[EM] SMD,TR fails the Plurality criterion.

[Chris Benham]

My previous message contained a small blunder. The corrected version is below

A candidate X's  "maximum approval oppostion" score is the approval score of the most approved
candidate only on ballots on which X is not approved.

In the example election I mistakenly gave A's MAO score as 11.

The definition of SMD,TR:

*Voters fill out 3-slot ratings ballots, default rating is bottom-most
(indicating least preferred and not approved).

Interpreting top and middle rating as approval, disqualify all candidates
with an approval score lower than their maximum approval-opposition 
(MAO) score.
(X's  MAO score is the approval score of the most approved candidate on
ballots that don't approve X).

Elect the undisqualified candidate with the highest top-ratings score.*

http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023530.html
Chris 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:  A23,   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