<html><body><div style="color:#000; background-color:#fff; font-family:times new roman, new york, times, serif;font-size:12pt"><div style="RIGHT: auto">I recently proposed (16 Nov 2012) the "Losing Votes (Equal-Ranking Above-Bottom Whole)"<BR>method:<BR><BR>*Voters rank from the top however many candidates they wish. Equal-ranking is allowed.<BR><BR>The result is determined from a pairwise matrix. On that matrix, ballots that rank above bottom<BR>any X=Y contribute one whole vote to X>Y and another to Y>X.<BR><BR>Ballots that truncate both X and Y have no effect on the X>Y and Y>X entries in the pairwise<BR>matrix.<BR><BR>With the thus created pairwise matrix, decide the winner with Schulze (Losing Votes).*<BR><BR>35 A<BR>10 A=B<BR>30 B>C<BR>25 C<BR><BR>A>B 35-30 (ignoring the 10 A=B ballots unlike my proposal, according to which A>B 45-40)</div>
<div style="RIGHT: auto">B>C 40-25<BR>C>A 55-45<BR style="RIGHT: auto"></div>
<div style="RIGHT: auto">(This is an old example from Kevin Venke in a different discussion.)<BR></div>
<div style="RIGHT: auto">B is pairwise beaten and positionally dominated by A and is the least "approved" (ranked above<BR>bottom) candidate. C is the most approved candidate and has the biggest single pairwise score<BR>(55 verus A). A has the most top rankings.</div>
<div style="RIGHT: auto"><BR style="RIGHT: auto">Both Winning Votes and Margins (using the Schulze or equivalent algorithm) elect B, the clearly<BR>weakest candidate. Notice that electing B is another outrageous failure of Later-no-Help.<BR><BR>Losing Votes elects A. Part of the case against electing C is that the 25 C truncators could be<BR>defecting from a sincere BC coalition (and if so, shouldn't be rewarded).<BR></div>
<div style="RIGHT: auto">Part (at least) of the case for electing C is that if the 30 B>C voters are sincere (and detest A)<BR>they have a strong incentive to order-reverse and maybe C has a disincentive to run.<BR><BR>But other than in effect just portraying the Margins or Winning Votes algorithms as in themselves<BR>standards, there is no case for electing B.</div>
<div style="RIGHT: auto"><BR style="RIGHT: auto">Of the various proposed ways of weighing "defeat strengths" in Schulze, Losing Votes is the one<BR>that elects most from the "tops of the ballots". Given that we are seeking to convert supporters<BR>of FPP (and to I hope a lesser extent, IRV), I think that is a marketing advantage.<BR><BR>Chris Benham<VAR id=yui-ie-cursor></VAR></div>
<div style="RIGHT: auto"><BR style="RIGHT: auto">But there is no case for electing B, other than <BR style="RIGHT: auto"><BR></div></div></body></html>