User:MarkusSchulze/Wikimedia Board of Trustees elections, 2008

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

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

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

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:

The strongest paths are:

	... 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 weakest links of the strongest paths are underlined.

The strengths of the strongest paths are:

	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:

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.

Weblinks

• Elections to Wikimedia's Board of Trustees 2008: Introduction and rules
• Elections to Wikimedia's Board of Trustees 2008: Results
• Elections to Wikimedia's Board of Trustees 2008: Complete ballot data