<html><head></head><body><div style="color:#000; background-color:#fff; font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px"><div id="yui_3_16_0_ym19_1_1501750267470_10605"><span id="yui_3_16_0_ym19_1_1501750267470_10604">Do you know what criteria this method passes/fails, and what advantages/disadvantages it has compared to other methods?</span></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1501750267470_10577"><br><br></div><div class="yahoo_quoted" id="yui_3_16_0_ym19_1_1501750267470_10502" style="display: block;"> <div id="yui_3_16_0_ym19_1_1501750267470_10501" style="font-family: Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 13px;"> <div id="yui_3_16_0_ym19_1_1501750267470_10500" style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif; font-size: 16px;"> <div id="yui_3_16_0_ym19_1_1501750267470_10595" dir="ltr"> <font id="yui_3_16_0_ym19_1_1501750267470_10594" face="Arial" size="2"> <hr size="1" id="yui_3_16_0_ym19_1_1501750267470_10596"> <b><span style="font-weight: bold;">From:</span></b> Ross Hyman <rahyman@sbcglobal.net><br> <b><span style="font-weight: bold;">To:</span></b> "election-methods@lists.electorama.com" <election-methods@lists.electorama.com> <br> <b><span style="font-weight: bold;">Sent:</span></b> Wednesday, 2 August 2017, 23:33<br> <b><span style="font-weight: bold;">Subject:</span></b> [EM] scale and shift independent ratings based Condorcet method<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_ym19_1_1501750267470_10499"><br><div dir="ltr">Sorry about the formatting. Second try.<br></div><div id="yui_3_16_0_ym19_1_1501750267470_10606" dir="ltr"><br></div><div id="yui_3_16_0_ym19_1_1501750267470_10498" dir="ltr"><br></div><div id="yui_3_16_0_ym19_1_1501750267470_10593" dir="ltr">Here is a ratings based Condorcet election method that uses ratings to determine how much each voter favors one candidate over another. But it does not use the ratings to compare candidates across ballots, as their ratings scales might be different. Perhaps they even used different ratings ballots. I believe it is the second simplest way to use a ratings ballot that gives the same results if each individual ballot undergoes an arbitrary rating shift or rescaling. (The simplist way is direct conversion of ratings to ranks. But this method includes more ratings information.) There is no need to ever shift or rescale any ballots as this can never change the results. The method uses the Tideman or Schulze method but will not always assign the same winner as those methods because it uses more ratings information than a direct conversion of ratings to rankings. The method uses more majority rule information than rankings based Condorcet. <br></div><div dir="ltr"><br></div><div dir="ltr">1.Voters rate candidates on ratings ballots of any type.<br></div><div dir="ltr">Example:<br></div><div dir="ltr">7 A = 1, B = 0.9, C=0<br></div><div dir="ltr">6 B=1,000,000,000 C = 400,000,000, A =1<br></div><div dir="ltr">5 C =1, A= - 0.7, B = -1<br></div><div dir="ltr"> <br></div><div dir="ltr">2. Each ratings ballot is turned into an individual ranked pair ballot. Each pair A>B is given the score Rating(A)-Rating(B) on a ballot. The pairs are ranked on each ballot from largest score to smallest score. From here on, the ratings ballots are dispensed with and only the ranked pair ballots are used.<br></div><div dir="ltr">Example:<br></div><div dir="ltr">7 A>C, B>C, A>B, B>A, C>B, C>A<br></div><div dir="ltr">6 B>A, B>C, C>A, A>C, C>B, A>B<br></div><div dir="ltr">5 C>B, C>A, A>B, B>A, A>C, B>C<br></div><div dir="ltr"> <br></div><div dir="ltr">3.For each pair of candidates, A,B if more voters rank A>B higher than B>A, then B>A is removed from each ballot. Steps 2 and 3 could easily be combined.<br></div><div dir="ltr">Example:<br></div><div dir="ltr">7 B>C, A>B, C>A<br></div><div dir="ltr">6 B>C, C>A, A>B<br></div><div dir="ltr">5 C>A, A>B, B>C<br></div><div dir="ltr"><br></div><div dir="ltr"><br></div><div dir="ltr">4. Now a societal ranking of pairs of ordered pairs is produced. This is done exactly as is done for Tideman or Schulze, except that the candidates are ordered pairs of candidates of the form (A>B) so the societal ordering will include entries like (A>B)>(C>D) if more voters<br></div><div dir="ltr">rank A>B higher than C>D. This is the step that uses more majority rule information than rankings based Condorcet. <br></div><div dir="ltr">Example:<br></div><div dir="ltr">(B>C)>(A>B) and (B>C)> (C>A) tied at 13, 5<br></div><div dir="ltr">(C>A)> (A>B) 11,7<br></div><div dir="ltr"> <br></div><div dir="ltr">5. Now the Tideman or Schulze method is used to turn the societal ranking of pairs of ordered pairs into a list of ranked pairs. <br></div><div dir="ltr">Example:<br></div><div dir="ltr">B>C<br></div><div dir="ltr">C>A<br></div><div dir="ltr">A>B<br></div><div dir="ltr"><br></div><div dir="ltr"><br></div><div dir="ltr">6.The Tideman or Schulze method is then used a second time to turn the ranked pairs list into an ordered list of candidates. <br></div><div dir="ltr">Example<br></div><div dir="ltr">B<br></div><div dir="ltr">C<br></div><div dir="ltr">A<br></div><div dir="ltr"> <br></div><div dir="ltr">7.The winner is the highest ranked on the candidate list.<br></div><div dir="ltr">Example <br></div><div dir="ltr">B wins<br></div><div dir="ltr"> <br></div><div dir="ltr">Using a direct conversion of ratings to rankings with just one Tideman/Schulze step, A.<br></div><div dir="ltr">----<br></div><div dir="ltr">Election-Methods mailing list - see <a href="http://electorama.com/em" target="_blank">http://electorama.com/em </a>for list info<br></div><br><br></div> </div> </div> </div></div></body></html>