<html><body><div style="color:#000; background-color:#fff; font-family:times new roman, new york, times, serif;font-size:12pt"><div style="RIGHT: auto"><SPAN style="RIGHT: auto">Hi Jameson,<BR class=yui-cursor style="RIGHT: auto"></SPAN></div>
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<DIV class=hr style="BORDER-RIGHT: #ccc 1px solid; PADDING-RIGHT: 0px; BORDER-TOP: #ccc 1px solid; PADDING-LEFT: 0px; FONT-SIZE: 0px; PADDING-BOTTOM: 0px; MARGIN: 5px 0px; BORDER-LEFT: #ccc 1px solid; LINE-HEIGHT: 0; PADDING-TOP: 0px; BORDER-BOTTOM: #ccc 1px solid; HEIGHT: 0px" readonly="true" contenteditable="false"></DIV><B><SPAN style="FONT-WEIGHT: bold">De :</SPAN></B> Jameson Quinn <jameson.quinn@gmail.com><BR><B><SPAN style="FONT-WEIGHT: bold">À :</SPAN></B> Kevin Venzke <stepjak@yahoo.fr> <BR><B><SPAN style="FONT-WEIGHT: bold">Cc :</SPAN></B> em <election-methods@electorama.com> <BR><B><SPAN style="FONT-WEIGHT: bold">Envoyé le :</SPAN></B> Mercredi 1 février 2012 11h12<BR><B><SPAN style="FONT-WEIGHT: bold">Objet :</SPAN></B> Re: [EM] SODA criteria<BR></FONT></DIV><BR>
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<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">2012/2/1 Kevin Venzke <SPAN dir=ltr><<A href="mailto:stepjak@yahoo.fr" target=_blank rel=nofollow ymailto="mailto:stepjak@yahoo.fr">stepjak@yahoo.fr</A>></SPAN><BR></DIV>
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<DIV style="RIGHT: auto"><SPAN style="RIGHT: auto">Hi Jameson,</SPAN></DIV>
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<DIV style="RIGHT: auto"><SPAN style="RIGHT: auto">I expect that unpredictability (whatever there may be) of candidates' decisions can only hurt criteria compliance.</SPAN></DIV>
<DIV style="RIGHT: auto"><SPAN style="RIGHT: auto">At least with cri<VAR></VAR>teria that are generally defined on votes, because with such criteria you usually have to assume</SPAN></DIV>
<DIV><SPAN>the worst about any other influences incorporated into the method.</SPAN></DIV></DIV></DIV></BLOCKQUOTE>
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<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">This is true. For most of the criteria, I was implicitly talking about a version of SODA where all candidates use optimum strategy according to their predeclared preferences. This is well-defined and unique, but is not necessarily polytime-calculable. Still, even without being able to calculate results, you can prove criteria compliances for this version by contradiction. </DIV>
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<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">For a polytime-calculable version which satisfies most of the same criteria, assume that each candidate, when it is their turn to assign delegated votes, looks at the two "distinct frontrunners"; that is:</DIV>
<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">Candidate X, their most-preferred member of the current Smith set</DIV>
<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">and candidate Y, the candidate, of those whom they prefer differently from X, who does best pairwise (again, using current assignments and unassigned preferences) against X</DIV>
<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">They approve as many candidates as possible without approving both X and Y.</DIV>
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<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">This version does not satisfy participation (though again, it's damn close) or IIA, and I'm not 100% sure about its cloneproofness (though I think it is). Otherwise, it satisfies the criteria I said.</DIV>
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<DIV style="RIGHT: auto"><SPAN style="RIGHT: auto">So I wonder, can you suggest a deterministic version of SODA, where the "negotiations" of SODA are instead</SPAN></DIV>
<DIV style="RIGHT: auto"><SPAN style="RIGHT: auto">calculated directly from the pre-announced preferences of the candidates? And if so, does it satisfy the same</SPAN></DIV>
<DIV style="RIGHT: auto"><SPAN style="RIGHT: auto">criteria in your view</SPAN><SPAN>?</SPAN></DIV>
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<DIV style="RIGHT: auto"><SPAN style="RIGHT: auto">I can say I would be skeptical of how a criterion is being applied, or how clearly it is being defined, if the </SPAN></DIV>
<DIV style="RIGHT: auto"><SPAN style="RIGHT: auto">satisfaction of it *depends* on </SPAN><SPAN>the </SPAN><SPAN>fact that candidates have post-voting decisions to make.</SPAN></DIV></DIV></DIV></BLOCKQUOTE>
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<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">Are you still suspicious of participation and [delegated] IIA, given that satisfying them depends on assuming optimal strategy?</DIV></BLOCKQUOTE></BLOCKQUOTE>
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<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">Hmm, I think so, just because "optimal strategy" is hard to define in general. Do you think that it will be possible to produce</DIV>
<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">convincing proofs when somebody asks for one? Pretty daunting task I would think.</DIV>
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<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">I find myself trying to suggest that it may never be necessary to delegate any power to the candidates. That would make it</DIV>
<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">easier to analyze. But in that case the method is basically Approval and doesn't even satisfy Majority Favorite. Right? In </DIV>
<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">your criteria list you had "Majority" but for that you must actually be assuming the opposite of what I am trying, namely that</DIV>
<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">*everyone* is delegating, is that right?</DIV>
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<DIV class=yiv1655698121gmail_quote style="RIGHT: auto">Kevin<VAR id=yui-ie-cursor></VAR></DIV></DIV></DIV></DIV></div></body></html>