Kevin Venzke has come up with an example that shows that my "Strong
Minimal Defense, Top Ratings"
(SMD,TR) method fails the Plurality criterion,contrary to what I've claimed.
21: A>C
08: B>A
23: B
11: C
Approval scores: A29, B31, C32
Maximum Approval Opposition scores: A11, B32, C31
Top-Ratings scores: A21, B31, C11.
By the rules of SMD,TR B is disqualified because B's MAO score (of 32,
C's approval score on
ballots that don't approve B) is greater than B's approval score.
Then A (as the undisqualified candidate with the highest TR score) wins.
But since B "has more first-place votes than A has total votes", or in
the language of this method
B's TR score is greater than A's total approval score, the Plurality
criterion says that A can't win.
This seems to show that compliance with my "Unmanipulable Majority"
criterion is a bit more
expensive than I thought. I still endorse SMD,TR as a good Favourite
Betrayal complying
method, but with less enthusiasm.
(My UM criterion says that if A is a winner and on more than half the
ballots is voted above B, it
is impossible to make B the winner by altering any ballots on which B is
voted above A without
raising on them B's ranking or rating.)
I was wrong to claim that compliance with Strong Minimal Defense implies
compliance with the
Plurality criterion.
Chris Benham
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