[EM] AWP versus AM (was "summary of Condorcet anti-strategy measures")

[James Green-Armytage]

James G-A replying to Chris Benham, on the topic of AWP versus AM and
DMC...

Chris:
>AM also frustrates the
>Buriers; except in one where AWP "cheated" by electing
>a "strongly defeated" candidate (pairwise beaten by a
>candidate with a higher approval score).
>
James:
> "I'm sorry, but I don't think that this definition of
>"strongly defeated" is especially useful. Nor do I
>think that it is "cheating" to drop such a defeat in
>the event of a majority rule cycle."
>
Chris:
>Well, its not supposed to be especially "useful" 
>so much as  *normative*.

	There are plenty of ways to define a strong defeat, e.g. an A>B. One is
if A has a higher approval score than B. Another is if the number of A>B
voters is especially large. Another is if the number of voters who
strongly prefer A to B is especially large. (Number of voters who place A
above cutoff and B below.) The first definition is related to DMC, the
second to WV, and the third to AWP. 
	All of these definitions imply normative criteria. "If A>B, and ____ ,
then B shouldn't be elected". Fill in the blank with any of the
definitions of a strong defeat above (perhaps replacing "especially" with
some numerical value, and adding a few restrictions and caveats), and you
have three separate normative criteria, each one providing an argument for
the corresponding method.
	"A method should never elect the 'least-approved' candidate." Yes, that's
a normative criterion.
	"A method should overrule defeats consisting of fewer strong preferences
before it overrules defeats consisting of more strong preferences." That's
another normative criterion. The two are incompatible, and for many, many
reasons (many of them provided in my last message to you), I consider the
latter criterion to be more important.

Chris:
>
>Recently I wrote strongly in favour of  the  Plurality
>criterion, which says that if  candidate y has more
>first-preferences than candidate x has
>above-last-preferences,then x can't win. Electing x
>gives those voters who prefer y  (to x) a very strong,
>virtually unanswerable complaint. When  an otherwise
>reasonable method fails Plurality,it is usually caused
>by a lot of the y supporters truncating. So I suppose
>an available (but not very strong) retort to the
>complainers might be: "Well, you shouldn't have
>truncated!".  That said, one of my current favourite
>plain ranked-ballot methods (CDTT,IRV)  does fail
>Plurality, but gives the voters incentive to fully
>rank so that
>failure  is very unlikely to occur in practice.
>Compared with failing the Plurality criterion,
>electing a candidate that is pairwise beaten by a more
>approved candidate can give more voters an even
>stronger,irresistible complaint. There isn't available
>the comeback: "This method encourages full ranking and
>so sometimes seems unfair to truncators. The winner's
>supporters didn't  truncate, and you shouldn't have",
>because in  AWP (as in your two examples)  the failure
>can occur when all the voters fully rank and use
>their cutoffs.

	Okay... So, a lot of good methods fail the Woodall plurality criterion,
right? Which ones pass, and which ones fail? AWP and AM both fail, right?
Are you saying that AM passes under conditions of strict full rankings,
whereas AWP fails under these conditions? Can you demonstrate this? 

Chris:
>
>Comparing AWP with DMC, AM and  Condorcet completed by
>Approval; AWP needs to collect more information. The
>other three are all happy with just the pairwise
>matrix and the approval  scores (of each candidate). I
> think it would be difficult to justify collecting
>that extra information (and explaining what you want
>to do with it)  to not particularly sophisticated, but
>fair-minded and not stupid people.  Suppose we have
>the pairwise rankings matrix and the candidates'
>approval tallies in front of us, and the  three
>candidates in a cycle. The supporters of  the
>different methods make their suggestions:
>
>(1) Approval. Lets elect the most approved  candidate.
>(2) DMC. Lets just eliminate the least approved
>candidate, and then elect  the pairwise winner of the
>two remaining.
>(3) AM. Lets elect the most approved candidate, unless
>the second-most approved candidate both pairwise beats
>the most approved candidate and has an approval
>score that is closer to the most approved's than to
>the least approved's; in which case we  elect the
>second-most approved.
>(4) AWP. I need more information, so that I
>can...[insert mumbo-jumbo]. I might want to elect the
>*least* approved candidate, partly because in cases
>like this I tend to assume that some of the voters are
>falsifying their preferences.

	This is unnecessarily insulting ("mumbo-jumbo"). AWP is not hard to
explain. For example: 
	"If there is a majority rule cycle (A beats B, B beats C, C beats A),
then we overrule the defeat that consists of the fewest strong
preferences. (If you approve of candidate A but not candidate B, then your
A>B preference is a "strong preference".)" 
	This explanation is perfectly intuitive. We know that every candidate is
defeated by some other candidate, and that we will have to ignore at least
one of these defeats. It makes perfect sense to ignore the defeat that
consists of the fewest strong preferences. I doubt that any further
justification will be needed. 
	There is no need to talk about approval scores. AWP doesn't pay attention
to approval scores; rather, it uses approval cutoffs to provide a defeat
strength definition that I consider to be more sensitive to preference
strength and more resistant to strategic manipulation.

Chris
>
>That just won't fly. You can't say to voters: "Ok,
>we're looking for a pairwise beats-all candidate.
>We're asking you for rankings information, and in case
>there is no such candidate, also your approval
>cutoffs";  and then try to tell them the right winner
>is pairwise beaten and also the *least* approved.
>AM doesn't do that, and yet I still can't see that it
>is significantly worse than AWP at  resisting Burying.

	It's irresponsible and insulting of you to make this assertion without
replying to *any* of the relevant arguments in the post that you were
ostensibly replying to here. I probably spent a solid two hours trying to
make the case for AWP's greater strategy-resistance, for your benefit, and
you reply by contradicting my thesis in less than a single sentence with
absolutely no justification. You are not being a good discussion partner
here.

Chris:
>(And  it would have to be a lot worse for me to accept
>that the extra resistance gained by AWP is worth the
>cost.)
>
	There is no extra cost of AWP over AM or DMC. Is AWP harder to explain? I
don't think so. As for 'needing to collect more information', AWP is
summable, if that kind of thing is important to you. 
>
Sincerely,
James
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