[EM] Re: Borda-Elimination

[Rob LeGrand]

Kevin Venzke wrote:
> I wonder if BE's result in such cases is just erratic and senseless, or
> if there's a reasoning behind it.

If by Borda-Elimination you mean repeatedly eliminating the candidate with
the smallest Borda score (which I call Baldwin), there's a reasoning behind
it.  A Condorcet winner always has an above-average Borda score.  This is
easy to see when you calculate the Borda score the way I do: look at the
raw pairwise matrix and subtract a candidate's column sum from its row sum.
 If a candidate wins each pairwise matchup, that score will always be
positive, and the sum of all Borda scores is zero, so a Condorcet winner's
Borda score is always above average.  Therefore it won't be eliminated at
any stage of Baldwin or Nanson, so Baldwin and Nanson are Condorcet methods.

=====
Rob LeGrand, psephologist
rob at approvalvoting.org
Citizens for Approval Voting
http://www.approvalvoting.org/

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