[EM] proposal: weighted pairwise comparison

[James Green-Armytage]

I wrote:
>>So, the standard pro-Condorcet counter-argument is to say that if we were
>>doing an IRV count that was repeated over and over again, you would
>>probably get to the point pretty quickly where B would win every time.
>>That is, in the first round, perhaps, people would give their sincere
>>rankings, and A would win the first IRV tally. But in subsequent rounds,
>>the C>B>A voters would be likely to realize that they could get a better
>>result for themselves (B instead of A) by voting B in first place. So C
>>would be eliminated first and B would win the tally. At this point, it
>>seems to me like the situation would be largely in equilibrium, in that
>>there wouldn't be a way for any of the voting blocs to get an immediately
>>preferable result.

David's examples again:
first example
>45 A 100 > B 70 > C 0
>10 B 100 > A 70 > C 0
>5  B 100 > C 70> A 0
>40 C 100 > B 70 > A 0
second example
>
>45 A 100 > B 10 > C 0
>10 B 100 > A 90 > C 0
>5  B 100 > C 90 > A 0
>40 C 100 > B 10 > A 0

David replied:
>
>In the second example B is barely preferable to A. C voters are left in
>the unenviable position of abandoning their favourite C and supporting
>somebody bad to prevent the election of somebody slightly worse. I don't
>think they'd do it. They'd continue supporting C since neither A or B are
>acceptable alternatives.

I reply:
	Well, I still disagree with you here, although we probably both
understand each others points already. It's kind of hard to make a
real-life analogy. What I'm describing is a series of rounds where the
candidates are the same, the voters' preferences are the same. I don't
even know if it ever has an end, or if it just keeps on going. I guess you
could imagine it as a "game" where the voters have good communication, are
rational, that people's preference ratings are known, and there are about
a hundred rounds where each voter gets a certain amount of points (or
money, maybe) for the candidate who is selected, that number of points
being determined by their (pre-determined) utility score for that
candidate. Using that analogy, I feel fairly confident that pretty soon
candidate B would win every time, paying the C 100 > B 10 > A 0 voters 10
points every time. So from that standpoint, a rather theoretical
standpoint, I feel pretty comfortable saying that B is an equilibrium
outcome in repeated IRV, despite his low utility score.
	It's hard to extend this analogy to a real life... I guess if there was
some weird country that did five separate IRV tallies with the same
candidates, and picked the candidate who won in the fifth tally, that
would be reasonably close. But if you can't assume that the vote in the
first round is sincere, then it is theoretically possible for people to
play some more complex games in this situation. Still, if such a
five-round procedure existed somewhere, and people's utility ratings
corresponded with your example, I would still lay pretty good odds on B
winning the last round. The thing is, sure, the C voters don't like B.
But, really, if they've given up hope of C winning, what do they have to
lose?
	Let's match some names to the numbers, for fun...
45 Bush 100 > Lieberman 10 > Dean 0
10 Lieberman 100 > Bush 90 > Dean 0
5  Lieberman 100 > Dean 90 > Bush 0
40 Dean 100 > Lieberman 10 > Bush 0
>
	I imagine Joe Lieberman as someone who is not particularly liked by
either the Democrats or the Republicans. (I'm immensely glad that he
didn't win the primary, and I find it amusing how poorly he did after all
his "electable Democrat" bullshit.) 
	I think Lieberman would be a very crappy president. (And I think that he
was the kiss of death on Gore's ticket.) Still, if I was convinced that I
could only chose between Lieberman and Bush, I'd hold my nose and vote for
Lieberman. At least his environmental record is okay...
	But the thing about this example that seems somewhat unrealistic is: in a
Condorcet-efficient election, why is the only centrist running such a dud?
This is my critique of these sorts of pro-IRV "weak middle" examples in
general. In a real Condorcet election, you would have some center
candidates who would be reasonably respectable, who, at the least, should
be at a utility of 50 for one side if they're at 50 for the other side, 60
for one side if 40 for the other, etc. So yeah, I don't know who the good
centrists are, since our system is a relatively polar one. Clark seemed a
little better than Lieberman, at least, and surely he was a centrist. Get
him in there. McCain, too, people seem to respect him a lot for some
reason (or is that just out of a wish that he had beat Bush in the
primary?). John Anderson seems like a pretty principled guy, maybe someone
like him could run, clobber Lieberman, and be a reasonably high-utility CW
rather than a low utility CW.
	That makes sense to me, at least.

David wrote:
>
>Collecting ranking and rating data and then only considering the rating
>data in the event of a Condorcet cycle seems a potentially perilous thing
>to do. People can look at the ratings data after the event and say well B
>was a generally preferred choice but 85% of people didn't like him/her.
>Related criticisms can be made of all ranked ballot methods. What your
>method seems to be doing is gathering additional information and then
>ignoring it in all but certain selected circumstances.

I reply:
	Well, you're right. I'm not using the ratings information quite as much
as I might like to. But you know, if you let the ratings override the
rankings, then you just have CR again, CR is likely to compress into
approval, and well, I like Condorcet better than approval. So, yes, the
ratings do take something of a back seat to the rankings, which is too bad
but in my opinion necessary.
	As for giving people information that undermines the credibility of your
winner, yeah, that's true. That information may not be pleasant, but I
don't see why people shouldn't have a right to know about it. Also, it
might inspire some more respectable centrists to run the next time. (You
know, they would say, "Hell, Lieberman won with a utility set like that? I
could have smashed him, why didn't I run?")