<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><BR>> I think Smith (or Shwartz),IRV is quite a good Condorcet method. It <BR>> completely fixes the failure of Condorcet while being more complicated<BR>> (to explain and at least sometimes to count) than plain IRV, and a Mutual<BR>> Dominant Third candidate can't be successfully buried.<BR>> But it fails Later-no-Harm and Later-no-Help, is vulnerable to Burying <BR>> strategy, fails mono-add-top, and keeps IRV's failure of mono-raise <BR>> and (related) vulnerability to Pushover strategy.</DIV>
<DIV><BR>Kristofer Munsterhjelm wrote (Sunday, 13 July, 2008 ):<BR><BR>"At the risk of taking this thread away from its original topic, I wonder <BR>what you think of Smith,X or Schwartz,X where X is one of the methods <BR>Woodall says he prefers to IRV - namely QTLD, DAC, or DSC."<BR></DIV>
<DIV>At one stage Woodall was looking for the method/s that meet as many of</DIV>
<DIV>his "monotonicty properties" as possible while keeping "Majority" (equivalent</DIV>
<DIV>to Majority for Solid Coalitions). That is what led him to Quota-Limited Trickle</DIV>
<DIV>Down (QLTD) and then Descending Acquiescing Coalitions (DAC).</DIV>
<DIV> </DIV>
<DIV>But I wouldn't conclude from this that for public political elections he currently</DIV>
<DIV>prefers those methods (or DSC) to IRV.<BR><BR></DIV>
<DIV>"(Since QLTD is not an elimination method, it would go like this: first <BR>generate a social ordering. Then check if the ones ranked first to last <BR>have a Condorcet winner among themselves. If not, check if the ones <BR>ranked first to (last less one), and so on. As soon as there is a CW <BR>within the subset examined, he wins. Schwartz,QLTD would be the same but <BR>"has a Schwartz set of just one member" instead of "has a CW".)<BR><BR>DAC and DSC only satisfy one of LNHelp/LNHarm, but they're monotonic in <BR>return. According to Woodall, you can't have all of LNHelp, LNHarm, and <BR>monotonicity, so in that respect, it's as good as you're going to get. I <BR>don't know if those set methods are vulnerable to burying, though, or if <BR>they preserve Mutual Dominant Third."<BR></DIV>
<DIV>They don't meet Mutual Dominant Third.</DIV>
<DIV> </DIV>
<DIV>49: A</DIV>
<DIV>48: B<BR>03: C>B</DIV>
<DIV> </DIV>
<DIV>The MDT winner is B, but DSC elects A.</DIV>
<DIV> </DIV>
<DIV>03: D</DIV>
<DIV>14: A</DIV>
<DIV>34: A>B</DIV>
<DIV>36: C>B</DIV>
<DIV>13: C<BR></DIV>
<DIV>The MDT winner is C, but DAC elects B.</DIV>
<DIV> </DIV>
<DIV>This latter example (from Michael Harman, aka Auros) I think put </DIV>
<DIV>Woodall off DAC. B is an absurd winner. Without the 3 ballots </DIV>
<DIV>that ignore all the competitive candidates the majority favourite is C.<BR><BR>But of course Smith implies MDT. </DIV>
<DIV> </DIV>
<DIV>DSC and DAC aren't just "monotonic" (meet mono-raise), they meet</DIV>
<DIV>Participation (which of course is lost when combined with Smith/Schwartz</DIV>
<DIV>because Participation and Condorcet are incompatible).</DIV>
<DIV> </DIV>
<DIV>I think all methods that meet Condorcet are vulnerable to Burial. By themselves</DIV>
<DIV>DSC is certainly vulnerable to burial (and has a 0-info. random-fill incentive) and</DIV>
<DIV>DAC has strong truncation incentive.<BR></DIV>
<DIV>Your question about QLTD has been asked before:<BR><A href="http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2005-March/015367.html">http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2005-March/015367.html</A></DIV>
<DIV> </DIV>
<DIV><A href="http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2005-March/015369.html">http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2005-March/015369.html</A><BR><BR>Possibly more later,</DIV>
<DIV> </DIV>
<DIV>Chris Benham</DIV></div><br>
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