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

[Chris Benham]

James,
Comparing Approval Margins (AM)  with 
Approval-Weighted Pairwise (AWP), I'd written:
In all your excellent examples given to demonstrate
AWP's resistance to Burying, 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).

You responded:

 "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."

CB: Well, its not supposed to be especially "useful" 
so much as  *normative*.
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.

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.

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.
(And  it would have to be a lot worse for me to accept
that the extra resistance gained by AWP is worth the
cost.)


Chris Benham










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