First of all, no one has found an example in which my most recent MMPO
tiebreaker
fails FBC.
"Solve MMPO's ties by MMPO".
I'll call that tiebreaker 1.
Tiebreaker 2:
Whenever there's a tie, the winner is the candidate whose next largest pairwise
opposition is the
least. ("next largest" after the pairwise opposition with which s/he is tied
with other
candidates)
Tiebreaker 3:
If there is a tie, the winner is the candidate with the most top-ratings.
MMPO with tiebreaker 1 is MMPO1
MMPO with tiebreaker 2 is MMPO2
MMPO with tiebreaker 3 is MMPO3.
MMPO2 and MMPO3 meet FBC.
No one has found an example in which MMPO1 fails FBC.
MDDTR meets FBC, CD, and Later-No-Harm (LNHa); and fails Mono-Add-Plump.
MMPO2 and MMPO3 meet FBC, CD & LNHa, and Mono-Add-Plump; and "fails" in Kevin's
MMPO bad-example:
9999: A
1: A=C
1: B=C
9999: B
In this example, MMPO elects C.
MCA, MTA, MDDTR, MDDA, ABucklin and MDD,ABucklin return a tie between A & B.
How bad is this result of MMPO's?
Notice that nearly all of the A voters are indifferent between B and C.
And the one A voter who isn't indifferent prefers C to B.
Likewise nearly all of the B voters are indifferent between A and C.
And the one B voter who isn't indiffefrent prefers C to A.
So how bad can c be? How bad can MMPO's result be?
So, the choice between MMPO and MDDTR is a choice between failing
Mono-Add-Plump, vs
"failing" in kevin's MMPO bad-example. Only polling will tell which "failure" is
more likely to appear bad to potential petition-signers and enaction-voters.
When we regard the pairwise comparison between C and A, and the pairwise
comparison
between C and B, in isolation, it's easy to forget that we aren't actually
holding those
two pairwise elections. We're used to looking at pairwise contests, because
we're used to
pairwise-count methods. But no one is saying that the one voter who votes C
over A is
more important than the greater number who vote A over c. I suggest that the
strong pairwise defeats against C look more important than they are, because
we're
used to looking at pairwise count methods, with the result that we actually
start
believing that there was a a 2-candidate election between A and C, and one
between B and C.
As I said, MDDTR and MMPO might be "controversial", because of failure of
Mono-Add-Plump,
or "failure" in Kevin's MMPO bad-example. So, I don't consider them to be the
easiest or
best public proposals. It would be necessary to talk to some people before
being sure
that they'd be winnable proposals.
A 3-slot version of SFC should be written, to tell of the SFC-like guarantee
offered by
MDDTR. (Strictly speaking, SFC can only be passed by full ranking methods.)
By the way, when people object to "random-fill incentive" for MDDTR, maybe
they're
forgetting that MDDTR is a 3-slot method.
And, if MMPO were proposed as a 3-slot method, that would avoid the
"random-fill incentive"
criticism of it too.
Mike Ossipoff
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