<html><head></head><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:12px"><div id="yui_3_16_0_1_1480114129033_68606"><font size="3" id="yui_3_16_0_1_1480114129033_68843">I'll define a simple "ballot space," meaning a range of scenarios that can occur given voter, candidate, and ballot limitations. Then I'll talk about the "method space" for that ballot space, meaning the range of methods that are possible to define.</font></div><div id="yui_3_16_0_1_1480114129033_68607"><font size="3"><br id="yui_3_16_0_1_1480114129033_68608"></font></div><div id="yui_3_16_0_1_1480114129033_68609"><font size="3" id="yui_3_16_0_1_1480114129033_70273">Let there be three factions, each preferring a different one of candidates labeled A, B, and C. The "A bloc" is the largest, with B being second-largest, and C being smallest. No bloc is a majority, but any two blocs would be a majority. Every voter within a bloc votes exactly the same (so that we see, total, only three unique ways of filling out the ballot). Every ballot is required to be a full, strict ranking. Additionally, each bloc will always rank their preferred candidate at the top.</font></div><div id="yui_3_16_0_1_1480114129033_68610"><font size="3"><br id="yui_3_16_0_1_1480114129033_68611"></font></div><div id="yui_3_16_0_1_1480114129033_68612"><font size="3" id="yui_3_16_0_1_1480114129033_68889">Since each bloc can only fill out the ballot in two ways (e.g. A>B>C or A>C>B for the A bloc), this ballot space has only 2^3 = 8 scenarios:</font></div><div id="yui_3_16_0_1_1480114129033_68613"><font size="3" id="yui_3_16_0_1_1480114129033_68890" face="Courier New, courier, monaco, monospace, sans-serif">1. A>B B>A C>A ballots. A+B mutual majority, A is CW.</font></div><div id="yui_3_16_0_1_1480114129033_68614"><font size="3" id="yui_3_16_0_1_1480114129033_68891" face="Courier New, courier, monaco, monospace, sans-serif">2. A>B B>A C>B. A+B mutual majority, B is CW.</font></div><div id="yui_3_16_0_1_1480114129033_68615"><font size="3" id="yui_3_16_0_1_1480114129033_68892" face="Courier New, courier, monaco, monospace, sans-serif">3. A>B B>C C>A. A>B>C>A preference cycle.</font></div><div id="yui_3_16_0_1_1480114129033_68616"><font size="3" id="yui_3_16_0_1_1480114129033_68893" face="Courier New, courier, monaco, monospace, sans-serif">4. A>B B>C C>B. B+C mutual majority, B is CW.</font></div><div id="yui_3_16_0_1_1480114129033_68617"><font size="3" id="yui_3_16_0_1_1480114129033_69056" face="Courier New, courier, monaco, monospace, sans-serif">5. A>C B>A C>A. A+C mutual majority, A is CW.</font></div><div id="yui_3_16_0_1_1480114129033_68618"><font size="3" id="yui_3_16_0_1_1480114129033_68894" face="Courier New, courier, monaco, monospace, sans-serif">6. A>C B>A C>B. A>C>B>A preference cycle.</font></div><div id="yui_3_16_0_1_1480114129033_68619"><font size="3" id="yui_3_16_0_1_1480114129033_69055" face="Courier New, courier, monaco, monospace, sans-serif">7. A>C B>C C>A. A+C mutual majority, C is CW.</font></div><div id="yui_3_16_0_1_1480114129033_68620"><font size="3" id="yui_3_16_0_1_1480114129033_69054" face="Courier New, courier, monaco, monospace, sans-serif">8. A>C B>C C>B. B+C mutual majority, C is CW.</font></div><div id="yui_3_16_0_1_1480114129033_68621"><font size="3"><br id="yui_3_16_0_1_1480114129033_68622"></font></div><div id="yui_3_16_0_1_1480114129033_68623"><font size="3" id="yui_3_16_0_1_1480114129033_68969">If we put a sequence of eight As, Bs, or Cs in a row to show who wins in each scenario, that sequence can define a method for this ballot space. I call this a DNA code.</font></div><div id="yui_3_16_0_1_1480114129033_68624"><font size="3"><br id="yui_3_16_0_1_1480114129033_68625"></font></div><div id="yui_3_16_0_1_1480114129033_68626"><font size="3" id="yui_3_16_0_1_1480114129033_68970">I have 343-digit codes, covering a larger ballot space, for a few dozen election methods. But in this eight-scenario space these reduce to a quite small number of codes. For methods that use an approval concept, I use the assumption that only the bottom candidate is unapproved. Here then is a full list (so far) of the 8-digit codes resulting from methods that are at least mostly serious:</font></div><div id="yui_3_16_0_1_1480114129033_68627"><font size="3"><br id="yui_3_16_0_1_1480114129033_68628"></font></div><div id="yui_3_16_0_1_1480114129033_68629"><font size="3" id="yui_3_16_0_1_1480114129033_68859">AAAAAAAA: FPP has its own code. Notice how it just elects A no matter what any lower preferences are.</font></div><div id="yui_3_16_0_1_1480114129033_68630"><font size="3"><br id="yui_3_16_0_1_1480114129033_68631"></font></div><div id="yui_3_16_0_1_1480114129033_68632"><font size="3" id="yui_3_16_0_1_1480114129033_68895">ABABAACC: The MinMax group. This includes most MinMax methods (including also Schulze, MAM, etc.), DMC, Approval-Elimination Runoff, MAMPO, some scenarios of Kristofer's "linear" Condorcet method, a couple of obscure Woodall methods (MinGS and 3MaxGS), Condorcet//FPP, and probably a lot of other methods.</font></div><div id="yui_3_16_0_1_1480114129033_68633"><font size="3"><br id="yui_3_16_0_1_1480114129033_68634"></font></div><div id="yui_3_16_0_1_1480114129033_68635"><font size="3" id="yui_3_16_0_1_1480114129033_69042">ABBBAACC: The Bucklin group. This includes Chris' IBIFA, Condorcet//Approval and ICA, MDDA, CdlA, MinMax(AWP), and probably many others. Note that, within this ballot space, these are a Condorcet method!</font></div><div id="yui_3_16_0_1_1480114129033_68636"><font size="3"><br id="yui_3_16_0_1_1480114129033_68637"></font></div><div id="yui_3_16_0_1_1480114129033_68638"><font size="3" id="yui_3_16_0_1_1480114129033_68896">AAABAAAC: The "descending coalitions" group. It includes DAC, DSC, and a couple of my methods (SPST, and both pairwise and Bucklinesque versions of "Venzke Bucklin Variant" aka VBV). </font></div><div id="yui_3_16_0_1_1480114129033_68639"><font size="3"><br id="yui_3_16_0_1_1480114129033_68640"></font></div><div id="yui_3_16_0_1_1480114129033_68641"><font size="3" id="yui_3_16_0_1_1480114129033_68858">ABABABAB: IRV group, including my "King of the Hill" (KH) method and IRV-without-elimination.</font></div><div id="yui_3_16_0_1_1480114129033_68642"><font size="3"><br id="yui_3_16_0_1_1480114129033_68643"></font></div><div id="yui_3_16_0_1_1480114129033_68644"><font size="3" id="yui_3_16_0_1_1480114129033_68949">ABABABCC: Condorcet//IRV group, including Raynaud, Condorcet//KH, and most scenarios of Kristofer's "linear" method. Off the top of my head it should also include the "Woodall" and "Benham" methods.</font></div><div id="yui_3_16_0_1_1480114129033_68645"><font size="3"><br id="yui_3_16_0_1_1480114129033_68646"></font></div><div id="yui_3_16_0_1_1480114129033_68647"><font size="3" id="yui_3_16_0_1_1480114129033_68897">ABABACAC: my QR, aka Chain Runoff.</font></div><div id="yui_3_16_0_1_1480114129033_68648"><font size="3"><br id="yui_3_16_0_1_1480114129033_68649"></font></div><div id="yui_3_16_0_1_1480114129033_68650"><font size="3" id="yui_3_16_0_1_1480114129033_69115">ABABACCC: Condorcet//QR.</font></div><div id="yui_3_16_0_1_1480114129033_68651"><font size="3"><br id="yui_3_16_0_1_1480114129033_68652"></font></div><div id="yui_3_16_0_1_1480114129033_68653"><font size="3" id="yui_3_16_0_1_1480114129033_68898">ABBBACCC: Forest's TACC method.</font></div><div id="yui_3_16_0_1_1480114129033_68654"><font size="3"><br id="yui_3_16_0_1_1480114129033_68655"></font></div><div id="yui_3_16_0_1_1480114129033_68656"><font size="3" id="yui_3_16_0_1_1480114129033_68950">ABCBABCC: BPW (Eivind Stensholt's "Beats Plurality Winner" Condorcet method).</font></div><div id="yui_3_16_0_1_1480114129033_68657"><font size="3"><br id="yui_3_16_0_1_1480114129033_68658"></font></div><div id="yui_3_16_0_1_1480114129033_68659"><font size="3" id="yui_3_16_0_1_1480114129033_68951">AAABAAAB: VDP (Venzke Disqualified Plurality, aka VFA). </font></div><div id="yui_3_16_0_1_1480114129033_68660"><font size="3"><br id="yui_3_16_0_1_1480114129033_68661"></font></div><div id="yui_3_16_0_1_1480114129033_68662"><font size="3" id="yui_3_16_0_1_1480114129033_68857">That's really it... Other known codes are limited to experiments like "IRV where you eliminate the wrong candidate" or "just elect the winner of the strongest pairwise contest." (Let me know if you think there's an unusual method I've missed, and that can operate on these ballots.)</font></div><div id="yui_3_16_0_1_1480114129033_68663"><font size="3"><br id="yui_3_16_0_1_1480114129033_68664"></font></div><div id="yui_3_16_0_1_1480114129033_68665"><font size="3" id="yui_3_16_0_1_1480114129033_68849">Here is an attempt at plotting the Hamming distances of these codes, so that more similar methods are plotted closer together:</font></div><div id="yui_3_16_0_1_1480114129033_68666"><font id="yui_3_16_0_1_1480114129033_68906" face="Courier New, courier, monaco, monospace, sans-serif" size="2"><br id="yui_3_16_0_1_1480114129033_68667"></font></div><div id="yui_3_16_0_1_1480114129033_68668"><font id="yui_3_16_0_1_1480114129033_68855" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . TACC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68669"><font id="yui_3_16_0_1_1480114129033_68850" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BPW . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68670"><font id="yui_3_16_0_1_1480114129033_68851" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68671"><font id="yui_3_16_0_1_1480114129033_68852" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68672"><font id="yui_3_16_0_1_1480114129033_68905" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68673"><font id="yui_3_16_0_1_1480114129033_68904" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. Bucklin . . . . . . . . . . . . C//QR . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68674"><font id="yui_3_16_0_1_1480114129033_68908" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ------- </font></div><div id="yui_3_16_0_1_1480114129033_68675"><font id="yui_3_16_0_1_1480114129033_68903" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ./. . . . </font></div><div id="yui_3_16_0_1_1480114129033_68676"><font id="yui_3_16_0_1_1480114129033_68888" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . C//IRV. . . . . . --------- . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68677"><font id="yui_3_16_0_1_1480114129033_68863" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ./. . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68678"><font id="yui_3_16_0_1_1480114129033_68887" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .------ . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68679"><font id="yui_3_16_0_1_1480114129033_68886" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68680"><font id="yui_3_16_0_1_1480114129033_68885" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . MinMax. . . . . . . . . . . . . . . . . ./. . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68681"><font id="yui_3_16_0_1_1480114129033_68909" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . --Condorcet-Boundary--- . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68682"><font id="yui_3_16_0_1_1480114129033_68884" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . ./. . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68683"><font id="yui_3_16_0_1_1480114129033_68883" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . / . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68684"><font id="yui_3_16_0_1_1480114129033_68910" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . ------. . . . . . QR. . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68685"><font id="yui_3_16_0_1_1480114129033_68882" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . ./. . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68686"><font id="yui_3_16_0_1_1480114129033_68881" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68687"><font id="yui_3_16_0_1_1480114129033_68845" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . .---------------------. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68688"><font id="yui_3_16_0_1_1480114129033_68844" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IRV .</font></div><div id="yui_3_16_0_1_1480114129033_68689"><font id="yui_3_16_0_1_1480114129033_68846" face="Courier New, courier, monaco, monospace, sans-serif" size="2">----. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68690"><font id="yui_3_16_0_1_1480114129033_68847" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68691"><font id="yui_3_16_0_1_1480114129033_68848" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68692"><font id="yui_3_16_0_1_1480114129033_68902" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68693"><font id="yui_3_16_0_1_1480114129033_68880" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68694"><font id="yui_3_16_0_1_1480114129033_68901" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . DAC/DSC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68695"><font id="yui_3_16_0_1_1480114129033_68879" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68696"><font id="yui_3_16_0_1_1480114129033_68878" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68697"><font id="yui_3_16_0_1_1480114129033_68914" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68698"><font id="yui_3_16_0_1_1480114129033_68877" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68699"><font id="yui_3_16_0_1_1480114129033_68865" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68700"><font id="yui_3_16_0_1_1480114129033_68869" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . VDP . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68701"><font id="yui_3_16_0_1_1480114129033_68870" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68702"><font id="yui_3_16_0_1_1480114129033_68871" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68703"><font id="yui_3_16_0_1_1480114129033_68872" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68704"><font id="yui_3_16_0_1_1480114129033_68873" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68705"><font id="yui_3_16_0_1_1480114129033_68874" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68706"><font id="yui_3_16_0_1_1480114129033_68875" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68707"><font id="yui_3_16_0_1_1480114129033_68876" face="Courier New, courier, monaco, monospace, sans-serif" size="2">. FPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . </font></div><div id="yui_3_16_0_1_1480114129033_68708"><font size="3"><br id="yui_3_16_0_1_1480114129033_68709"></font></div><div id="yui_3_16_0_1_1480114129033_68710"><font size="3" id="yui_3_16_0_1_1480114129033_68968">That is 11 methods in a method space containing 3^8 = 6561 methods. Can we find any more methods?</font></div><div id="yui_3_16_0_1_1480114129033_68711"><font size="3"><br id="yui_3_16_0_1_1480114129033_68712"></font></div><div id="yui_3_16_0_1_1480114129033_68713"><font size="3" id="yui_3_16_0_1_1480114129033_68984">In all of those 6561, only nine of them are Condorcet methods. I can describe all of them:</font></div><div id="yui_3_16_0_1_1480114129033_68714"><font size="3" face="Courier New, courier, monaco, monospace, sans-serif"><br id="yui_3_16_0_1_1480114129033_68715"></font></div><div id="yui_3_16_0_1_1480114129033_68716"><font size="3" id="yui_3_16_0_1_1480114129033_69002" face="Courier New, courier, monaco, monospace, sans-serif">ABABAACC: MinMax</font></div><div id="yui_3_16_0_1_1480114129033_68717"><font size="3" id="yui_3_16_0_1_1480114129033_69001" face="Courier New, courier, monaco, monospace, sans-serif">ABABABCC: C//IRV</font></div><div id="yui_3_16_0_1_1480114129033_68718"><font size="3" id="yui_3_16_0_1_1480114129033_69000" face="Courier New, courier, monaco, monospace, sans-serif">ABABACCC: C//QR</font></div><div id="yui_3_16_0_1_1480114129033_68719"><font size="3" id="yui_3_16_0_1_1480114129033_68999" face="Courier New, courier, monaco, monospace, sans-serif">ABBBAACC: Bucklin</font></div><div id="yui_3_16_0_1_1480114129033_68720"><font size="3" id="yui_3_16_0_1_1480114129033_68998" face="Courier New, courier, monaco, monospace, sans-serif">ABBBABCC: (???) always elect B in a cycle</font></div><div id="yui_3_16_0_1_1480114129033_68721"><font size="3" face="Courier New, courier, monaco, monospace, sans-serif" id="yui_3_16_0_1_1480114129033_71602">ABBBACCC: TACC</font></div><div id="yui_3_16_0_1_1480114129033_68722"><font size="3" id="yui_3_16_0_1_1480114129033_68997" face="Courier New, courier, monaco, monospace, sans-serif">ABCBAACC: Condorcet//"IRV where you eliminate second-lowest tally"</font></div><div id="yui_3_16_0_1_1480114129033_68723"><font size="3" face="Courier New, courier, monaco, monospace, sans-serif" id="yui_3_16_0_1_1480114129033_71603">ABCBABCC: BPW</font></div><div id="yui_3_16_0_1_1480114129033_68724"><font size="3" id="yui_3_16_0_1_1480114129033_68996" face="Courier New, courier, monaco, monospace, sans-serif">ABCBACCC: (???) always elect C in a cycle</font></div><div id="yui_3_16_0_1_1480114129033_68725"><font size="3"><br id="yui_3_16_0_1_1480114129033_68726"></font></div><div id="yui_3_16_0_1_1480114129033_68727"><font size="3" id="yui_3_16_0_1_1480114129033_68995">Only two scenarios lack a CW, leaving not a lot of room to experiment.</font></div><div id="yui_3_16_0_1_1480114129033_68728"><font size="3"><br id="yui_3_16_0_1_1480114129033_68729"></font></div><div id="yui_3_16_0_1_1480114129033_68730"><font size="3" id="yui_3_16_0_1_1480114129033_68994">How about non-Condorcet methods? Where is their diversity located? Let's ignore FPP and remove the cycle scenarios, so that we can just see where and why methods choose not to elect a CW:</font></div><div id="yui_3_16_0_1_1480114129033_68731"><font size="3"><br id="yui_3_16_0_1_1480114129033_68732"></font></div><div id="yui_3_16_0_1_1480114129033_68733"><font size="3" id="yui_3_16_0_1_1480114129033_68993" face="Courier New, courier, monaco, monospace, sans-serif">AB_BA_CC: Condorcet methods</font></div><div id="yui_3_16_0_1_1480114129033_68734"><font size="3" id="yui_3_16_0_1_1480114129033_69024" face="Courier New, courier, monaco, monospace, sans-serif">AA_BA_AB: VDP</font></div><div id="yui_3_16_0_1_1480114129033_68735"><font size="3" id="yui_3_16_0_1_1480114129033_69023" face="Courier New, courier, monaco, monospace, sans-serif">AB_BA_AB: IRV</font></div><div id="yui_3_16_0_1_1480114129033_68736"><font size="3" id="yui_3_16_0_1_1480114129033_69027" face="Courier New, courier, monaco, monospace, sans-serif">AB_BA_AC: QR</font></div><div id="yui_3_16_0_1_1480114129033_68737"><font size="3" id="yui_3_16_0_1_1480114129033_69022" face="Courier New, courier, monaco, monospace, sans-serif">AA_BA_AC: DAC/DSC </font></div><div id="yui_3_16_0_1_1480114129033_68738"><font size="3"><br id="yui_3_16_0_1_1480114129033_68739"></font></div><div id="yui_3_16_0_1_1480114129033_68740"><font size="3" id="yui_3_16_0_1_1480114129033_69003">The disagreements come in scenarios 2, 7, and 8. If you check you'll see that they can be summarized in one statement: Non-Condorcet methods may prefer to elect the candidate of the larger bloc of a mutual majority, rather than the candidate of the majority who is the CW. (Note that the CW is the second preference of the faction excluded from the majority.)</font></div><div id="yui_3_16_0_1_1480114129033_68741"><font size="3"><br id="yui_3_16_0_1_1480114129033_68742"></font></div><div id="yui_3_16_0_1_1480114129033_68743"><font size="3" id="yui_3_16_0_1_1480114129033_69004">In the scenarios where the CW is also from the larger bloc of the mutual majority, all methods agree (except for FPP in scenario 4). And no method outside of FPP will elect the Condorcet Loser (in this ballot space), as it would violate mutual majority. So it seems likely there are few possibilities for reasonable methods. If you don't think it's reasonable to elect C in the cycles, it might only be 2^5 = 32 possible methods.</font></div><div id="yui_3_16_0_1_1480114129033_68744"><font size="3"><br id="yui_3_16_0_1_1480114129033_68745"></font></div><div id="yui_3_16_0_1_1480114129033_68746"><font size="3" id="yui_3_16_0_1_1480114129033_69005">That's all for now. I hope in the future to discuss scenarios with more ballot types.</font></div><div id="yui_3_16_0_1_1480114129033_68747"><font size="3"><br id="yui_3_16_0_1_1480114129033_68748"></font></div><div id="yui_3_16_0_1_1480114129033_68749"><font size="3" id="yui_3_16_0_1_1480114129033_69006">Kevin Venzke</font></div><div dir="ltr" id="yui_3_16_0_1_1480114129033_68750"><br id="yui_3_16_0_1_1480114129033_68751"></div></div></body></html>