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