<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:12px"><div id="yui_3_16_0_1_1432764762629_15088"><span id="yui_3_16_0_1_1432764762629_15424">Hi Chris,</span></div><div id="yui_3_16_0_1_1432764762629_15088"><span><br></span></div><div id="yui_3_16_0_1_1432764762629_15088"><span id="yui_3_16_0_1_1432764762629_15425">I like this kind of method where you pick a pivotal candidate and check if the other </span></div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr"><span id="yui_3_16_0_1_1432764762629_15426">candidates can defeat him, but typically these methods don't satisfy FBC or mono-raise.</span></div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr"><span><br></span></div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr"><span id="yui_3_16_0_1_1432764762629_15201">Off the top of my head, what if some voters rank Favorite=Compromise>...>Worst, </span></div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr"><span id="yui_3_16_0_1_1432764762629_15441">resulting in </span>Favorite being the seeded candidate and the winner being Worst. Isn't it</div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">possible that if the voters lower Favorite in their rankings that Favorite will no longer</div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">be the seed, and instead someone else will be the seed? If so, I don't think there's</div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">a way to promise that Compromise would not go on to win the election.</div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr"><br></div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">Regarding mono-raise, while it's obvious that getting raised can't stop you from being</div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">the seed if you were the seed, what if you weren't the seed but you won via approval in</div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">the second phase? Getting raised/lowered could change who the seed is, and it may</div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">be that you can only win in phase 2 when certain candidates are the seed. In fact,</div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">becoming the seed when you hadn't been the seed could even make you lose.</div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr"><br></div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr">Kevin</div><div id="yui_3_16_0_1_1432764762629_15088" dir="ltr"><br></div><br> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12px;" id="yui_3_16_0_1_1432764762629_15086"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 16px;" id="yui_3_16_0_1_1432764762629_15085"> <div dir="ltr" id="yui_3_16_0_1_1432764762629_15084"> <hr size="1" id="yui_3_16_0_1_1432764762629_15159"> <font size="2" face="Arial" id="yui_3_16_0_1_1432764762629_15083"> <b><span style="font-weight:bold;">De :</span></b> C.Benham <cbenham@adam.com.au><br> <b><span style="font-weight: bold;">À :</span></b> "election-methods@lists.electorama.com" <election-methods@lists.electorama.com> <br> <b><span style="font-weight: bold;">Envoyé le :</span></b> Mardi 26 mai 2015 1h57<br> <b><span style="font-weight: bold;">Objet :</span></b> Approval seeded by MinGS (etrw)<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_1_1432764762629_15087"><br>I've been trying to come up with a better method with Bucklin-like <br>virtues including Later-no-Help, even though<br>there seems to be no call for any such thing and it results in a method <br>with a stronger truncation incentive than<br>I like.<br><br>The closest I came fills the bill with 3 candidates, but can probably <br>fail Majority for Solid Coalitions (aka Mutual Majority)<br>with more.<br><br> Approval seeded by Minimum Gross Score (equal-top rating whole):<br><br>*Voters fill out a multi-slot ratings ballot (I suggest as many slots as <br>there are candidates, up to say 4).<br>Default rating (truncation) is bottom.<br><br>Construct a pairwise matrix in which any ballot that rates/ranks <br>candidate X and Y equal-top gives a whole vote to both<br>in the X v Y pairwise comparison. Those that rate at least one of them <br>in a lower position give a whole vote to one if they<br>rate that one above the other, otherwise give no vote to either.<br><br>We are only concerned with pairwise scores, not defeats or victories or <br>ties. Select the candidate S whose lowest pairwise<br>score is higher than any other candidate's lowest pairwise score.<br><br>Then interpret all the ballots that rate S above bottom as approving S <br>and all other candidates they rate no lower than S,<br>and all the other ballots as approving all the candidates they rate <br>above bottom.<br><br>Based on that interpretation, elect the most approved candidate.*<br><br>I claim that this meets the Favorite Betrayal Criterion, Plurality, <br>Irrelevant Ballots, Later-no-Help (maybe barring some fantastic<br>scenario with many candidates), Condorcet(Gross), Minimal Defense, <br>mono-raise, mono-add-top, mono-switch-plump, mono-add-plump,<br>mono-append, and 3-candidate Majority for Solid Coalitions.<br><br>Because I'm sure that it doesn't properly meet Majority for Solid <br>Coalitions, I don't count this as a complete success.<br><br>Without the approval stage and the rule about equal-top rating/ranking, <br>it is Douglas Woodall's "MinGS" method (one of many<br>he devised for test purposes).<br><br>46 A<br>44 B>C<br>10 C<br><br>C> A 54-46, A>B 46-44, B>C 44-10. The method "seeds" A and then <br>elects C.<br><br>Electing A would be a failure of Minimal Defense and electing B would <br>show a failure of Later-no-Help. Unfortunately the election of C<br>is a failure of Chicken Dilemma (not compatible with the method's <br>compliance with Plurality and Minimal Defense).<br><br>46 A<br>44 B>C (sincere might be B or B>A)<br>05 C>A<br>05 C>B<br><br>C> A 54-46, A>B 51-49, B>C 44-10. The method "seeds" A and elects C.<br><br>Here it resists Burial strategy better than the MinMax (Margins) and <br>(Losing Votes) Condorcet methods, which both elect B.<br><br>46 A>C<br>10 B>A<br>10 B>C<br>34 B=C<br><br>C>B 80-54, B>A 54-46. A>C 56-44. The method seeds B and elects C.<br><br>Not electing the only candidate that is top-rated on more than half the <br>ballots may be an odd look by comparison with Bucklin, but I'm not bothered.<br>All the candidates are pairwise beaten and the winner is rated above <br>bottom on 90% of the ballots.<br><br><br>40 A>C<br>15 B>A<br>20 B<br>15 C>A<br>10 C<br><br>A>B 55-35, A>C 55-25, C>B 65-35. The method seeds A and elects A.<br><br>There are 100 ballots and A is the Condorcet(Gross) winner (meaning that <br>in each and all of A's pairwise contests A is<br>strictly preferred to the other candidate by more than half the voters). <br>Bucklin elects C.<br><br>Chris Benham<br><br><br><br><br><br></div> </div> </div> </div></body></html>