<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:12pt"><div><span>Hi Ross,</span></div><div style="color: rgb(0, 0, 0); font-size: 16px; font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; background-color: transparent; font-style: normal;"><b style="font-family: Arial; font-size: 13px;"><br></b></div><div style="color: rgb(0, 0, 0); font-size: 13px; font-family: Arial; background-color: transparent; font-style: normal; font-weight: bold;"><b style="font-family: Arial; font-size: 13px;"> :</b><span style="font-family: Arial; font-size: small;"> Ross Hyman <rahyman@sbcglobal.net></span></div><div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12pt;" class="yui_3_13_0_7_1398469210518_17"><div style="font-family: HelveticaNeue, Helvetica
Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12pt;" class="yui_3_13_0_1_1398469210518_3808"><div dir="ltr"><font size="2" face="Arial"> <b><span style="font-weight: bold;">À :</span></b> "election-methods@electorama.com" <election-methods@electorama.com> <br> <b><span style="font-weight: bold;">Envoyé le :</span></b> Vendredi 25 avril 2014 17h10<br> <b><span style="font-weight: bold;">Objet :</span></b> [EM] monotonicity + clone independence = Condorcet?<br> </font> </div> <div class="y_msg_container"><br></div></div></div><blockquote style="border: none; padding: 0px;"><div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12pt;" class="yui_3_13_0_7_1398469210518_17"><div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12pt;" class="yui_3_13_0_1_1398469210518_3808"><div class="y_msg_container"><div
id="yiv4113179740"><div><div style="color:#000;background-color:#fff;font-family:times new roman, new york, times, serif;font-size:12pt;" class="yui_3_13_0_1_1398469210518_3814"><div>Conjecture: If ballots rank all candidates with no equal ranking then any method that is both monotonic and independent of clones will elect the Condorcet winner if there is one.</div></div></div></div></div></div></div><div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12pt;" class="yui_3_13_0_7_1398469210518_17"><div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12pt;" class="yui_3_13_0_1_1398469210518_3808"><div class="y_msg_container"><div id="yiv4113179740"><div><div style="color:#000;background-color:#fff;font-family:times new roman, new york, times, serif;font-size:12pt;" class="yui_3_13_0_1_1398469210518_3814"><div>Can anyone supply a proof
or provide a counter example showing it is not true?</div></div></div></div></div></div></div></blockquote><div style="font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-size: 12pt;"><div style="font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial, 'Lucida Grande', sans-serif; font-size: 12pt;"><div class="y_msg_container"><div id="yiv4113179740"><div><div style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); font-family: 'times new roman', 'new york', times, serif; font-size: 12pt;"><div class="yiv4113179740yqt1126691046" id="yiv4113179740yqtfd37233"><div><br></div><div>Woodall made a few methods that violate Condorcet but satisfy Clone-Winner, Clone-Loser,</div><div>and Mono-Raise. They all use the "descending coalition" concept. The simplest one is Descending Solid </div><div>Coalitions (DSC). He gives this example of Condorcet <span style="font-size: 12pt;">failure, which
works for both DSC and DAC:</span></div><div><br></div><div>46 A>B>C</div><div>3 A>C>B</div><div>3 B>C>A</div><div>48 C>A>B</div><div><br></div><div>The CW is C, but in DSC and DAC the winner is A. What happens is that the ACB and CAB voters form</div><div>the largest coalition (for {A,C}), which disqualifies B from winning, but the 49 voters liking A best are </div><div>stronger than the 48 voters that like <span style="font-size: 12pt;">C best, or alternatively the 3 voters that like A the least.</span></div><div><span style="font-size: 12pt;"><br></span></div><div>What he calls "Approval AV" (i.e. IRV eliminating based on the initial "votes in total" figure, which can't</div><div>change due to eliminations, selecting the winner once someone has a majority of the transferable votes) also</div><div>may count. (Depends on whether you say the cloning operation can cause a candidate <span style="font-size: 12pt;">on
a ballot to </span><span style="font-size: 12pt;">split </span></div><div><span style="font-size: 12pt;">into candidates that are not uniformly either ranked or unranked just as the original </span><span style="font-size: 12pt;">candidate.)</span></div><div><br></div><div>I think Random Ballot might count depending on your definitions.</div><div><br></div><div>Kevin Venzke</div><div><br></div></div></div></div></div></div> </div> </div> </div></body></html>