[EM] Reversal Symmetry Criterion & Borda-Elimination

[Joe Weinstein]

Thanks to all of you - Steve Barney, Rob LeGrand and Blake Cretney - for 
interesting discussion concerning Borda-elimination and Symmetry reversal.

Thanks to Steve for posing the question precisely, notably for including a 
precise statement of the suggestive but readily misinterpreted phrase 
'Reversal Symmetry Criterion'.

Thanks to Rob and Blake for crisp counterexamples to Saari.  Suppose we 
amend Rob's example by substituting 'B' for 'A' and 'A' for 'B', and 
interchanging the first two rows.  We then get Blake's example, but with 
somewhat different row percentages of voters.  Namely, (as amended) Rob's 
percentages are approx. 45, 45, and 10;  whereas Blake's are 40, 35, 25.  
Either way, fine examples.

In effect - as Blake notes aptly - is that Saari's quoted deductions are 
true but don't settle the point at issue!

Joe Weinstein
Long Beach CA USA


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