Mike,
Sorry, there was a typo (20 B>A voters instead of 10) in my
demonstration of MMT2's failure of FBC in my last post. So I'll go
through it again.
MMT2 defines "mutual-majority candidate set" as:
A set of candidates who are each voted above bottom by each member of the
same majority of voters--where that set includes at least one
top-rated candidate
on the ballot of every member of that majority.
45: C
06: D>A
39: A>B
10: B>A
So in this example {A,B,D} isn't a "mutual-majority candidate set"
because D isn't "voted above bottom by each member of the same majority
of voters", right? And because there is no such set the MMT2 winner is
C, right?
Say those votes were all sincere. If the 6 D>A voters change to A>B (or
A=B or B>A) the winner changes to A, a candidate those voters prefer to C.
45: C
06: A>B (sincere is D>A)
39: A>B
10: B>A
Now {A,B} is a "mutual-majority candidate set" and MMT2 elects A.If the
method meets the FBC, those 6 voters must have some way of voting D not
below equal-top and get a result they like as much. What is it?
Mono-Add-Plump makes even less sense for MMT than for MDDTR.
The failure scenario is:
Your favorite wins by having the most top ratings among a
mutual-majority candidate
set. Now some new voters arrive and plump for hir. As plumpers, they
aren't counted
in the mutual majority. But they are counted in the total number of
voters, thereby
increasing the majority requirement. No longer is there a
mutual-majority candidate
set. No longer is your favorite the winner.
Is anyone claiming that that result is wrong?
Err..yes, I claim that at least one of the results must be "wrong". Even
if we ignore the mono-add-plump failure and look at the two elections
independently (of each other), it is highly likely that at least one of
them will be a failure of some other desirable criterion compliance.
And, by the way, with MMT, the Mono-Add-Plump "failure", and the LNHa
compliance
and LNHe "failure" don't create a random-fill incentive.
Logically, I don't see how it couldn't.
49: C
21: A (new voters, whose ballots switch the MMT2 winner from A to C)
27: A>B
24: B>A
(121 ballots, majority threshold = 61)
If the 21 A truncators randomly choose between middle-rating B or C then
A's chance of winning changes from zero to more than 50% (more than
11/21 have to middle-rate C for A to not win).
Chris Benham
Mike Ossipoff wrote (8 Dec 2011):
FBC:
In MMT2, if you top-rate a compromise, along with your favorite, then you'll
be counted in the majority supporting a mutual-majority candidate set that
s/he is in.
That's because MMT2 defines "mutual-majority candidate set" as:
A set of candidates who are each voted above bottom by each member of the
same majority of voters--where that set includes at least one top-rated
candidate
on the ballot of every member of that majority.
Mono-Add-Plump:
Mono-Add-Plump makes even less sense for MMT than for MDDTR.
The failure scenario is:
Your favorite wins by having the most top ratings among a
mutual-majority candidate
set. Now some new voters arrive and plump for hir. As plumpers, they
aren't counted
in the mutual majority. But they are counted in the total number of
voters, thereby
increasing the majority requirement. No longer is there a
mutual-majority candidate
set. No longer is your favorite the winner.
Is anyone claiming that that result is wrong?
Your favorite initially won only because of mutual majority support. The
plumpers
declined that mutual support, as is their right. Having declined mutual
support,
should it be surprising or unfair if they no longer have it?
And, by the way, with MMT, the Mono-Add-Plump "failure", and the LNHa
compliance
and LNHe "failure" don't create a random-fill incentive.
The LNHe "failure" consists only of perhaps being able to benefit from
mutual majority
support.
I should say again that, henceforth, when I say "MMT", without a
distinguishing number,
I'm referring to MMT2, the MMT version that I discussed above here.
I'm curious about MMMPO's compliance with FBC, LNHa and Mono-Add-Plump,
and its
compliance in Kevin's MMPO bad-example--a previously unattainable
combination of
properties. If MMMPO can be presented to the public in a simple,
naturally and obviously
motivated manner, then it would have the advantage that it wouldn't even
be necessary
to answer any Mono-Add-Plump criticism.
Mike Ossipoff
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