Prologue:
Here's the scenario, which I call "Kevin's MMPO bad-example:
9999: A
1: A=C
1: B=C
9999: B
Some object to C winning.
But note that half the voters say that C is just as good as B; and the other
half say that
C is just as good as B.
C is hardly a Hitler. A and B are big favorites, and so, given what I said in
the previous paragraph,
the election of C couldn't be much of a tragedy, mistake or error.
Sure, nearly everyone thinks that _someone_ is better than C. But, then, that's
also true of A and B.
In fact, they have _more_ people saying that some particular candidate is
worse. (Yes I know, that's
MMPO's standard, so you might accuse me of using MMPO's standard to defend
MMPO. But note that you
brought it up, if you objected to how many people think someone is worse than
C).
The objection to C's election amounts to a sleight-of-hand that fallaciously
attempts to portray the set
[A,B] as a single aggreived "person".
What makes the above MMPO result "look bad" is it's un-plurality-like nature.
In terms of favoriteness,
C looks terrible. But I remind you that, in general, pairwise-count methods are
not about favoriteness,
nor are they intended or expected to be. ....even though some want to compare
them by a criterion
that is based on favoriteness.
The trial:
Mr. A-Spokesman:
Your Honor, Mr. B-Spokesman and I, representing an aggreived group, consisting
of the A voters and the B voters,
come here in unity to protest the election of C. We claim that it's clear that
either A or B should win, and we strongly
believe that A or B should win, and we all strongly want A or B to win."
Judge:
Let's clarify something: Do you mean that, if A doesn't win, you want B to win
instead of C? Or are you really just saying
that you want A to win, and the B voters want B to win?
Mr. A-Spokesman:
It's very important to all of us that, even if our favorite doesn't win, the
other member of [A,B] win. Therefore it is
an outrage against us all if that doesn't happen.
Mr. C-Spokesman:
Your Honor, I enter into evidence exhibit A, the summary of the A-voters'
ballots; and exhibit B, the summary of the
B-voters' ballots.
Judge:
Mr. A-Spokesman, having looked at this evidence, I must question your claim
that it's very important to you that,
if A doesn't win, then at least B should win. The evidence clearly shows that
your A group was entirely indifferent
between B and C. (except for one person who preferred C). Likewise, the B
voters were entirely indifferent between
A and C. How do you answer that?
(A-Spokesman doesn't answer)
Judge continues:
Mr. A-Spokesman, I recommend that, in subsequent elections, you demonstrate, in
the election, some of that
solidarity, mutual support, unity and common purpose that you claim, in this
courtroom, to feel.
I dismiss the claims of the A voters and B voters. Case dismissed.
(Bangs gavel)
Mike Ossipoff
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