[EM] AWP versus DMC and AM

[James Green-Armytage]

Chris,
	Your DMC>AWP argument, while simple (in my opinion, overly simplistic),
is quite abstract. I offer you an AWP>DMC argument that is somewhat more
concrete, i.e. more tied to particular election scenarios.

Brief statement of argument:	
	Let's say that the electorate is heavily divided between two factions,
the Democrats and Republicans. 
	Let's say that one and only one Democratic candidate pairwise defeats all
of the Republican candidates. AWP guarantees the election of this
candidate, but DMC and AM do not. 
	Furthermore, if there is a multi-candidate set of Democratic candidates
who pairwise defeat all of the Republican candidates, then AWP guarantees
that the winner will come from this set. DMC and AM cannot make this
guarantee.

Definition of "heavily divided" between Democrats and Republicans:
	More than 2/3 of the voters who prefer any Democrat Di over any
Republican Ri place their cutoff between this Di and Ri. Same for voters
who prefer any Ri over any Di.
	Less than 1/3 of the voters who prefer any Democrat Di over any other
Democrat Dj place their cutoff between this Di and Dj. Same for voters who
prefer any Ri over any Rj.
	Assume no equal rankings, or adjust the 2/3 minimum and/or the 1/3
maximum upward on a pair-by-pair basis to compensate for them. Assume also
that candidates in neither faction are not viable.

Commentary:
	Chris, you like to make up imaginary voters who complain about my method,
so I will do the same to you. My imaginary voter is named Chucky. He has
just participated in a DMC election that fits my definition of a "heavily
divided" electorate as stated above. For the sake of example, the two
factions are named the Republicans and the Imperials (kind of like in Star
Wars). 
	The winner of the election was an Imperial (named Dr. Sinistro), and yet
there was a Republican candidate (named Mr. Fabulous) who beat not only
Dr. Sinistro but all other Imperial candidates pairwise. This is why
Chucky (who is a Republican) has decided to complain to you.
	Chucky says to you, "Chris, I don't get it. Why didn't a Republican win
this election? We had this great candidate Mr. Fabulous, who beat all of
the Imperials right out of the park in one-to-one matchups. What happened?
Why are we stuck with Dr. Sinistro?"
	What do you say to poor Chucky, Chris? I'll imagine a hypothetical
dialogue. You say, "Well, Chucky, you see, Dr. Sinistro was more approved
than Mr. Fabulous."
	Chucky says, "More-approved? Who cares about that? I just told you that
Mr. Fabulous beat Dr. Sinistro pairwise. That means that if there was an
election between the two of them, Mr. Fabulous would win hands down."
	You say, "That's true, Chucky, but there was another Republican candidate
named Mr. Groovy who would have beaten Mr. Fabulous in a one-on-one
matchup as well. And Mr. Groovy would have lost to Dr. Sinistro. So you
see, Chucky, the important thing is what sort of approval scores the
candidates got."
	Chucky says, "But Chris, approval scores don't have any inherent meaning!
We rejected approval voting years ago because of the lack of MMC
compliance and the cooperation/defection dilemma. Why do you think
approval scores make any more sense lurking in a pairwise tally rule than
they do on their own? Listen: maybe Mr. Groovy did pairwise beat Mr.
Fabulous, but we Republicans don't care about that. What we care about
most of all is keeping those scary Imperials from controlling things.
Didn't you notice what a heavily divided electorate this was? Didn't you
notice that almost everyone who voted Fabulous>Sinistro put their cutoff
in between them, while almost nobody put their cutoff between Groovy and
Fabulous? If we Republicans have a candidate who can beat the Imperials,
then that's our man. Mr. Groovy will say exactly the same thing, and so
will most of the people who voted Groovy>Fabulous>Sinistro. If they had
known that this was going to happen, they wouldn't have voted out their
sincere full ranking, but now it's too late, Dr. Sinistro rules the
galaxy, and it's all your fault, you and your damned approval scores!"
	You'll have to forgive Chucky for shouting, Chris; he is very upset about
the results of that DMC election. Can you say anything to convince poor
Chucky that the Imperial victory was justified, or will you beg his
forgiveness for advocating such a misguided election method that went so
terribly wrong?

I had written:
>
>"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? ."
Chris, you wrote:
>
>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?"  

	I don't think that this consideration should carry much weight at all, in
part because of the concerns that Chucky raised in your discussion. I'm
just not convinced that the use of approval scores is helpful to majority
rule systems, even if you're using them in conjunction with a pairwise
tally.

Chris, you wrote:
>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.

	I don't think that either DMC/RAV or AM are equivalent to this. (Not that
I would support this method either.)

Chris, you wrote:
>
>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.
>
	The idea will certainly catch on if people ever start paying serious
attention to the relevant issues.

Sincerely,
James
>
>
>
>
>