<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_1506874326165_3159">It gives the same result (at least for this instance) if we change the method to <br></div><div id="yui_3_16_0_ym19_1_1506874326165_3160" dir="ltr"><span id="yui_3_16_0_ym19_1_1506874326165_3163">Repeatedly remove the weakest link whose removal leaves at least one transitive
ranking of all of the candidates in which there is a beat path from each higher ranked candidate to each lower ranked candidate. When only one such
ranking exists, elect that ranking of candidates. <br></span></div><div dir="ltr" id="yui_3_16_0_ym19_1_1506874326165_3291"><span id="yui_3_16_0_ym19_1_1506874326165_3363">The ranking it produces for the previous example: </span><span id="yui_3_16_0_ym19_1_1506874326165_3163"><span id="yui_3_16_0_ym19_1_1506874326165_3364">D>C>B>A, differs from Tideman, Schulze, and River. The local links that it keeps: D>C, C>B, and B>A are in a sense better than the Tidman order local links C>B, B>A, A>D. Since D>C is stronger than A>D. <br></span></span></div><div dir="ltr" id="yui_3_16_0_ym19_1_1506874326165_3355"><span id="yui_3_16_0_ym19_1_1506874326165_3163"><br></span></div><div dir="ltr" id="yui_3_16_0_ym19_1_1506874326165_3195"><span id="yui_3_16_0_ym19_1_1506874326165_3163"><br></span></div><div id="yui_3_16_0_ym19_1_1506874326165_3060"><span></span></div> <div class="qtdSeparateBR"><br><br></div><div class="yahoo_quoted" style="display: block;"> <div style="font-family: Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 13px;"> <div style="font-family: HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif; font-size: 16px;"> <div dir="ltr"><font size="2" face="Arial"> On Sunday, October 1, 2017 7:42 AM, Ross Hyman <rahyman@sbcglobal.net> wrote:<br></font></div> <br><br> <div class="y_msg_container"><div id="yiv3974442255"><div><div style="color:#000;background-color:#fff;font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px;"><div dir="ltr" id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3076"><span id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3664">Repeatedly remove the weakest link whose removal leaves at least one
ranking of all of the candidates in which there is a direct win for the
higher candidate over the next lower candidate. When only one such
ranking exists, elect that ranking of candidates. <br clear="none"></span></div><div dir="ltr" id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3364"><span><br clear="none"></span></div><div dir="ltr" id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3355"><span id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3354">This method is different from Tideman Ranked pairs.</span></div><div dir="ltr" id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3350"><span id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3349">Consider the pair ordering B>D, B>A, C>B, D>C, C>A, A>D.<br clear="none"></span></div><div dir="ltr" id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3374"><span id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3349">The above method produces: D>C>B>A. The Tideman order is C>B>A>D. The Tideman order is better. The Schulze winner is also C.<br clear="none"></span></div><div dir="ltr" id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3648"><div dir="ltr" id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3657"><br id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3649" clear="none"></div></div><div dir="ltr" id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3615"><span id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3349"></span></div><div dir="ltr" id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3594"><span id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3349"><br clear="none"></span></div><div dir="ltr" id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3595"><span id="yiv3974442255yui_3_16_0_ym19_1_1506860581955_3349"><br clear="none"></span></div> <div class="yiv3974442255qtdSeparateBR"><br clear="none"><br clear="none"></div><div class="yiv3974442255yqt3460377046" id="yiv3974442255yqt89119"><div class="yiv3974442255yahoo_quoted" style="display:block;"> <div style="font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px;"> <div style="font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:16px;"> <div dir="ltr"><font size="2" face="Arial"> On Saturday, September 30, 2017 12:57 PM, Ross Hyman <rahyman@sbcglobal.net> wrote:<br clear="none"></font></div> <br clear="none"><br clear="none"> <div class="yiv3974442255y_msg_container"><div dir="ltr">Let’s play Jenga!<br clear="none"></div><div dir="ltr"><br clear="none"></div><div dir="ltr">I think that Schulze has pointed out in earlier posts that his method is equivalent to the following:<br clear="none"></div><div dir="ltr"><br clear="none"></div><div dir="ltr">Repeatedly remove the weakest link whose removal leaves at least one candidate with a beat path to every other candidate. When only one such candidate has a beat path to every other candidate, elect that candidate.<br clear="none"></div><div dir="ltr"><br clear="none"></div><div dir="ltr"><br clear="none"></div><div dir="ltr">This way of looking at the Schulze method resembles the game Jenga, where one repeatedly removes blocks from a tower, attempted to preserve some structure in the tower to hold it up. (Ok, I know that in real Jenga you put the blocks back at the top but it’s the best analogy I can think of.)<br clear="none"></div><div dir="ltr"><br clear="none"></div><div dir="ltr"><br clear="none"></div><div dir="ltr">The Schulze method preserves the simplest possible structure for which there is one winner. But one can imagine more complicated structures, each resulting in a different method. <br clear="none"></div><div dir="ltr">For example: Repeatedly remove the weakest link whose removal leaves at least one ranking of all of the candidates in which there is a direct win for the higher candidate over the next lower candidate. When only one such ranking exists, elect that ranking of candidates. <br clear="none"></div><div dir="ltr"><br clear="none"></div><div dir="ltr">Schulze’s method produces a tree structure like Jobst Heitzig’s River method but I believe the two methods in general produce different results. The method I just proposed above produces a ranking like Tideman’s Ranked Pairs method. Will it in general produce a different ranking than Tideman?<br clear="none"></div><div dir="ltr"><br clear="none"></div><div dir="ltr">Let’s say you wanted to elect two candidates. Perhaps you would want to preserve that structure that produces a unique winner and a unique runner up by preserving a structure that is a combination of Ranking and River.<br clear="none"></div><div dir="ltr"><br clear="none"></div><div dir="ltr">Repeatedly remove the weakest link whose removal leaves at least one pair of candidates with the property that the first one has a direct win over the second candidate and the second candidate has a beat path to every other candidate. When only one such pair of candidates exist, elect them to the first and second position. </div><br clear="none"><br clear="none"></div> </div> </div> </div></div></div></div></div><br><br></div> </div> </div> </div></div></body></html>