<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>Marcus,<BR></DIV>
<DIV>Thanks for the prompt explanation. You wrote:</DIV>
<DIV><BR>"I had already proposed this criterion in 1997."<BR></DIV>
<DIV>Why then do you list it as "Woodall's CDTT criterion"<BR>instead of your own "Generalised Majority Criterion"?<BR></DIV>
<DIV>Did, as far as you know, Woodall ever actually propose</DIV>
<DIV>the "CDTT criterion" as something that is desirable for</DIV>
<DIV>methods to meet (instead of just defining the CDTT set)?</DIV>
<DIV> </DIV>
<DIV>Would you agree that it (and your GMC) is essentially the</DIV>
<DIV>same thing as the "Truncation Resistance" criterion on</DIV>
<DIV>Steve Eppley's MAM page?</DIV>
<DIV> </DIV>
<DIV><A href="http://alumnus.caltech.edu/~seppley/Strategic%20Indifference.htm">http://alumnus.caltech.edu/~seppley/Strategic%20Indifference.htm</A></DIV>
<DIV> </DIV>
<DIV>One of several wordings given there:<BR></DIV>
<DIV><STRONG><EM>Truncation Resistance</EM>:</STRONG> If no voter votes any insincere strict preferences, <BR>alternative <I>x</I> is not in the sincere top cycle, and an alternative in the sincere top <BR>cycle is ranked over <I>x</I> by more than half of the voters, then <I>x</I> must not be chosen<BR></DIV>
<DIV><BR>And also to Mike Ossipoff's "Strategy-Free Criterion"?<BR><BR><A href="http://www.barnsdle.demon.co.uk/vote/stfree.html">http://www.barnsdle.demon.co.uk/vote/stfree.html</A></DIV>
<DIV> </DIV>
<DIV>Strategy-Free Criterion (SFC): </DIV>
<DIV><EM>Preliminary definition: </EM>A "Condorcet winner" (CW) is a candidate who, <BR>when compared separately to each one of the other candidates, is preferred <BR>to that other candidate by more voters than vice-versa. Note that this is about <BR>sincere preference, which may sometimes be different than actual voting. <BR><BR>SFC:
<P>If no one falsifies a preference, and there's a CW, and a majority of all the voters <BR>prefer the CW to candidate Y, and vote sincerely, then Y shouldn't win.
<P>[end of definition] <BR></P>
<P>In the interesting link you gave, and elsewhere in the EM archive, I see reference</P>
<P>to the "Smith//Condorcet[EM]" method. What is that method, and what does</P>
<P>the "[EM]" stand for and mean? I gather "Condorcet" meant 'MinMax'?</P>
<P> </P>
<P> </P>
<P>Chris Benham</P></DIV>
<DIV><BR> </DIV>
<DIV>Marcus Schulze wrote (Tues.Dec 23:<BR></DIV>
<DIV>Dear Chris Benham,<BR><BR>you wrote (23 Dec 2008):<BR><BR>><I> In one of your recent papers and on the Schulze<BR></I>><I> method Wikipedia page you list "Woodall's CDTT<BR></I>><I> criterion" as one of the criteria satisfied by<BR></I>><I> the Schulze (Winning Votes) method.<BR></I>><I><BR></I>><I> What, in your opinion, is supposed to be the<BR></I>><I> positive point of compliance with that criterion?<BR></I>><I> In other words, how would Schulze(WV) be worse<BR></I>><I> if it satisfied all the criteria presently on<BR></I>><I> your list of satisfied criteria except that one?<BR></I><BR>Woodall's CDTT criterion can be rephrased as<BR>follows:<BR><BR> When (1) the partial individual rankings can be<BR> completed in such a manner that candidate A is<BR> a Schwartz candidate and candidate B is not a<BR> Schwartz candidate and (2) the partial individual<BR>
rankings cannot be completed in such a manner<BR> that candidate B is a Schwartz candidate and<BR> candidate A is not a Schwartz candidate, then<BR> candidate B must not be elected.<BR><BR>This guarantees that not needlessly a candidate is<BR>elected who would not have been a Schwartz candidate<BR>when not some voters had cast only a partial ranking<BR>because of strategic considerations or other reasons.<BR><BR>When Woodall's CDTT criterion is violated, then this<BR>means that casting partial individual rankings could<BR>needlessly lead to the election of a candidate B who<BR>is not a Schwartz candidate; "needlessly" because<BR>Woodall's CDTT criterion is compatible with the<BR>Smith criterion, independence of clones, monotonicity,<BR>reversal symmetry, Pareto, resolvability, etc..<BR><BR>****************************************************<BR><BR>I had already proposed this criterion in 1997.<BR>See e.g.:<BR><BR><A
href="http://lists.electorama.com/pipermail/election-methods-electorama.com/1997-October/001569.html"><FONT color=#0000ff>http://lists.electorama.com/pipermail/election-methods-electorama.com/1997-October/001569.html</FONT></A><BR><BR>In that mail, this criterion is formulated as<BR>follows:<BR><BR>><I> "X >> Y" means, that a majority of the voters<BR></I>><I> prefers X to Y.<BR></I>><I><BR></I>><I> "There is a majority beat-path from X to Y,"<BR></I>><I> means, that X >> Y or there is a set of candidates<BR></I>><I> C[1], ..., C[n] with X >> C[1] >> ... >> C[n] >> Y.<BR></I>><I><BR></I>><I> A method meets the "Generalized Majority Criterion"<BR></I>><I> (GMC) if and only if: If there is a majority<BR></I>><I> beat-path from A to B, but no majority beat-path<BR></I>><I> from B to A, then B must not be elected.<BR></I><BR>The motivation for this criterion was that I wanted<BR>to find a
truncation resistance criterion<BR><BR>(a) that is compatible with the Smith criterion and<BR>with independence of clones and that is otherwise<BR>as strong as possible and<BR><BR>(b) that is defined on the cast preferences and<BR>not on the sincere preferences.<BR><BR>Markus Schulze<BR></DIV></div><br>
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