[EM] Reversal Symmetry Criterion & Borda-Elimination

[Steve Barney]

I don't believe the Borda-Elimination method fails the Reversal Symmetry
Criterion, as claimed on the "Electoral Methods: Standards and Criteria"
webpage (which is listed in the EM list's bookmarks in Yahoo Groups). I am
referring to the following statement from the:

        Name: Reversal Symmetry Criterion 
        Definition: 
        If alternative X wins (excluding ties), and all rankings on all ballots
are reversed, then X must lose. 
        Pass: Approval, Average Rating, Black, Borda, Kemeny-Young, Median
Rating, Nanson (original), Ranked Pairs, Schulze 
        Fail: Borda-Elimination, Bucklin, Condorcet(EM), Coombs, Dodgson, IRV,
Minmax, Pairwise-Elimination, Smith//Minmax, Total Defeats
--"Electoral Methods: Standards and Criteria,"
http://www.fortunecity.com/meltingpot/harrow/124/criteria.html


According to _Chaotic Elections_, the recent voting theory book by UC-Irvine
professor Donald Saari, all methods based on pairwise rankings and tallies
satisfy this condition. Saari ought to know, as he is probably the original
source of this criterion. I asked Dr. Saari about this, and he said "...they
are wrong in the comment about Borda elimination. If all individual rankings
are reversed, then the Borda ranking is reversed. (This is in Chaotic
elections.)   Thus, if X was top-ranked before, X is bottom ranked now. As
such, X is the first candidate to be eliminated."


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