 definition:
>
> A "mutual majority" candidate set is a set of candidates who are each
> rated above bottom by each member of the same majority of the voters--
> where that set includes at least one top-rated candidate on the ballot
> of every voter in that majority.
>
> If there are one or more mutual-majority candidate sets, then the winner
> is the most top-rated candidate who is in a mutual-majority candidate set.
>
> If there are no mutual-majority candidate sets, then the winner is the 
> most
> top-rated candidate.
>
> [end of MMT2 definition]


As far as I can see the examples I gave apply equally well to "MMT2".  
I've pasted them in at the bottom.

Chris Benham


Mike Ossipoff wrote (7 Dec 2011):

Chris:

You wrote:

I think this fails the FBC.
 
[endquote]

But you're specifically referring to what I now call "MMT1", which
isn't my main MMT proposal now. Sorry that I've kept changing my
MMT definitions--I know that's a nuisance--but now it's a matter of
whether MMT2 meets FBC and Mono-Add-Plump.

Of course, if MMT2 turned out to fail FBC, then of course I
wouldn't propose it.

And if it turned out to fail Mono-Add-Plump, that would eliminate
its main advantage over MDDTR.

Mike Ossipoff


Mike,

I think this fails the FBC. Say sincere is:

45: C
06: D>A
39: A>B
20: B>A

There is no "mutual majority set" (by your latest definition) so C
wins.  That is also true if the 6 D>A voters change to D=A or D=A=B or
D=A>B or anything else except A>B or A=B or B>A in which case the winner
changes to A.

It also fails Mono-add-Plump.

49: C
27: A>B
24: B>A

Your latest version of MMT elects A, but if we add between 2  and 21
ballots that plump for A then there is no longer a "majority candidate
set"  and so the MMT winner changes from A to C.

49: C
21: A  (new voters, whose ballots switch the MMT winner from A to C)
27: A>B
24: B>A

(121 ballots, majority threshold = 61)

I think all reasonable methods will elect A in both cases. Electing C in
the second case will have voters wondering why they bothered switching
from FPP, and is a very bad case of failing Condorcet
and  Mutual Dominant Third (DMT). A is voted above all other candidates
on nearly 40% of the ballots, and pairwise  A>C 72-49 and A>B 48-24.

Chris Benham