[EM] Median bifurcation using pairwise matrix

Rob LeGrand honky1998 at yahoo.com
Wed Aug 15 13:29:11 PDT 2001

Roy wrote:
> The pairwise matrix version doesn't use median rank, it uses wins vs.
> losses, which may be some kind of median, but it's not an equivalent
> method. I recommend calling it Win-Loss bifurcation; it is (as Rob
> LeGrand pointed out) very similar to Nanson's. In fact, it's probably
> equivalent: the only difference is that mine uses Row_total -
> Column_total and compares to zero (which is average), whereas Nanson
> compares row totals to the average of the row totals. It's the first
> example I've seen of bifurcation in election methods. But then, I'm
> not particularly well-read yet.

Depends on how you define the pairwise matrix.  When I say pairwise matrix, I
mean P, where Pij is the number of voters who ranked candidate i over candidate
j.  The Nanson I had in mind eliminates the candidates whose column total is
more than their row total at each stage, which seems to be the same as the
method you describe above (although yours generates a full ranking).

Rob LeGrand
honky98 at aggies.org

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