In June 2008, Wikimedia used the Schulze method for the election to its Board of Trustees: One vacant seat had to be filled. There were 15 candidates, about 26,000 eligible voters, and 3,019 valid ballots.
Each ballot contains a list of all candidates. Each voter ranks these candidates in order of preference. Each voter gives a '1' to his favorite candidate, a '2' to his second favorite candidate, a '3' to his third favorite candidate, etc..
Each voter may ...
In total, 3019 valid ballots were cast. Each figure represents the number of voters who ranked the candidate at the left better than the candidate at the top. A figure in green represents a victory in that pairwise comparison by the candidate at the left. A figure in red represents a defeat in that pairwise comparison by the candidate at the left.
TC | AB | SK | HC | AH | JH | RP | SS | RS | DR | CS | MB | KW | PW | GK | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Ting Chen | 1086 | 1044 | 1108 | 1135 | 1151 | 1245 | 1190 | 1182 | 1248 | 1263 | 1306 | 1344 | 1354 | 1421 | |
Alex Bakharev | 844 | 932 | 984 | 950 | 983 | 1052 | 1028 | 990 | 1054 | 1073 | 1109 | 1134 | 1173 | 1236 | |
Samuel Klein | 836 | 910 | 911 | 924 | 983 | 980 | 971 | 941 | 967 | 1019 | 1069 | 1099 | 1126 | 1183 | |
Harel Cain | 731 | 836 | 799 | 896 | 892 | 964 | 904 | 917 | 959 | 1007 | 1047 | 1075 | 1080 | 1160 | |
Ad Huikeshoven | 674 | 781 | 764 | 806 | 832 | 901 | 868 | 848 | 920 | 934 | 987 | 1022 | 1030 | 1115 | |
Jussi-Ville Heiskanen | 621 | 720 | 712 | 755 | 714 | 841 | 798 | 737 | 827 | 850 | 912 | 970 | 943 | 1057 | |
Ryan Postlethwaite | 674 | 702 | 726 | 756 | 772 | 770 | 755 | 797 | 741 | 804 | 837 | 880 | 921 | 1027 | |
Steve Smith | 650 | 694 | 654 | 712 | 729 | 750 | 744 | 778 | 734 | 796 | 840 | 876 | 884 | 1007 | |
Ray Saintonge | 629 | 703 | 641 | 727 | 714 | 745 | 769 | 738 | 789 | 812 | 848 | 879 | 899 | 987 | |
Dan Rosenthal | 595 | 654 | 609 | 660 | 691 | 724 | 707 | 699 | 711 | 721 | 780 | 844 | 858 | 960 | |
Craig Spurrier | 473 | 537 | 498 | 530 | 571 | 583 | 587 | 577 | 578 | 600 | 646 | 721 | 695 | 845 | |
Matthew Bisanz | 472 | 498 | 465 | 509 | 508 | 534 | 473 | 507 | 531 | 513 | 552 | 653 | 677 | 785 | |
Kurt M. Weber | 505 | 535 | 528 | 547 | 588 | 581 | 553 | 573 | 588 | 566 | 595 | 634 | 679 | 787 | |
Paul Williams | 380 | 420 | 410 | 435 | 439 | 464 | 426 | 466 | 470 | 471 | 429 | 521 | 566 | 754 | |
Gregory Kohs | 411 | 412 | 434 | 471 | 461 | 471 | 468 | 461 | 467 | 472 | 491 | 523 | 513 | 541 |
A " circular tie" is a situation where a majority prefers candidate A to candidate B, a majority prefers candidate B to candidate C, and a majority prefers candidate C to candidate A.
In 2008, there was a circular tie between the candidates Jussi-Ville Heiskanen (JH), Ryan Postlethwaite (RP), Steve Smith (SS), and Ray Saintonge (RS). JH beat RP. RP beat SS. SS beat RS. RS beat JH.
JH | RP | SS | RS | |
---|---|---|---|---|
Jussi-Ville Heiskanen | 841 | 798 | 737 | |
Ryan Postlethwaite | 770 | 755 | 797 | |
Steve Smith | 750 | 744 | 778 | |
Ray Saintonge | 745 | 769 | 738 |
This circular tie had to be resolved with the Schulze method. This method is defined as follows:
The graph of pairwise defeats looks as follows:
The weakest links of the strongest paths are underlined.
p[*,JH] | p[*,RP] | p[*,SS] | p[*,RS] | |
---|---|---|---|---|
p[JH,*] | 841 | 798 | 797 | |
p[RP,*] | 745 | 755 | 797 | |
p[SS,*] | 745 | 745 | 778 | |
p[RS,*] | 745 | 745 | 745 |
As 841 = p[JH,RP] > p[RP,JH] = 745, JH is better than RP.
As 798 = p[JH,SS] > p[SS,JH] = 745, JH is better than SS.
As 797 = p[JH,RS] > p[RS,JH] = 745, JH is better than RS.
As 755 = p[RP,SS] > p[SS,RP] = 745, RP is better than SS.
As 797 = p[RP,RS] > p[RS,RP] = 745, RP is better than RS.
As 778 = p[SS,RS] > p[RS,SS] = 745, SS is better than RS.
Therefore, the Schulze ranking was:
As one vacant seat had to be filled, the winner was Ting Chen.
In June 2008, Wikimedia used the Schulze method for the election to its Board of Trustees: One vacant seat had to be filled. There were 15 candidates, about 26,000 eligible voters, and 3,019 valid ballots.
Each ballot contains a list of all candidates. Each voter ranks these candidates in order of preference. Each voter gives a '1' to his favorite candidate, a '2' to his second favorite candidate, a '3' to his third favorite candidate, etc..
Each voter may ...
In total, 3019 valid ballots were cast. Each figure represents the number of voters who ranked the candidate at the left better than the candidate at the top. A figure in green represents a victory in that pairwise comparison by the candidate at the left. A figure in red represents a defeat in that pairwise comparison by the candidate at the left.
TC | AB | SK | HC | AH | JH | RP | SS | RS | DR | CS | MB | KW | PW | GK | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Ting Chen | 1086 | 1044 | 1108 | 1135 | 1151 | 1245 | 1190 | 1182 | 1248 | 1263 | 1306 | 1344 | 1354 | 1421 | |
Alex Bakharev | 844 | 932 | 984 | 950 | 983 | 1052 | 1028 | 990 | 1054 | 1073 | 1109 | 1134 | 1173 | 1236 | |
Samuel Klein | 836 | 910 | 911 | 924 | 983 | 980 | 971 | 941 | 967 | 1019 | 1069 | 1099 | 1126 | 1183 | |
Harel Cain | 731 | 836 | 799 | 896 | 892 | 964 | 904 | 917 | 959 | 1007 | 1047 | 1075 | 1080 | 1160 | |
Ad Huikeshoven | 674 | 781 | 764 | 806 | 832 | 901 | 868 | 848 | 920 | 934 | 987 | 1022 | 1030 | 1115 | |
Jussi-Ville Heiskanen | 621 | 720 | 712 | 755 | 714 | 841 | 798 | 737 | 827 | 850 | 912 | 970 | 943 | 1057 | |
Ryan Postlethwaite | 674 | 702 | 726 | 756 | 772 | 770 | 755 | 797 | 741 | 804 | 837 | 880 | 921 | 1027 | |
Steve Smith | 650 | 694 | 654 | 712 | 729 | 750 | 744 | 778 | 734 | 796 | 840 | 876 | 884 | 1007 | |
Ray Saintonge | 629 | 703 | 641 | 727 | 714 | 745 | 769 | 738 | 789 | 812 | 848 | 879 | 899 | 987 | |
Dan Rosenthal | 595 | 654 | 609 | 660 | 691 | 724 | 707 | 699 | 711 | 721 | 780 | 844 | 858 | 960 | |
Craig Spurrier | 473 | 537 | 498 | 530 | 571 | 583 | 587 | 577 | 578 | 600 | 646 | 721 | 695 | 845 | |
Matthew Bisanz | 472 | 498 | 465 | 509 | 508 | 534 | 473 | 507 | 531 | 513 | 552 | 653 | 677 | 785 | |
Kurt M. Weber | 505 | 535 | 528 | 547 | 588 | 581 | 553 | 573 | 588 | 566 | 595 | 634 | 679 | 787 | |
Paul Williams | 380 | 420 | 410 | 435 | 439 | 464 | 426 | 466 | 470 | 471 | 429 | 521 | 566 | 754 | |
Gregory Kohs | 411 | 412 | 434 | 471 | 461 | 471 | 468 | 461 | 467 | 472 | 491 | 523 | 513 | 541 |
A " circular tie" is a situation where a majority prefers candidate A to candidate B, a majority prefers candidate B to candidate C, and a majority prefers candidate C to candidate A.
In 2008, there was a circular tie between the candidates Jussi-Ville Heiskanen (JH), Ryan Postlethwaite (RP), Steve Smith (SS), and Ray Saintonge (RS). JH beat RP. RP beat SS. SS beat RS. RS beat JH.
JH | RP | SS | RS | |
---|---|---|---|---|
Jussi-Ville Heiskanen | 841 | 798 | 737 | |
Ryan Postlethwaite | 770 | 755 | 797 | |
Steve Smith | 750 | 744 | 778 | |
Ray Saintonge | 745 | 769 | 738 |
This circular tie had to be resolved with the Schulze method. This method is defined as follows:
The graph of pairwise defeats looks as follows:
The weakest links of the strongest paths are underlined.
p[*,JH] | p[*,RP] | p[*,SS] | p[*,RS] | |
---|---|---|---|---|
p[JH,*] | 841 | 798 | 797 | |
p[RP,*] | 745 | 755 | 797 | |
p[SS,*] | 745 | 745 | 778 | |
p[RS,*] | 745 | 745 | 745 |
As 841 = p[JH,RP] > p[RP,JH] = 745, JH is better than RP.
As 798 = p[JH,SS] > p[SS,JH] = 745, JH is better than SS.
As 797 = p[JH,RS] > p[RS,JH] = 745, JH is better than RS.
As 755 = p[RP,SS] > p[SS,RP] = 745, RP is better than SS.
As 797 = p[RP,RS] > p[RS,RP] = 745, RP is better than RS.
As 778 = p[SS,RS] > p[RS,SS] = 745, SS is better than RS.
Therefore, the Schulze ranking was:
As one vacant seat had to be filled, the winner was Ting Chen.