<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:12pt"><div class="" style=""><span class="" style="">A better random ballot Condorcet method is: Chose a random ballot (and if it is not complete, draw others to break ties until there is a complete ranking). Eliminate the pair-wise loser of the two lowest ranked candidates. Repeat until one candidate remains. Elect that candidate.</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;" class=""><span class="" style=""><br class="" style=""></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;" class=""><span class="" style=""><span style="font-size: 12pt;" class="">I believe it has the following desired properties: monotonic, clone independent, only Smith candidates get a non-zero probability of being elected, independence of zero probability alternatives, and it requires the fewest number of pair comparisons and chooses the candidate that tends to be higher ranked than the previous version.</span> In the three candidate case, if there is a cycle, it will always choose the top ranked candidate from the random ballot. </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;" class=""><span class="" style=""><br class="" style=""></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;" class=""><span class="" style="">One can form a complete social ranking by starting from the lowest ranked candidate and moving candidates down if they lose to the one below it. The social ranking from the previous method is equivalent to starting from the highest ranked candidate and moving candidates up if they beat the one above it.</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;" class=""><span class="" style=""><br></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;" class=""><span class="" style=""><br class="" style=""></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;" class=""><br class="" style=""></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;" class=""><span style="background-color: transparent;" class=""> </span><br class="" style=""></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;" class=""><span class="" style=""><br class="" style=""></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;"
class=""><span class="" style=""> </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;" class=""><span class="" style=""><br class="" style=""></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;" class=""><span class="" style=""><br class="" style=""></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;" class=""><span class="" style=""><br class="" style=""></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;" class=""><span class="" style=""><br class="" style=""></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;" class=""><span class="" style=""><br class="" style=""></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;" class=""><span class="" style=""><br class="" style=""><br></span></div><div class="yahoo_quoted" style="display: block;"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 12pt;" class=""> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size:
12pt;" class=""> <div dir="ltr" class="" style=""> <font size="2" face="Arial" class="" style=""> On Wednesday, May 7, 2014 6:51 PM, Ross Hyman <rahyman@sbcglobal.net> wrote:<br class="" style=""> </font> </div> <br class="" style=""><br class="" style=""> <div class="" style=""><div id="yiv4724370862" class="" style=""><div class="" style=""><div style="color:#000;background-color:#fff;font-family:times new roman, new york, times, serif;font-size:12pt;" class=""><div class="" style="">Random Ballot Condorcet: Choose a random ballot. <span style="font-size:12pt;" class="">Elect the lowest ranked candidate that pairwise beats all higher ranked candidates.</span></div><div style="color:rgb(0, 0, 0);font-size:12pt;font-family:'times new roman', 'new york', times, serif;background-color:transparent;font-style:normal;" class=""><span style="font-size:12pt;" class=""><br clear="none" class="" style=""></span></div><div style="color:rgb(0,
0, 0);font-size:16px;font-family:'times new roman', 'new york', times, serif;background-color:transparent;font-style:normal;" class="">Has this method been discussed before? I believe that the following are true: It will always elect a Condorcet candidate if there is one. Otherwise it will elect a member of the Smith set with some nonzero probability for each member of the Smith set.
Non-Smith set candidates will have zero probability of being elected. It is monotonic in that raising a candidate on some ballots cannot decrease its probability of being elected. It is clone proof in that the probability of electing from the clone set is independent of the number of clones in the set. It is independent of irrelevant alternatives in that deleting a candidate with zero probability of winning cannot effect the probabilities for electing other candidates. </div><div class="" id="yiv4724370862yqtfd00675" style=""><div style="color:rgb(0, 0, 0);font-size:16px;font-family:'times new roman', 'new york', times, serif;background-color:transparent;font-style:normal;" class=""> </div><div style="color:rgb(0, 0, 0);font-size:16px;font-family:'times new roman', 'new york', times, serif;background-color:transparent;font-style:normal;" class=""><br clear="none" class="" style=""></div><div style="color:rgb(0, 0,
0);font-size:16px;font-family:'times new roman', 'new york', times, serif;background-color:transparent;font-style:normal;" class=""> </div><div class="" style=""><br clear="none" class="" style=""></div><div style="color:rgb(0, 0, 0);font-size:16px;font-family:'times new roman', 'new york', times, serif;background-color:transparent;font-style:normal;" class=""><br clear="none" class="" style=""></div><div style="color:rgb(0, 0, 0);font-size:16px;font-family:'times new roman', 'new york', times, serif;background-color:transparent;font-style:normal;" class=""><br clear="none" class="" style=""></div> </div></div></div></div><br class="" style=""><br class="" style=""></div> </div> </div> </div> </div></body></html>