[EM]Re: AWP versus AM (and DMC)

[Chris Benham]

James,
You wrote (beginning with a quote from me):

>The AM criterion, on the other hand, is the perfectly
>natural putting together of  two obviously
fundamental
>ideas: "that pairwise beaten candidates should tend
to
>lose" and "that more approved candidates should tend
>to win"!

"You mean the "AP criterion", right? "Don't elect a
candidate that is pairwise beaten by a more approved
candidate." If you want to call it the AM criterion,
that's fine, just let me know. But I'm pretty sure
that it was the AP criterion last time."

CB: Oops! Yes I mean the "Approval Plurality" (AP)
criterion.

"If you can't keep enough of an open mind to avoid
calling my logic "mad", we should probably stop trying
to converse on this subject.
Maybe sometime you could write a note to me off-list
and let me know whence came this impulse to needlessly
insult me... as I remember we used to have a rather
pleasant and cooperative correspondence."

CB: I conceded that the Approval-Weighted Pairwise
(AWP) method "has its own mad logic". Someone with a
thicker skin might even interpret that as a grudging
compliment. Nothing I wrote was meant as an insult to
you personally.

"What is the logic behind the AP criterion? If A is
"more approved" than B, he's probably better, and if A
pairwise beats B, he's probably better, so if A is
"more approved" then a candidate B whom he pairwise
beats, he's definitely better, so why elect B? Is that
it? ."

CB: Close enough. In election theory,  lots of of
obvious desirable properties are in contradiction with
each other, and we can give very strong objections to
most of  the simplest proposed  rules/standards.
We can have a sort of catechism consisting of  a
probabilistic standard, a strict rule motivated by
that standard, and strong objections to that rule.
So for example:
"More approved candidates should tend to win" 
suggests "Why not always elect the most approved
candidate?"  We can answer "If ranking information is
also collected, it might reveal that another candidate
pairwise beats all the others, and may even be the
first preference of more than half the voters"; and we
can give the same answer to the question
"Why not never elect the least-approved candidate?".
Likewise, "Pairwise beaten candidates should tend to
lose" prompts the question "Why not never elect a
pairwise beaten candidate?".  We have the very easy
answer that it is possible that all the candidates can
be pairwise beaten, and the office needs to be filled.

To the question "Why not always elect the most
approved candidate whenever all the candidates are
pairwise beaten?", our answer is much more complicated
(being about strategy) and our objection much weaker.

The exasperated questioner (say a potential voter)
then says "There must be some simple straight-forward
based-on-elementary-principles rule/guarantee that we
can have! What about 'never elect a candidate that
is pairwise beaten by a more approved candidate'?"
I would say "Fine!",  and not  "When all the
candidates are pairwise beaten, we need to determine
which of the pairwise defeats is to be over-ridden.
James G-A insists that we do that based only on the
number of ballots that approve the pairwise winner and
not the loser. Your proposed rule is incompatible 
with that  obviously wonderful idea!"

While there seems to be no danger at all that the idea
that it is acceptable to elect  the least approved and
pairwise beaten candidate will catch on, I'd prefer to
post on  things I consider more interesting and
important.

Chris  Benham















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