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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal>Here is a simple plurality-based Condorcet election method.<o:p></o:p></p><p class=MsoNormal>The method consists of a series of rounds. Each round permanently eliminates 1 candidate and elects all other uneliminated candidates to the next round. Repeat until just 1 candidate is elected to the next round. That candidate is the winner of the election. <o:p></o:p></p><p class=MsoNormal>V_A equals the sum of ballots with candidate A the highest ranked hopeful candidate.<o:p></o:p></p><ol style='margin-top:0in' start=1 type=1><li class=MsoListParagraphCxSpFirst style='margin-left:0in;mso-add-space:auto;mso-list:l1 level1 lfo1'>All elected candidates from the previous round are declared hopeful (If this is the first round, all candidates are hopeful).<o:p></o:p></li><li class=MsoListParagraphCxSpLast style='margin-left:0in;mso-add-space:auto;mso-list:l1 level1 lfo1'>Identify hopeful candidate A with the largest V_A. Declare candidate A elected. Repeat until there is just one remaining hopeful candidate. Eliminate the one remaining hopeful candidate. This ends the round. <o:p></o:p></li></ol><p class=MsoNormal>The method is Condorcet since eliminated candidates are the losers of a two-candidate election and Condorcet winners cannot lose an election with two candidates.<o:p></o:p></p><p class=MsoNormal>Example<o:p></o:p></p><p class=MsoNormal>7 R D P<o:p></o:p></p><p class=MsoNormal>6 P D R<o:p></o:p></p><p class=MsoNormal>5 D P R<o:p></o:p></p><p class=MsoNormal>Round 1: R is the plurality winner and is elected to the next round. D is next plurality winner is elected to the next round (ballots that had R as the highest ranked hopeful candidate now have D the highest ranked hopeful candidate). P is eliminated<o:p></o:p></p><p class=MsoNormal>Round 2 D is the plurality winner and the winner of the election.<o:p></o:p></p><p class=MsoNormal>Generalization to elect N candidates proportionally.<o:p></o:p></p><p class=MsoNormal>The method consists of a series of rounds. Each round permanently eliminates 1 candidate and elects all other uneliminated candidates to the next round. Continue until just N candidates are elected to the next round. Elect those N candidates. <o:p></o:p></p><p class=MsoNormal>V_A equals the sum of ballots with candidate A the highest ranked hopeful candidate.<o:p></o:p></p><p class=MsoNormal><a name="_Hlk526590374">S_A equals the sum of seat values of all ballots with candidate A the highest ranked hopeful candidate.<o:p></o:p></a></p><span style='mso-bookmark:_Hlk526590374'></span><p class=MsoNormal><a name="_Hlk526588008">Steps for a round.<o:p></o:p></a></p><ol style='margin-top:0in' start=1 type=1><li class=MsoListParagraphCxSpFirst style='margin-left:0in;mso-add-space:auto;mso-list:l0 level1 lfo2'><span style='mso-bookmark:_Hlk526588008'>All elected candidates from the previous round are declared hopeful (If this is the first round, all candidates are hopeful). All ballots are assigned seat value s=0.<o:p></o:p></span></li><li class=MsoListParagraphCxSpMiddle style='margin-left:0in;mso-add-space:auto;mso-list:l0 level1 lfo2'><span style='mso-bookmark:_Hlk526588008'>If there are more than N+1 hopeful candidates, identify hopeful candidate A with the largest V_A. Declare candidate A elected. Repeat until there are N+1 hopeful candidates.<o:p></o:p></span></li><li class=MsoListParagraphCxSpLast style='margin-left:0in;mso-add-space:auto;mso-list:l0 level1 lfo2'><span style='mso-bookmark:_Hlk526588008'>Identify hopeful candidate A with largest priority V_A/(S_A+1). Assign new seat value s= (S_A+1)/V_A to all ballots with candidate A the highest ranked hopeful candidate. Declare candidate A elected. Repeat until there is just one remaining hopeful candidate. Eliminate the one remaining hopeful candidate. This ends the round. </span><o:p></o:p></li></ol><p class=MsoNormal>The method won’t eliminate candidates that are the winners of ever N+1 candidate election that they are in.<o:p></o:p></p><p class=MsoNormal>Elect 2.<o:p></o:p></p><p class=MsoNormal>100 A1>A2<o:p></o:p></p><p class=MsoNormal>49 B1>B2<o:p></o:p></p><p class=MsoNormal>48 C1>C2<o:p></o:p></p><p class=MsoNormal>47 D1>D2<o:p></o:p></p><p class=MsoNormal>46 E1>E2<o:p></o:p></p><p class=MsoNormal>45 F1>F2<o:p></o:p></p><p class=MsoNormal>Round 1: <a name="_Hlk527199513">Step2 elects A1,A2,B1,B2,C1,C2,D1,D2,E1. Step 3 elects E2,F1. F2 is eliminated.</a><o:p></o:p></p><p class=MsoNormal>Round 2: Step2 elects A1,A2,B1,B2,C1,C2,D1,D2. Step 3 elects E1,F1. E2 is eliminated.<o:p></o:p></p><p class=MsoNormal>Round 3: Step2 elects A1,A2,B1,B2,C1,C2,D1. Step 3 elects D2,E1. F1 is eliminated.<o:p></o:p></p><p class=MsoNormal>Round 4: Step2 elects A1,A2,B1,B2,C1,C2. Step 3 elects D1,E1,. D2 is eliminated.<o:p></o:p></p><p class=MsoNormal><a name="_Hlk527200075">Round 5: Step2 elects A1,A2,B1,B2,C1. Step 3 elects C2,D1. E1 is eliminated.</a><o:p></o:p></p><p class=MsoNormal><a name="_Hlk527200080">Round 6: Step2 elects A1,A2,B1,B2. Step 3 elects C1, D1. C2 is eliminated.<o:p></o:p></a></p><span style='mso-bookmark:_Hlk527200080'></span><p class=MsoNormal>Round 7: Step2 elects A1,A2,B1. Step 3 elects B2, C1. D1 is eliminated.<o:p></o:p></p><p class=MsoNormal><a name="_Hlk527200201">Round 8: Step2 elects A1,A2. Step 3 elects B1,C1. B2 is eliminated.<o:p></o:p></a></p><span style='mso-bookmark:_Hlk527200201'></span><p class=MsoNormal><a name="_Hlk527200247">Round 9: Step2 elects A1. Step 3 elects A2, B1. C1 is eliminated.<o:p></o:p></a></p><span style='mso-bookmark:_Hlk527200247'></span><p class=MsoNormal>Round 10: Step 3 elects A1,A2. B1 is eliminated.<o:p></o:p></p><p class=MsoNormal>A1,A2 are elected.<o:p></o:p></p><p class=MsoNormal>Elect 2<o:p></o:p></p><p class=MsoNormal>20 A B <o:p></o:p></p><p class=MsoNormal>12 B C D A<o:p></o:p></p><p class=MsoNormal>14 C D B A<o:p></o:p></p><p class=MsoNormal>15 D C B A<o:p></o:p></p><p class=MsoNormal>Round 1: Step 2 elects A. Step 3 elects B,C. D is eliminated.<o:p></o:p></p><p class=MsoNormal>Round 2. Step 3 elects C,B. A is eliminated<o:p></o:p></p><p class=MsoNormal>B,C are elected.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>