<html><head><style type="text/css"><!-- DIV {margin:0px;} --></style></head><body><div style="font-family:times new roman, new york, times, serif;font-size:12pt"><DIV>I have an idea for a new defeat-strength measure for the Schulze algorithm</DIV>
<DIV>(and similar such as Ranked Pairs and River), which I'll call:<BR><BR>"Approval-Domination prioritised Margins":<BR><BR>*Voters rank from the top however many candidates they wish.</DIV>
<DIV>Interpreting ranking (in any position, or alternatively above at least one other</DIV>
<DIV>candidate) as approval, candidate A is considered as "approval dominating"</DIV>
<DIV>candidate B if A's approval-opposition to B (i.e. A's approval score on ballots<BR>that don't approve B) is greater than B's total approval score.</DIV>
<DIV><BR>All pairwise defeats/victories where the victor "approval dominates" the loser</DIV>
<DIV>are considered as stronger than all the others.</DIV>
<DIV> </DIV>
<DIV>With that sole modification, we use Margins as the measure of defeat strength.*</DIV>
<DIV> </DIV>
<DIV>This aims to meet SMD (and so Plurality and Minimal Defense, criteria failed</DIV>
<DIV>by regular Margins) and my recently suggested "Smith- Comprehensive 3-slot<BR>Ratings Winner" criterion (failed by Winning Votes).</DIV>
<DIV><BR><A href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023595.html">http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023595.html</A></DIV>
<DIV><BR>Here is an example where the result differs from regular Margins, Winning Votes</DIV>
<DIV>and Schwartz//Approval.<BR></DIV>
<DIV>44: A</DIV>
<DIV>46: B>C</DIV>
<DIV>07: C>A<BR>03: C</DIV>
<DIV> </DIV>
<DIV>A>B 51-46 = 5 * </DIV>
<DIV>B>C 46-10 = 36 <BR>C>A 56-44 = 12</DIV>
<DIV> </DIV>
<DIV>Plain Margins would consider B's defeat to be the weakest and elect B, but that is the only</DIV>
<DIV>one of the three pairwise results where the victor "approval-dominates" the loser. A's approval<BR>opposition to B is 51, higher than B's total approval score of 46.</DIV>
<DIV> </DIV>
<DIV>So instead my suggested alternative considers A's defeat (with the next smallest margin) to be</DIV>
<DIV>the weakest and elects A. Looking at it from the point of view of the Ranked Pairs algorithm</DIV>
<DIV>(MinMax, Schulze, Ranked Pairs, River are all equivalent with three candidates), the A>B result<BR>is considered strongest and so "locked", followed by the B>C result (with the greatest margin)</DIV>
<DIV>to give the final order A>B>C.</DIV>
<DIV> </DIV>
<DIV>Winning Votes considers C's defeat to be weakest and so elects C. Schwartz//Approval also<BR>elects C.</DIV>
<DIV> </DIV>
<DIV>Margins election of B is a failure of Minimal Defense. Maybe the B supporters are Burying</DIV>
<DIV>against A and A is the sincere Condorcet winner.<BR></DIV>
<DIV>I have a second suggestion for measuring "defeat strengths" which I think is equivalent to</DIV>
<DIV>Schwartz//Approval, and that is simply "Loser's Approval" (interpreting ranking as approval as</DIV>
<DIV>above, defeats where the loser's total approval score is higher are considered to be weaker than</DIV>
<DIV>those where the loser's total approval score is lower).</DIV>
<DIV> </DIV>
<DIV>Some may see this as more elegant than Schwartz//Approval, and maybe in some more complicated</DIV>
<DIV>example it can give a different result.<BR></DIV>
<DIV> </DIV>
<DIV>Chris Benham</DIV>
<DIV><BR> </DIV></div><br>
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