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

[James Green-Armytage]

Chris:
>"A method should never elect a candidate that is
>pairwise beaten by a more approved candidate", 
>which of course implies:
>"A method should never elect the 'least-approved'
>candidate,  unless   that  candidate  is the CW"

	Thanks, that's a helpful clarification. Let me clarify my criterion. To
keep things simple, I'll call it the approval weighted pairwise (AWP)
criterion, since it's obviously designed just to support AWP. Here's the
definition:
	"A voter expresses a strong preference for X over Y if the voter approves
X but not Y. If A pairwise beats B, and there is no beatpath from B to A
such that each defeat includes as many or more strong preferences than the
A>B preference, then B shouldn't win." 
	This basically says that the winner should come from the "immune set"
when defeat strengths are defined as in AWP.
	So, the bottom line is that the AWP criterion and your approval plurality
criterion (both normative criteria) are incompatible, and I find the AWP
criterion to be the more valuable of the two. I have made many arguments
for this. You have not replied to most of my arguments. I do not want to
repeat them. I encourage you to go back and read earlier messages that I
have written to you (e.g. the one on April 3rd) and reply to the argument
in full.

Chris:
>
>I find the phrase  "defeats consisting of..." an odd
>formulation with an unclear meaning. Arguably "defeat"
>is just a label for a result which just is, and so
>doesn't really "consist of"  anything.  

	Would the word "include" be more grammatical in place of "consist of"? I
will make that replacement below.
	 By "defeat", I meant "pairwise defeat". In AWP, a pairwise defeat of A
over B consists of multiple A>B preferences. Some of these are "strong"
preferences, in that they approve of A but not B. Some of them are "weak"
preferences, in that they approve or disapprove of both candidates. 
	Let's say that A beats B, 52-48. 52 voters prefer A to B, and 48 prefer B
to A. Let's say that 45 of the 52 A>B voters "strongly prefer" A to B, in
that they approve A but not B. Thus, I say that 45 voters "strongly
prefer" A to B. The A>B defeat consists of 45 strong preferences and 7
weak preferences. Thus, it includes 45 strong preferences. I say that this
defeat would be stronger than another defeat in the same election that
only includes 44 strong preferences. I argue that there is nothing weird
or counterintuitive about this definition.

James:
>
>> Which ones pass, and which ones fail
 [the plurality criterion]
>?

Chris:
>
>Some methods that pass the Plurality criterion:
>FPP, IRV, Approval, Winning Votes (RP,BP,River,MM),
>DSC, DAC, QLTD, Bucklin, Raynaud (Gross
>Loser),SCRIRVE,
>Point Count (e.g.Borda), Black
>Some methods that fail the Plurality criterion:
>CDTT methods, Any pairwise Margins method,
>Raynaud(Winning Votes), Young, Condorcet-Kemeny,
>Descending Half-Solid Coalititions, SC-DC
>AM and DMC definitely meet it, and I'm pretty sure
>AWP does too.
>Any non-absurd method  "passes under conditions of
>strict full rankings". 

	Again, thanks for clearing that up.
>
>One of the original justifications of the Plurality
>criterion was about inferring (conservatively) 
>approval from rankings.  

	This can't be done. 

>Repeating myself again: '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.

>in hybrid ranking/approval
>methods failing the somewhat similar "Don't elect a
>candidate that is pairwise beaten by a more approved
>candidate" criterion is IMO impossible to justify. 

	I don't agree with you. I'll repost the example that I made for you on
April 3 to illustrate my reasoning.

Preferences
26: B>>D>K
22: B>>K>D
19: D>K>>B
6: D>>K>B
22: K>D>>B
5: K>>B>D

Direction of defeats
B>D 52-48
D>K 51-49
K>B 52-48

Strong preferences on either side of defeats
B>D 48-47
D>K 6-5
K>B 46-48

	By your reasoning, ignoring the D>K defeat is impossible to justify. By
my reasoning, the D>K defeat is the obvious choice to drop. To you, the
fact that Dean is more approved than Kerry and also pairwise beats him
means that voters can irresistibly complain if Kerry is elected instead of
Dean. To me, the D>K defeat is the weakest defeat because only 6 voters
have a strong D>K preference. This is entirely intuitive to me. I don't
know why it seems so hopelessly weird to you.
	By the way, if AWP elects Kerry, the Dean voters (who by your logic have
a huge and unanswerable complaint) will not be interested in arguing for
your AM method, because it results in the election of Bush. All 25 Dean
voters rank Bush in last place, and 19 of them strongly prefer Kerry to
Bush. If your AM method elects Bush, I argue that most of the Dean
supporters will regret not compromising by voting D=K>B. AWP reduces the
spoiler effect in a way that AM and DMC does not... but now I'm repeating
my arguments for AWP... most of which you have yet to reply to as it is,
so why should I repeat them?
>
James:
>> 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:
>
>In this context "preference strength"  seems to be a
>bit vague and abstract. But aside from that, how  does
>using half as much approval information as
>AM  make it  "more sensitive to preference strength"?

	We've been over this already. 	The more people strongly agree with a
defeat, the stronger I consider the defeat to be. This means that AWP
protects pairwise defeats that the winners feel strongly about. AM doesn't
have this property.

>Maybe AWP  is a bit more strategy resistant than AP,

	I think that it is more than "a bit".

>but only at the huge cost of  flouting AP.

	I could just as easily say that AM and DMC have a huge cost in that they
flout the AWP criterion. Where does this get us?
>
>AWP is a  clever and sophisticated idea, but when you
>are using it to try to justify the election of the
>least-approved (and pairwise beaten) candidate,
>it will sound like "mumbo-jumbo"  to many fair-minded,
>not-stupid voters.
>
	Only if you assume that all such voters will find the AP criterion to be
more important than the AWP criterion. What makes you assume that?

Sincerely,
James