<br><br><div class="gmail_quote">2012/2/1 Kevin Venzke <span dir="ltr"><<a href="mailto:stepjak@yahoo.fr">stepjak@yahoo.fr</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div><div style="font-size:12pt;font-family:times new roman,new york,times,serif"><div><span>Hi Jameson,<br></span></div>
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</div><b><span style="FONT-WEIGHT:bold">De :</span></b> Jameson Quinn <<a href="mailto:jameson.quinn@gmail.com" target="_blank">jameson.quinn@gmail.com</a>><br><b><span style="FONT-WEIGHT:bold">À :</span></b> Kevin Venzke <<a href="mailto:stepjak@yahoo.fr" target="_blank">stepjak@yahoo.fr</a>> <br>
<b><span style="FONT-WEIGHT:bold">Cc :</span></b> em <<a href="mailto:election-methods@electorama.com" target="_blank">election-methods@electorama.com</a>> <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>2012/2/1 Kevin Venzke <span dir="ltr"><<a href="mailto:stepjak@yahoo.fr" rel="nofollow" target="_blank">stepjak@yahoo.fr</a>></span><br></div>
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<div><span>Hi Jameson,</span></div>
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<div><span>I expect that unpredictability (whatever there may be) of candidates' decisions can only hurt criteria compliance.</span></div>
<div><span>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>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>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>Candidate X, their most-preferred member of the current Smith set</div>
<div>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>They approve as many candidates as possible without approving both X and Y.</div>
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<div>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><span>So I wonder, can you suggest a deterministic version of SODA, where the "negotiations" of SODA are instead</span></div>
<div><span>calculated directly from the pre-announced preferences of the candidates? And if so, does it satisfy the same</span></div>
<div><span>criteria in your view</span><span>?</span></div>
<div><span></span> </div>
<div><span>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><span>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>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><div>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>convincing proofs when somebody asks for one? Pretty daunting task I would think.</div></div></div></div></div></div></blockquote><div><br></div><div>The proofs for the condorcet-related properties using optimal strategy are pretty simple and obvious. </div>
<div><br></div><div>The participation criterion only applies for delegated voters. The proof for that is a bit harder, but not too tough. For approval ballots, it is possible to fail the (voted) participation criterion only if the delegation order changes, and there are at least 5 candidates (in a delicate balance, and for voters whose ballots cannot make sense in a one-dimensional ideology space).</div>
<div><br></div><div>I just discovered a hole in my proof for delegated IIA. It works if all votes for the new candidate are and were approval-style. It can fail if there are at least 4/5 candidates in a tricky balance and the 5th/extra candidate pulls delegated votes in a way that changes the delegation order. In that case, there is always still a rational strategy for those voters which would still preserve IIA. (This proof is tricky.)</div>
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<div>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>easier to analyze. But in that case the method is basically Approval and doesn't even satisfy Majority Favorite. Right?</div></div></div></div></div></div></blockquote><div><br></div><div>No. In my previous message, I suggested two versions which leave no freedom for the candidates, automatically assigning delegated ballots. The first – optimal strategy – is not polytime computable that I know of (I strongly suspect it's NP-complete in theory, though in practical cases it will be easy to compute). The second – vote-one-frontrunner – is easy to compute, but it causes violations of IIA and participation.</div>
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<div style="FONT-SIZE:12pt;FONT-FAMILY:times new roman,new york,times,serif"><div><div> In </div>
<div>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>*everyone* is delegating, is that right?</div></div></div></div></div></div></blockquote><div><br></div><div>Everyone who votes for the majority candidate is either delegating to them, or voting them above all other alternatives - that is, approving only them but checking "do not delegate". This is the standard meaning of the majority criterion. For instance, by this meaning, approval meets the majority criterion.</div>
<div><br></div><div>For MMC, everyone in the mutual majority is either delegating to one of the candidates, or approving all of them and nobody else.</div><div><br></div><div><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<div>Kevin<var></var></div></font></span></div></div></div></div></div><br>----<br>
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