<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></DIV>
<DIV>You wrote (11 Jan 2009):</DIV>
<DIV> </DIV>
<DIV>"There are reasons for criteria to be "important" other than how easy they are to satisfy. <BR>Otherwise why would we ever bother to satisfy the difficult criteria?"</DIV>
<DIV> </DIV>
<DIV>Well, if as I said "none of the criteria were incompatible with each other" then</DIV>
<DIV>presumably none of the criteria would be "difficult".</DIV>
<DIV> </DIV>
<DIV><EM>>With mono-add-top and Participation, the </EM><I>quasi-intelligent device in<BR></I>><I> reviewing its decision to elect X gets (possibly</I><I> relevant) information </I></DIV>
<DIV><I>>about </I><I>other candidates besides X.<BR></I><BR>"How can it be relevant? X was winning and X is the preferred candidate<BR>on the new ballots."</DIV>
<DIV><BR>You know that Condorcet is incompatible with mono-add-top (and so of course<BR>Participation), so if we value compliance with the Condorcet criterion information</DIV>
<DIV>about candidates ranked below X must sometimes be relevant. But even if the </DIV>
<DIV>quasi-intelligent device is mistaken in treating them as relevant, then that is a much</DIV>
<DIV>more understandable and much less serious a blunder than the mono-add-plump</DIV>
<DIV>failure.</DIV>
<DIV> </DIV>
<DIV>><I> It's absurd that ballots that plump for X should in any </I><I>way be considered </I></DIV>
<DIV><I>> relevant </I><I>to the "strength" of the pairwise comparison </I><I>between two other candidates.<BR></I>><I> This absurdity only arises from the </I><I>algorithm specifically using (and relying on) </I></DIV>
<DIV><I>> a </I><I>majority threshold.</I></DIV>
<P><I></I> </P>
<P>"We have Mutual Majority and beatpath GMC displaying the same phenomenon."</P>
<P> </P>
<P>No. I don't accept that 'being tossed out of the favoured (not excluded from winning)<BR>set' is exactly "the same phenomenon" as 'being joined by others in the favoured set'.</P>
<P>The latter is obviously far less serious.</P>
<P><BR>><I> "I don't feel there's an advantage to tending<BR></I>><I> to elect candidates with more approval, because <BR></I>><I> in turn this should just make voters approve fewer<BR></I>><I> candidates when they doubt how the method <BR></I>><I> will use their vote."<BR></I>><I> <BR></I>><I> And why is that a negative? I value LNHarm as an absolute<BR></I>><I> guarantee, but in inherently- </I><I>vulnerable-to-Burial Condocet </I></P>
<P><I>> methods, I think it is </I><I>better if they have a "watch who you rank<BR></I>><I> because you could help elect them" Approval flavour.<BR></I><BR>"This is a negative because it suggests that your positional criterion<BR>will be self-defeating."</P>
<P> </P>
<P>How can it possibly be "self-defeating"? What is there to defeat?<BR></P>
<P>><I> From your earlier post:<BR></I>><I> "In the three-candidate case, at least, I think </I><I>it's a problem to elect a </I></P>
<P><I>> candidate who isn't in the </I><I>CDTT."<BR></I>><I> <BR></I>><I> Why?<BR></I><BR>"Because in the three-candidate case this is likely to be a failure of MD or SFC, </P>
<P>or close to it."</P>
<P> </P>
<P>I'm happy to have MD, and I don't care about SFC or "close failures" of MD.</P>
<P> </P>
<P><EM>> I'm still a bit confused as to why </EM><I>anyone would be interested in<BR></I>><I> "beatpath GMC".<BR></I><BR>"Well, it's a majority-rule criterion that is compatible with clone<BR>independence and monotonicity."</P>
<P> </P>
<P>Other "majority-rule" criteria with those same properties will suffice. <BR></P>
<P>"In the three-candidate case it's also compatible with LNHarm. By adding a vote for </P>
<P>your second choice, you can't inadvertently remove your first preference from the CDTT."</P>
<P> </P>
<P>Well since Condorcet is incompatible with LNHarm, that doesn't explain why Condorcet<BR>fans should like it. Also I think this is mainly just putting a positive spin on gross unfairness<BR>to truncators and the related silly random-fill incentive.</P>
<P> </P>
<P>25: A>B<BR>26: B>C<BR>23: C>A<BR>26: C<BR>100 ballots (majority threshold = 51)<BR><BR>B>C 51-27, C>A 75-25, A>B 48-26.</P>
<P> </P>
<P>In Schulze(Winning Votes), and I think also in any method that meets "beatpath GMC"<BR>and mono-raise, the 26C truncators can virtually guarantee that C be elected by using</P>
<P>the "random-fill" strategy. That is silly and unfair.</P>
<P> </P>
<P>Also, by artificially denying the clearly strongest candidate any method that doesn't</P>
<P>elect C must be vulnerable to Pushover, certainly much more than those that do elect C.</P>
<P><BR><A href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023590.html">http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023590.html</A></P>
<P> </P>
<P>(not that that is a very relevant strategy problem for the methods like WV that have the</P>
<P>much easier and safer random-fill strategy for the C>>(B<=>C) voters.)</P>
<P> </P>
<P><BR>Chris Benham<BR><BR><BR></P>
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<DIV> </DIV>
<DIV> </DIV></div><br>
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