<div dir="auto">Evidently, at some point it became apparent that complete rankings (or symmetrically completed partial rankings) were inadequate for defense against certain kinds of offensive maneuvers ... we needed to have partial rankings to distinguish between winning votes and margins to measure defeat strength, etc.<div dir="auto"><br></div><div dir="auto">But, it seems to me that we have to go further if we want a method that can reasonably defend against both Burial and Chicken attacks.</div><div dir="auto"><br></div><div dir="auto">The classic ballot profile</div><div dir="auto"><br></div><div dir="auto">49 C</div><div dir="auto">26 A>B</div><div dir="auto">25 B</div><div dir="auto"><br></div><div dir="auto">is well known as a Chicken attack against the sincere Condorcet candidate A by the B faction when it's honest preferences were 25 B>A. So this ballot set must elect C or reward the delinquent faction B, or fail Plurality by electing A.</div><div dir="auto"><br></div><div dir="auto">But the same profile could arise just as well from a truncation attack against the sincere Condorcet candidate B by the C faction when its honest preferences were 49 C>B. So this ballot set must not elect C if it is to disappoint its naughty gambit.</div><div dir="auto"><br></div><div dir="auto">In summary, to satisfy Plurality, we cannot elect A. To deter Chicken attacks on a possible sincere CW we cannot elect B, and to deter truncation/burial attacks on a possible sincere CW we cannot elect C.</div><div dir="auto"><br></div><div dir="auto">But Universal Domain says our method has to pick one of the three candidates.</div><div dir="auto"><br></div><div dir="auto">What would IRV do?</div><div dir="auto"><br></div><div dir="auto">It would happily eliminate B and then elect C, the same as it would do if the true preferences were 49 C>B: defeat of the CW by truncation or burial is not a problem for IRV: it never made any promises about Condorcet. </div><div dir="auto"><br></div><div dir="auto">However the 51 IRVvoters that preferred B over C would be highly disappointed by this outcome ... in fact, it is quite likely that some of the A>B faction would forestall it by insincerely reversing their preference to B>A.</div><div dir="auto"><br></div><div dir="auto">How could relaxing Universal Domain slightly get us out of this dilemma?</div><div dir="auto"><br></div><div dir="auto">I think the answer is to use the traditional Sequential Pairwise Elimination factorization of a Condorcet method into two parts ... one part for setting an agenda ... and the other part for sorting the agenda pairwise (always giving priority to rectifying the order of the out-of-order pair nearest the least promising end of the agenda).</div><div dir="auto"><br></div><div dir="auto">It is only the agenda setting part that requires going slightly beyond "Universal" in Universal Domain. For example, setting the agenda by some kind of approval, implicit or otherwise. </div><div dir="auto"><br></div><div dir="auto">The other factor, the Pairwise win/loss/tie matrix is completely determined by the ordinal information in the ballots.</div><div dir="auto"><br></div><div dir="auto">In our example, what if the A faction could distinguish the Chicken attack from the other scenario by use of an explicit approval cutoff: 26 A>>B ?</div><div dir="auto"><br></div><div dir="auto">This is enough to change the SPE (Sequential Pairwise Elimination) agenda so that B with the least approval is pitted against A and so is eliminated first and does not get rewarded for the attack.</div><div dir="auto"><br></div><div dir="auto">In the second scenario the default/implicit approval cutoff (truncation) is assumed which gives B the greatest approval ... pitting A against C, and then C against B, making the sincere Condorcet candidate B the winner.</div><div dir="auto"><br></div><div dir="auto">It seems to me that this factorization idea is the safest and most transparent way of resolving this dilemma. Since it (SPE) is an ancient method with lots of pragmatic use in all sorts or traditional "deliberative assemblies" (Robert's Rules terminology) we should not feel too timid in proposing it for public elections.</div><div dir="auto"><br></div><div dir="auto">What say ye?</div></div><br><div class="gmail_quote"><div dir="ltr">El sáb., 11 de sep. de 2021 9:01 p. m., Kevin Venzke <<a href="mailto:stepjak@yahoo.fr">stepjak@yahoo.fr</a>> escribió:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div style="font-family:Helvetica Neue,Helvetica,Arial,sans-serif;font-size:16px"><div></div>
<div>All options being ranked equal is certainly allowed, what I'm saying is that it can only have one meaning.</div><div><br></div><div>I think your first method satisfies UD but the second doesn't. I wouldn't agree that this makes the definition inadequate. It doesn't only say that every possible ordering has to be admissible, it says that the method's result should be "definite" for any set of these orderings. If you may need to know other information from the ballots, then the result isn't defined for the orderings alone.</div><div><br></div><div>I guess that the point of UD is to set a baseline for how (quite a lot of very reasonable) election methods work, so that certain proofs will succeed, which depend only on preference orderings... It explains formally how we can set aside objections like "my method doesn't allow this kind of preference order, so the proof fails" or "my method can't be resolved with only this information, so the proof fails" etc.</div><div><br></div><div>Kevin</div><div><br></div><div><br></div><div><br></div>
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Le samedi 11 septembre 2021, 21:14:03 UTC−5, Forest Simmons <<a href="mailto:forest.simmons21@gmail.com" target="_blank" rel="noreferrer">forest.simmons21@gmail.com</a>> a écrit :
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<div><div id="m_-8569280499727363135ydp7af29ddeyiv6724280001"><div><div><div><div><h1 style="margin:0.8em 0px 15px;padding:0px;font-weight:normal;font-stretch:normal;font-size:1.85em;line-height:normal;font-family:arial,helvetica,sans-serif;background-color:rgb(255,255,255);color:rgb(35,31,32)">universal domain<span style="display:inline-block;width:20px;min-height:20px;vertical-align:middle;margin-left:5px;background-image:initial;background-size:initial;background-origin:initial;background-clip:initial;background-color:transparent"> </span></h1><p style="margin:0px 0px 1em;line-height:1.5;font-family:arial,helvetica,sans-serif;font-size:13px;background-color:rgb(255,255,255)"><span style="color:rgb(60,64,67);font-family:roboto,arial,sans-serif;font-size:18px">In social choice, the requirement that a procedure should be able to produce a definite outcome for every logically possible input of individual preference orderings.</span><br clear="none"></p><p style="margin:0px 0px 1em;line-height:1.5;font-family:arial,helvetica,sans-serif;font-size:13px;background-color:rgb(255,255,255)"><span style="color:rgb(60,64,67);font-family:roboto,arial,sans-serif;font-size:18px">So, all ranked equal is a "logically possible preference ordering." </span></p><p style="margin:0px 0px 1em;line-height:1.5;font-family:arial,helvetica,sans-serif;font-size:13px;background-color:rgb(255,255,255)"><span style="color:rgb(60,64,67);font-family:roboto,arial,sans-serif;font-size:18px">The main thing I'm wondering is how to modify ASM (Approval Sorted Margins) to make it more broadly acceptable ... and to perhaps comply with Universal Domain as a bonus.</span></p><p style="margin:0px 0px 1em;line-height:1.5;font-family:arial,helvetica,sans-serif;font-size:13px;background-color:rgb(255,255,255)"><span style="color:rgb(60,64,67);font-family:roboto,arial,sans-serif;font-size:18px">Here's my best attempt so far:</span></p><p style="margin:0px 0px 1em;line-height:1.5;background-color:rgb(255,255,255)"><font color="#3c4043" face="roboto, helvetica neue, arial, sans-serif">FIASM Fractional Implicit Approval Sorted Margins: Ballots are ranked preference style with equal rankings and truncations allowed. Each candidate's fractional implicit approval score is the number of ballots on which it is ranked equal top plus half the number of ballots on which it is ranked above at least one candidate, but not ranked top.</font></p><p style="margin:0px 0px 1em;line-height:1.5;background-color:rgb(255,255,255)"><font color="#3c4043" face="roboto, helvetica neue, arial, sans-serif">The candidates are listed in fractional implicit approval order. While there is any adjacent pair where the fractional implicit approval order contradicts the pairwise (head-to-head) win order, transpose the members of the out-of-order pair with the smallest absolute discrepancy in fractional implicit approval.</font></p><p style="margin:0px 0px 1em;line-height:1.5;background-color:rgb(255,255,255)"><font color="#3c4043" face="roboto, helvetica neue, arial, sans-serif">The resulting list is a social order that satisfies a reverse symmetry property ... reversing all of the ballot ranking inputs (so that equal top becomes equal bottom [or truncated] and vice versa) reverses the social order output.</font></p><p style="margin:0px 0px 1em;line-height:1.5;background-color:rgb(255,255,255)"><font color="#3c4043" face="roboto, helvetica neue, arial, sans-serif">Does this method satisfy Universal Domain?</font></p><p style="margin:0px 0px 1em;line-height:1.5;background-color:rgb(255,255,255)"><font color="#3c4043" face="roboto, helvetica neue, arial, sans-serif">Now, what if optional explicit cutoff marks were allowed to demarcate the three levels (0, 1/2, or 1) of fractional approval. Would that violate Universal Domain? </font></p><p style="margin:0px 0px 1em;line-height:1.5;background-color:rgb(255,255,255)"><font color="#3c4043" face="roboto, helvetica neue, arial, sans-serif">If so, then the Oxford definition quoted above is inadequate, since it does not logically rule out optional marks when the lack of any optional mark defaults to a standard ranking, and the only stated requirement is that no standard ranking be unusable.</font></p><p style="margin:0px 0px 1em;line-height:1.5;background-color:rgb(255,255,255)"><font color="#3c4043" face="roboto, helvetica neue, arial, sans-serif">Thoughts?</font></p></div><br clear="none"><div id="m_-8569280499727363135ydp7af29ddeyiv6724280001yqt96986"><div><div dir="ltr">El vie., 10 de sep. de 2021 10:56 p. m., Kevin Venzke <<a shape="rect" href="mailto:stepjak@yahoo.fr" rel="nofollow noreferrer" target="_blank">stepjak@yahoo.fr</a>> escribió:<br clear="none"></div><blockquote style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div style="font-family:Helvetica Neue,Helvetica,Arial,sans-serif;font-size:16px"><div></div>
<div>To my mind Implicit Approval (as a method in itself) only satisfies it if you can define the ballot format while discussing only relative rankings. So, for example, if the voter ranks all candidates totally equal to each other (no matter whether they are explicitly so ranked, or the ballot is submitted with all preferences truncated), this can only be allowed to mean that all are approved or that none are approved, since there is no way to differentiate these two stances using relative rankings only.</div><div><br clear="none"></div><div>Kevin</div><div><br clear="none"></div><div><br clear="none"></div>
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Le vendredi 10 septembre 2021, 21:49:14 UTC−5, Forest Simmons <<a shape="rect" href="mailto:forest.simmons21@gmail.com" rel="nofollow noreferrer" target="_blank">forest.simmons21@gmail.com</a>> a écrit :
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</div></div></blockquote></div></div></div><div><br clear="none"><div>El 10 sep. 2021 10:56 p. m., "Kevin Venzke" <<a shape="rect" href="mailto:stepjak@yahoo.fr" rel="nofollow noreferrer" target="_blank">stepjak@yahoo.fr</a>> escribió:<br clear="none"><blockquote style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div style="font-family:Helvetica Neue,Helvetica,Arial,sans-serif;font-size:16px"><div></div>
<div>To my mind Implicit Approval (as a method in itself) only satisfies it if you can define the ballot format while discussing only relative rankings. So, for example, if the voter ranks all candidates totally equal to each other (no matter whether they are explicitly so ranked, or the ballot is submitted with all preferences truncated), this can only be allowed to mean that all are approved or that none are approved, since there is no way to differentiate these two stances using relative rankings only.</div><div><br clear="none"></div><div>Kevin</div><div><br clear="none"></div><div><br clear="none"></div>
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Le vendredi 10 septembre 2021, 21:49:14 UTC−5, Forest Simmons <<a shape="rect" href="mailto:forest.simmons21@gmail.com" rel="nofollow noreferrer" target="_blank">forest.simmons21@gmail.com</a>> a écrit :
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