<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="yiv7308356533"><div id="yui_3_16_0_ym19_1_1507406983353_5163"><div style="color:#000;background-color:#fff;font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px;" id="yui_3_16_0_ym19_1_1507406983353_5162"><div id="yiv7308356533"><div id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_2848"><div id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_2847" style="color:#000;background-color:#fff;font-family:Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:13px;"><div id="yiv7308356533yui_3_16_0_ym19_1_1507399274219_11493">Hi Kristofer,</div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507399274219_11494"><div id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3492">I found Warren Smith's votedesc.pdf document on M. Schulze's site: <a rel="nofollow" shape="rect" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_2878" target="_blank" href="http://m-schulze.9mail.de/votedesc.pdf">http://m-schulze.9mail.de/votedesc.pdf</a></div></div><div id="yiv7308356533yui_3_16_0_ym19_1_1507399274219_11471"><span></span></div> <div class="yiv7308356533qtdSeparateBR" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_2896"><br clear="none"><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_2948">This is a great document. I think it should be on the Election Methods website, especially since most of the other links to election method descriptions are broken. <br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3552"><br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3555"><div dir="ltr" id="yui_3_16_0_ym19_1_1507406983353_5248">The variation I am proposing to Warren's Maxtree method is to constrain the form of the spanning tree to a directed chain (or whatever the official name is) A>B>C>D.... and then maximize the minimum link. I haven't had time to think about it too much but I am hoping the method will satisfy local independence of irrelevant alternatives. <br></div></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3213"><br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3256">What's up with the election methods list? I have not seen my posting or your response to it on the archive, which is what I read. I don't get the emails. The last posting in the archive is from Sept 28. <br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3290"><br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3395">Best,</div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3396">Ross<br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3182"><br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3188"><br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3156"><br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3181"><br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3140"><br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3165"><br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3110"><br clear="none"></div><div dir="ltr"><br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3092"><br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3108"><br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3057"><br clear="none"></div><div dir="ltr" id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_3077"><br clear="none"></div><div id="yiv7308356533yui_3_16_0_ym19_1_1507406983353_2995"><br clear="none"></div><div><br clear="none"></div></div><div class="yiv7308356533yqt9943091480" id="yiv7308356533yqt43183"></div></div></div></div><div class="yiv7308356533yqt1003259898" id="yiv7308356533yqt92627"><div> <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 face="Arial" size="2"> On Sunday, October 1, 2017 2:02 PM, Kristofer Munsterhjelm <km_elmet@t-online.de> wrote:<br clear="none"></font></div> <br clear="none"><br clear="none"> <div class="yiv7308356533y_msg_container"><div dir="ltr">On 10/01/2017 02:42 PM, Ross Hyman wrote:<div class="yiv7308356533yqt3506351302" id="yiv7308356533yqtfd48515"><br clear="none">> Repeatedly remove the weakest link whose removal leaves at least one<br clear="none">> ranking of all of the candidates in which there is a direct win for the<br clear="none">> higher candidate over the next lower candidate. When only one such<br clear="none">> ranking exists, elect that ranking of candidates.<br clear="none">><br clear="none">> This method is different from Tideman Ranked pairs.<br clear="none">> Consider the pair ordering B>D, B>A, C>B, D>C, C>A, A>D.<br clear="none">> The above method produces: D>C>B>A. The Tideman order is C>B>A>D. The<br clear="none">> Tideman order is better. The Schulze winner is also C.</div><br clear="none"><br clear="none">Warren's Maxtree method is another Ranked-Pairs-like that it might be <br clear="none">interesting to investigate. The method's logic is akin to:<br clear="none"><br clear="none">- Ranked Pairs is similar to Kruskal's algorithm for finding a minimum <br clear="none">spanning tree in an undirected graph.<br clear="none">- But the graph induced by the Condorcet matrix is directed.<br clear="none">- So use an MST algorithm for weighted graphs instead.<br clear="none">- This algorithm is Chu-Liu-Edmonds and the method becomes max-tree. <br clear="none">(See Warren's votedesc.pdf for more information)<br clear="none"><br clear="none">I've never got around to implementing it, though.<div class="yiv7308356533yqt3506351302" id="yiv7308356533yqtfd69060"><br clear="none"></div></div><br clear="none"><br clear="none"></div> </div> </div> </div></div></div></div></div></div></body></html>