[EM] SMD,TR fails the Plurality criterion.

[C.Benham]

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