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User:MarkusSchulze/Wikimedia Board of Trustees elections, 2008

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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.

Stage 1

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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 ...

  • ... give the same preference to more than one candidate. This indicates that this voter is indifferent between these candidates.
  • ... skip preferences. However, skipping preferences has no impact on the result of the elections, since only the order, in which the candidates are ranked, matters and not the absolute numbers of the preferences.
  • ... keep candidates unranked. When a voter doesn't rank all candidates, then this is interpreted as if this voter (1) strictly prefers all ranked to all unranked candidates and (2) is indifferent between all unranked candidates.

Stage 2

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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

Stage 3

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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:

d[A,B] is the number of voters who prefer candidate A to candidate B.
A path from candidate X to candidate Y of strength z is a sequence of candidates C(1),...,C(n) with the following properties:
  1. C(1) is identical to X.
  2. C(n) is identical to Y.
  3. d[C(i),C(i+1)] > d[C(i+1),C(i)] for all i = 1,...,(n-1).
  4. d[C(i),C(i+1)] ≥ z for all i = 1,...,(n-1).
p[A,B], the strength of the strongest path from candidate A to candidate B, is the maximum value such that there is a path of this strength from candidate A to candidate B.
If there is no path from candidate A to candidate B at all, then p[A,B] : = 0.
Candidate D is better than candidate E if and only if p[D,E] > p[E,D].

The graph of pairwise defeats looks as follows:

... to JH ... to RP ... to SS ... to RS
from JH ...
JH-(841)-RP
JH-(798)-SS
JH-(841)-RP-(797)-RS
from RP ...
RP-(797)-RS-(745)-JH
RP-(755)-SS
RP-(797)-RS
from SS ...
SS-(778)-RS-(745)-JH
SS-(778)-RS-(745)-JH-(841)-RP
SS-(778)-RS
from RS ...
RS-(745)-JH
RS-(745)-JH-(841)-RP
RS-(745)-JH-(798)-SS
The strongest paths are:

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
The strengths of the strongest paths are:

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:

  1. Ting Chen
  2. Alex Bakharev
  3. Samuel Klein
  4. Harel Cain
  5. Ad Huikeshoven
  6. Jussi-Ville Heiskanen
  7. Ryan Postlethwaite
  8. Steve Smith
  9. Ray Saintonge
  10. Dan Rosenthal
  11. Craig Spurrier
  12. Matthew Bisanz
  13. Kurt M. Weber
  14. Paul Williams
  15. Gregory Kohs

As one vacant seat had to be filled, the winner was Ting Chen.

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