[EM] AWP versus DMC and AM

[Chris Benham]

James,
Here is an example of yours that we've been
discussing.

Preferences
26: A>>C>B
22: A>>B>C
19: C>B>>A
06: C>>B>A
22: B>C>>A
05: B>>A>C

Direction of defeats
A>C 52-48
C>B 51-49
B>A 52-48

Approvals: A48,  B46,  C47.

A is the only candidate that is not pairwise beaten by
a more approved candidate, so the Approval Plurality
criterion says only A can win. DMC and  AM meet that
criterion, while AWP elects B.
While I think that for the "real world" any case for
violating AP (especially in favour of the least
approved candidate) is too subtle and sophisticated,
suppose for the sake of  argument that I agree to
demote AP  from "essential" to merely "highly
desirable".  One of  your arguments against DMC and 
AM in this example has been that if  B is elected, the
complaint of  the C supporters is undermined by the
fact that they won't want to insist on the AP
criterion being met because that would result in the
election of  the candidate they all rank last.
Here at least is a method that elects C, that  I'll
label  "Approval  Regret".

"Voters rank the candidates and insert an approval
cutoff. Elect the CW if there is one.
If not, compute the "approval regret" score of each
Smith-set member thus: consider each in turn as the
provisional winner and count how many ballots that
don't approve this candidate could have made a
candidate they do approve the CW by Compromising. 
Elect the candidate with the lowest such score. Break
a tie by electing the tied candidate with the larger
approval score."

Taking the example above, there is no CW and all the
candidates are in the Smith set. A's approval regret
score is 19 because the the 19 C>B>>A voters could
have made B the CW by voting B>C>>A. The scores for B
and C are 0.  C is more approved  and so wins.
(Without this tiebreaking provision, "Approval Regret"
could be a criterion that AWP maybe meets.)

So what do you think of this mad idea?  Of  course its
big problem is the complaint of  those who prefer A to
C (more than half the voters) who can demand that the
method meets the AP criterion.
Denying such a "motherhood" criterion is just too
messy.


Chris Benham







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