<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>Kevin,<BR><BR>You wrote (10 Jan 2009):</DIV>
<DIV> </DIV>
<DIV>26 A>B<BR>25 B>A<BR>49 C<BR><BR>"Mutual Majority elects {A,B}<BR><BR>Now add 5 A bullet votes:<BR><BR>26 A>B<BR>25 B>A<BR>49 C<BR>5 A<BR><BR>Now Mutual Majority elects {A,B,C}."</DIV>
<DIV> </DIV>
<DIV>Oops! (I knew that!) Sorry for falsely contradicting you.<BR><BR>><I> "Why is mono-add-plump important?"<BR></I>><I> <BR></I>><I> Because as an election method algorithm that fails it<BR></I>><EM> simply can't have any credibility as a quasi-intelligent <BR>> device (which is what it is supposed to be) </EM><EM>and because </EM></DIV>
<DIV><EM>> satisfying it should be (and is) very cheap.</EM></DIV>
<DIV><BR>"I feel that cheapness isn't relevant to whether a criterion is important,<BR>and certainly not to whether failing it is absurd. I save the term <BR>"absurd" for ideas that are bad regardless of what else is available."<BR></DIV>
<DIV>Well I don't. If none of the election criteria were incompatible with each</DIV>
<DIV>other, wouldn't we say that nearly all of them are "important"?</DIV>
<DIV><BR>"Regarding your first reason: Why is it acceptable to fail mono-add-top<BR>or Participation, but not acceptable to fail mono-add-plump? I guess<BR>that you based this distinction almost entirely on the relative cheapness<BR>of the criteria."</DIV>
<DIV> </DIV>
<DIV>No. With mono-add-top and Participation, the quasi-intelligent device in</DIV>
<DIV>reviewing its decision to elect X gets (possibly relevant) information about</DIV>
<DIV>other candidates besides X. With mono-add-plump it gets nothing but information</DIV>
<DIV>about and purely in favour of X, so it has no excuse at all for changing its "mind"</DIV>
<DIV>about electing X.</DIV>
<DIV><BR> ><I> "If we view CDTT somehow as an election method, then </I><I>when it fails </I></DIV>
<DIV><EM>> mono-add-plump, the bullet votes for X are not simply </EM><I>"strengthening"<BR></I>><I> X, they are also *weakening* some pairwise victory of Y </I><I>over Z, which X<BR></I>><I> had relied upon in order to have a majority beatpath to</I><I> Z."<BR></I>><I> <BR></I>><I> That just testifies to the absurdity of an algorithm </I><I> specifically putting some </I><I> </I></DIV>
<DIV><I>> special significance on "majority beatpaths" </I><I>versus other beatpaths.<BR></I><BR>"You're saying it's absurd, but what is absurd about it?"</DIV>
<DIV><BR>It's absurd that ballots that plump for X should in any way be considered relevant</DIV>
<DIV>to the "strength" of the pairwise comparison between two other candidates.<BR>This absurdity only arises from the algorithm specifically using (and relying on) a<BR>majority threshold. </DIV>
<DIV><BR>"It would be better, as in less arbitrary, if you simply criticized that beatpath GMC is </DIV>
<DIV>incompatible with ratings summation."</DIV>
<DIV> </DIV>
<DIV>So is Condorcet. I don't think it's particularly "arbitrary" to value electing a voted<BR>Shwartz winner. I'm still a bit confused as to why anyone would be interested in</DIV>
<DIV>"beatpath GMC".<BR><BR>"So essentially, Schwartz//Approval is preferable to any method that satisfies SMD, </DIV>
<DIV>Schwartz, and beatpath GMC."<BR><BR>Yes, much preferable to any method that satisfies "beatpath GMC" period</DIV>
<DIV> </DIV>
<DIV>"I don't feel there's an advantage to tending to elect candidates with more approval, because </DIV>
<DIV>in turn this should just make voters approve fewer candidates when they doubt how the method </DIV>
<DIV>will use their vote."</DIV>
<DIV><BR>And why is that a negative? I value LNHarm as an absolute guarantee, but in inherently- </DIV>
<DIV>vulnerable-to-Burial Condocet methods, I think it is better if they have a "watch who you rank</DIV>
<DIV>because you could help elect them" Approval flavour.<BR></DIV>
<DIV>From your earlier post:</DIV>
<DIV>"In the three-candidate case, at least, I think it's a problem to elect a candidate who isn't in the <BR>CDTT."</DIV>
<DIV> </DIV>
<DIV>Why?</DIV>
<DIV><BR>25: A>B<BR>26: B>C<BR>23: C>A<BR>26: C<BR></DIV>
<DIV>In this "situation 2" election from my demonstration, can you seriously contend (with a straight face)</DIV>
<DIV>that electing C is "a problem"? Refresh my memory: who first suggested "Max. Approval Opposition" </DIV>
<DIV>as a way of measuring a candidate's strength?<BR></DIV>
<DIV><BR>Chris Benham<BR><BR><BR><BR><BR><BR><BR><BR></DIV>
<DIV> </DIV>
<DIV><BR> </DIV></div><br>
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