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| {{Electoral systems}}
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| The '''Schulze method''' is a [[voting system]] developed in 1997 by Markus Schulze that selects a [[single-winner voting system|single winner]] using votes that express [[Ranked voting systems|preferences]]. The method can also be used to create a sorted list of winners. The Schulze method is also known as '''Schwartz Sequential Dropping''' ('''SSD'''), '''Cloneproof Schwartz Sequential Dropping''' ('''CSSD'''), the '''Beatpath Method''', '''Beatpath Winner''', '''Path Voting''', and '''Path Winner'''.
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| The Schulze method is a [[Condorcet method]], which means the following: if there is a candidate who is preferred over every other candidate in pairwise comparisons, then this candidate will be the winner when the Schulze method is applied. | | The actual amend [http://search.un.org/search?ie=utf8&site=un_org&output=xml_no_dtd&client=UN_Website_en&num=10&lr=lang_en&proxystylesheet=UN_Website_en&oe=utf8&q=delivers&Submit=Go delivers] a bunch of notable enhancements, mid-foot of which could indeed be the new Dynasty Conflict Manner. In distinct mode, you can said combating dynasties and alleviate utter rewards aloft her beat.<br><br>Shun purchasing big title games near their launch times. Waiting means that you're prone to look for clash of clans cheats after using a patch or two features emerge to mend manifest holes and bugs which will impact your pleasure and game play. Simply because keep an eye through for titles from parlors which are understood healthy patching and support.<br><br>Guilds and clans have ended up popular ever since the initial beginning of first-person displayed shooter and MMORPG avid gamers. World of WarCraft develops for that concept with their personally own World associated Warcraft guilds. A real guild can easily always stay understood as a having to do with players that band lower down for companionship. Individuals the guild travel back together again for fun and delight while improving in challenge and gold.<br><br>No matter the reason, computer game tricks are widespread and dust fairly rapidly over the net. The gaming community is hoping to find means cease cheaters from overrunning regarding game; having lots off cheaters playing a game can really end result honest players to eliminate playing, or play only with friends they trust. This poses a extensive problem particularly for reoccuring games for example EverQuest, wherein a loss in players ultimately result in a loss of income.<br><br>Conserve some money on your personal games, think about opt-in into a assistance an individual can rent payments adventure from. The charge of these lease accords for the year are normally under the amount of two video gaming applications. You can preserve the field titles until you hit them and simply pass out them back after more and purchase another one.<br><br>Outstanding are not really cheats, they are excuses. The odds are quality that unless you really are dating a certain as a professional golfer or a piece of rock star along the method by which this is not gonna happen to you. In John 4:23 and as well 24 Jesus tells usa we are to worship God "in spirit during truth. Once entered, the Ruzzle cheat can show a list of all the possible words that can be built. Using a PSP Market Emulator is a basic way to hack your entire PSP and open together new worlds of fun. s these university students played Poker and other casino activities simply for fun. |
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| The output of the Schulze method (defined below) gives an ordering of candidates. Therefore, if several positions are available, the method can be used for this purpose without modification, by letting the ''k'' top-ranked candidates win the ''k'' available seats. Furthermore, for [[proportional representation]] elections, a [[Schulze STV|single transferable vote variant]] has been proposed.
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| The Schulze method is used by several organizations including [[Debian]], [[Ubuntu (operating system)|Ubuntu]], [[Gentoo Linux|Gentoo]], and [[Software in the Public Interest]].
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| == Description of the method == | |
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| === Ballot === | |
| {{refimprove|1=section|date=April 2013}}
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| [[Image:Preferential ballot.svg|140px|right|thumb]]
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| The input to the Schulze method is the same as for other [[Ranked voting systems|ranked]] [[single-winner voting system|single-winner election methods]]: each voter must furnish an [[total order|ordered preference list]] on candidates where [[Tie (draw)|ties]] are allowed.
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| One typical way for voters to specify their preferences on a [[Ranked voting systems#Ballot variations|ballot]] (see right) is as follows. Each ballot lists all the candidates, and each voter ranks this list in order of preference using numbers: the voter places a '1' beside the most preferred candidate(s), a '2' beside the second-most preferred, and so forth. Each voter may optionally:
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| * give the same preference to more than one candidate. This indicates that this voter is indifferent between these candidates.
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| * use non-consecutive numbers to express preferences. This has no impact on the result of the elections, since only the order in which the candidates are ranked by the voter matters, and not the absolute numbers of the preferences.
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| * keep candidates unranked. When a voter doesn't rank all candidates, then this is interpreted as if this voter (i) strictly prefers all ranked to all unranked candidates, and (ii) is indifferent among all unranked candidates.
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| === Computation ===
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| <math>d[V,W]</math> is assumed to be the number of voters who prefer candidate <math>V</math> to candidate <math>W</math>. | |
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| A ''path'' from candidate <math>X</math> to candidate <math>Y</math> of ''strength'' <math>p</math> is a [[sequence]] of candidates <math>C(1),...,C(n)</math> with the following properties:
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| # <math>C(1) = X</math> and <math>C(n) = Y</math>.
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| # For all <math>i = 1,...,(n-1): d[C(i),C(i+1)] > d[C(i+1),C(i)]</math>.
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| # For all <math>i = 1,...,(n-1): d[C(i),C(i+1)] \text{≥} p</math>.
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| <math>p[A,B]</math>, the ''strength of the strongest path'' from candidate <math>A</math> to candidate <math>B</math>, is the maximum value such that there is a path from candidate <math>A</math> to candidate <math>B</math> of that strength. If there is no path from candidate <math>A</math> to candidate <math>B</math> at all, then <math>p[A,B] = 0</math>.
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| Candidate <math>D</math> is ''better'' than candidate <math>E</math> if and only if <math>p[D,E] > p[E,D]</math>.
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| Candidate <math>D</math> is a ''potential winner'' if and only if <math>p[D,E] \text{≥} p[E,D]</math> for every other candidate <math>E</math>.
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| It can be proven that <math>p[X,Y] > p[Y,X]</math> and <math>p[Y,Z] > p[Z,Y]</math> together imply <math>p[X,Z] > p[Z,X]</math>.<ref name=schulze2011/>{{rp|§4.1}} Therefore, it is guaranteed (1) that the above definition of "''better''" really defines a [[transitive relation]] and (2) that there is always at least one candidate <math>D</math> with <math>p[D,E] \text{≥} p[E,D]</math> for every other candidate <math>E</math>.
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| == Example ==
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| In the following example 45 voters rank 5 candidates.
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| * 5 <math>ACBED</math> (meaning, 5 voters have order of preference: <math>A > C > B > E > D</math>)
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| * 5 <math>ADECB</math>
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| * 8 <math>BEDAC</math>
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| * 3 <math>CABED</math>
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| * 7 <math>CAEBD</math>
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| * 2 <math>CBADE</math>
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| * 7 <math>DCEBA</math>
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| * 8 <math>EBADC</math>
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| The pairwise preferences have to be computed first. For example, when comparing <math>A</math> and <math>B</math> pairwise, there are <math>5+5+3+7=20</math> voters who prefer <math>A</math> to <math>B</math>, and <math>8+2+7+8=25</math> voters who prefer <math>B</math> to <math>A</math>. So <math>d[A, B] = 20</math> and <math>d[B, A] = 25</math>. The full set of pairwise preferences is:
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| [[Image:Schulze method example1.svg|thumb|300px|right|Directed [[graph (mathematics)|graph]] labeled with pairwise preferences d[*, *] ]]
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| {| class="wikitable" style="text-align:center"
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| |+ Matrix of pairwise preferences
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| |-
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| ! !! d[*,A] !! d[*,B] !! d[*,C] !! d[*,D] !! d[*,E]
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| |-
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| ! d[A,*]
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| | || bgcolor=#ffdddd|20 || bgcolor=#ddffdd|26 || bgcolor=#ddffdd|30 || bgcolor=#ffdddd|22
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| |-
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| ! d[B,*]
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| | bgcolor=#ddffdd|25 || || bgcolor=#ffdddd|16 || bgcolor=#ddffdd|33 || bgcolor=#ffdddd|18
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| |-
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| ! d[C,*]
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| | bgcolor=#ffdddd|19 || bgcolor=#ddffdd|29 || || bgcolor=#ffdddd|17 || bgcolor=#ddffdd|24
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| |-
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| ! d[D,*]
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| | bgcolor=#ffdddd|15 || bgcolor=#ffdddd|12 || bgcolor=#ddffdd|28 || || bgcolor=#ffdddd|14
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| |-
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| ! d[E,*]
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| | bgcolor=#ddffdd|23 || bgcolor=#ddffdd|27 || bgcolor=#ffdddd|21 || bgcolor=#ddffdd|31 ||
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| |}
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| The cells for d[X, Y] have a light green background if d[X, Y] > d[Y, X], otherwise the background is light red. There is no undisputed winner by only looking at the pairwise differences here. | |
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| Now the strongest paths have to be identified. To help visualize the strongest paths, the set of pairwise preferences is depicted in the diagram on the right in the form of a [[directed graph]]. An arrow from the node representing a candidate X to the one representing a candidate Y is labelled with d[X, Y]. To avoid cluttering the diagram, an arrow has only been drawn from X to Y when d[X, Y] > d[Y, X] (i.e. the table cells with light green background), omitting the one in the opposite direction (the table cells with light red background).
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| One example of computing the strongest path strength is p[B, D] = 33: the strongest path from B to D is the direct path (B, D) which has strength 33. But when computing p[A, C], the strongest path from A to C is not the direct path (A, C) of strength 26, rather the strongest path is the indirect path (A, D, C) which has strength min(30, 28) = 28.The ''strength'' of a path is the strength of its weakest link.
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| For each pair of candidates X and Y, the following table shows the strongest path from candidate X to candidate Y in red, with the weakest link <u>underlined</u>.
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| {{clear}}
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| {| class="wikitable" style="text-align:center"
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| |+Strongest paths
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| |-
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| ! !! ... to A !! ... to B !! ... to C !! ... to D !! ... to E !!
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| |-
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| ! from A ...
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| | || [[Image:Schulze method example1 AB.svg|border|none|150px|left]] A-(30)-D-<u>(28)</u>-C-(29)-B || [[Image:Schulze method example1 AC.svg|border|none|150px|left]] A-(30)-D-<u>(28)</u>-C || [[Image:Schulze method example1 AD.svg|border|none|150px|left]] A-<u>(30)</u>-D || [[Image:Schulze method example1 AE.svg|border|none|150px|left]] A-(30)-D-(28)-C-<u>(24)</u>-E
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| ! from A ...
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| |-
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| ! from B ...
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| | [[Image:Schulze method example1 BA.svg|border|none|150px|left]] B-<u>(25)</u>-A || || [[Image:Schulze method example1 BC.svg|border|none|150px|left]] B-(33)-D-<u>(28)</u>-C || [[Image:Schulze method example1 BD.svg|border|none|150px|left]] B-<u>(33)</u>-D || [[Image:Schulze method example1 BE.svg|border|none|150px|left]] B-(33)-D-(28)-C-<u>(24)</u>-E
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| ! from B ...
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| |-
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| ! from C ...
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| | [[Image:Schulze method example1 CA.svg|border|none|150px|left]] C-(29)-B-<u>(25)</u>-A || [[Image:Schulze method example1 CB.svg|border|none|150px|left]] C-<u>(29)</u>-B || || [[Image:Schulze method example1 CD.svg|border|none|150px|left]] C-<u>(29)</u>-B-(33)-D || [[Image:Schulze method example1 CE.svg|border|none|150px|left]] C-<u>(24)</u>-E
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| ! from C ...
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| |-
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| ! from D ...
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| | [[Image:Schulze method example1 DA.svg|border|none|150px|left]] D-(28)-C-(29)-B-<u>(25)</u>-A || [[Image:Schulze method example1 DB.svg|border|none|150px|left]] D-<u>(28)</u>-C-(29)-B || [[Image:Schulze method example1 DC.svg|border|none|150px|left]] D-<u>(28)</u>-C || || [[Image:Schulze method example1 DE.svg|border|none|150px|left]] D-(28)-C-<u>(24)</u>-E
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| ! from D ...
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| |-
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| ! from E ...
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| | [[Image:Schulze method example1 EA.svg|border|none|150px|left]] E-(31)-D-(28)-C-(29)-B-<u>(25)</u>-A || [[Image:Schulze method example1 EB.svg|border|none|150px|left]] E-(31)-D-<u>(28)</u>-C-(29)-B || [[Image:Schulze method example1 EC.svg|border|none|150px|left]] E-(31)-D-<u>(28)</u>-C || [[Image:Schulze method example1 ED.svg|border|none|150px|left]] E-<u>(31)</u>-D ||
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| ! from E ...
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| |-
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| ! !! ... to A !! ... to B !! ... to C !! ... to D !! ... to E !!
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| |}
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| {| class="wikitable" style="text-align:center"
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| |+Strengths of the strongest paths
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| |-
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| ! !! p[*,A] !! p[*,B] !! p[*,C] !! p[*,D] !! p[*,E]
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| |-
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| ! p[A,*]
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| | || bgcolor=#ddffdd|28 || bgcolor=#ddffdd|28 || bgcolor=#ddffdd|30 || bgcolor=#ffdddd|24
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| |-
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| ! p[B,*]
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| | bgcolor=#ffdddd|25 || || bgcolor=#ffdddd|28 || bgcolor=#ddffdd|33 || bgcolor=#ffdddd|24
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| |-
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| ! p[C,*]
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| | bgcolor=#ffdddd|25 || bgcolor=#ddffdd|29 || || bgcolor=#ddffdd|29 || bgcolor=#ffdddd|24
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| |-
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| ! p[D,*]
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| | bgcolor=#ffdddd|25 || bgcolor=#ffdddd|28 || bgcolor=#ffdddd|28 || || bgcolor=#ffdddd|24
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| |-
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| ! p[E,*]
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| | bgcolor=#ddffdd|25 || bgcolor=#ddffdd|28 || bgcolor=#ddffdd|28 || bgcolor=#ddffdd|31 ||
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| |}
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| Now the output of the Schulze method can be determined. For example, when comparing A and B,
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| since 28 = p[A,B] > p[B,A] = 25, for the Schulze method candidate A is ''better'' than candidate B. Another example is that 31 = p[E,D] > p[D,E] = 24, so candidate E is ''better'' than candidate D. Continuing in this way, the result is that the Schulze ranking is E > A > C > B > D, and E wins. In other words, E wins since p[E,X] ≥ p[X,E] for every other candidate X.
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| == Implementation ==
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| The only difficult step in implementing the Schulze method is computing the strongest path strengths. However, this is a well-known problem in graph theory sometimes called the [[widest path problem]]. One simple way to compute the strengths therefore is a variant of the [[Floyd–Warshall algorithm]]. The following [[pseudocode]] illustrates the algorithm.
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| <source line lang="text"> | |
| # Input: d[i,j], the number of voters who prefer candidate i to candidate j.
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| # Output: p[i,j], the strength of the strongest path from candidate i to candidate j.
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| for i from 1 to C
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| for j from 1 to C
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| if (i ≠ j) then
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| if (d[i,j] > d[j,i]) then
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| p[i,j] := d[i,j]
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| else
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| p[i,j] := 0
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| for i from 1 to C
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| for j from 1 to C
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| if (i ≠ j) then
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| for k from 1 to C
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| if (i ≠ k and j ≠ k) then
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| p[j,k] := max ( p[j,k], min ( p[j,i], p[i,k] ) )
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| </source> | |
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| This algorithm is [[Efficiency (statistics)|efficient]], and has running time proportional to ''C''<sup>3</sup> where ''C'' is the number of candidates. (This does not account for the running time of computing the d[*,*] values, which if implemented in the most straightforward way, takes time proportional to ''C''<sup>2</sup> times the number of voters.)
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| == Ties and alternative implementations ==
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| When allowing users to have ties in their preferences, the outcome of the Schulze method naturally depends on how these ties are interpreted in defining d[*,*]. Two natural choices are that d[A, B] represents either the number of voters who strictly prefer A to B (A>B), or the ''margin'' of (voters with A>B) minus (voters with B>A). But no matter how the ''d''s are defined, the Schulze ranking has no cycles, and assuming the ''d''s are unique it has no ties.<ref name="schulze2011"/>
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| Although ties in the Schulze ranking are unlikely,<ref>Under reasonable probabilistic assumptions when the number of voters is much larger than the number of candidates</ref> they are possible. Schulze's original paper<ref name="schulze2011"/> proposed breaking ties in accordance with a voter selected at random, and iterating as needed.
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| An alternative, slower, way to describe the winner of the Schulze method is the following procedure:
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| # draw a complete [[directed graph]] with all candidates, and all possible edges between candidates
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| # iteratively [a] delete all candidates not in the [[Schwartz set]] (i.e. any candidate which cannot reach all others) and [b] delete the weakest link
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| # the winner is the last non-deleted candidate.
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| == Satisfied and failed criteria ==
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| === Satisfied criteria ===
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| The Schulze method satisfies the following criteria:
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| * [[Unrestricted domain]]
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| * [[Arrow's impossibility theorem|Non-imposition]] ([[Aka (initialism)|a.k.a.]] [[Arrow's impossibility theorem|citizen sovereignty]])
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| * [[Non-dictatorship]]
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| * [[Pareto efficiency|Pareto criterion]]<ref name=schulze2011 />{{rp|§4.3}}
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| * [[Monotonicity criterion]]<ref name=schulze2011 />{{rp|§4.5}}
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| * [[Majority criterion]]
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| * [[Majority loser criterion]]
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| * [[Condorcet criterion]]
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| * [[Condorcet loser criterion]]
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| * [[Schwartz set|Schwartz criterion]]
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| * [[Smith criterion]]<ref name=schulze2011 />{{rp|§4.7}}
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| * [[Independence of Smith-dominated alternatives]]<ref name=schulze2011 />{{rp|§4.7}}
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| * [[Mutual majority criterion]]
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| * [[Independence of clones criterion|Independence of clones]]<ref name=schulze2011 />{{rp|§4.6}}
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| * [[Reversal symmetry]]<ref name=schulze2011 />{{rp|§4.4}}
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| * Mono-append<ref name="woodall1994">Douglas R. Woodall, [http://www.votingmatters.org.uk/ISSUE3/P5.HTM Properties of Preferential Election Rules], ''Voting Matters'', issue 3, pages 8-15, December 1994</ref>
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| * Mono-add-plump<ref name=woodall1994/>
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| * [[Resolvability criterion]]<ref name=schulze2011 />{{rp|§4.2}}
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| * [[Polynomial time|Polynomial runtime]]<ref name=schulze2011 />{{rp|§2.3"}}
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| * prudence<ref name=schulze2011 />{{rp|§4.9"}}
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| * MinMax sets<ref name=schulze2011 />{{rp|§4.8"}}
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| * [[Plurality criterion|Woodall's plurality criterion]] if [[Condorcet method#Defeat strength|winning votes]] are used for d[X,Y]
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| * Symmetric-completion<ref name=woodall1994/> if [[Condorcet method#Defeat strength|margins]] are used for d[X,Y]
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| === Failed criteria ===
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| Since the Schulze method satisfies the [[Condorcet criterion]], it automatically fails the following criteria:
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| * [[Participation criterion|Participation]]<ref name=schulze2011 />{{rp|§3.4}}
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| * [[Consistency criterion|Consistency]]
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| * [[Tactical voting|Invulnerability to compromising]]
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| * [[Tactical voting|Invulnerability to burying]]
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| * [[Later-no-harm criterion|Later-no-harm]]
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| Likewise, since the Schulze method is not a dictatorship and agrees with unanimous votes, [[Arrow's Theorem]] implies it fails the criterion
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| * [[Independence of irrelevant alternatives]]
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| The Schulze method also fails
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| * [[Peyton Young]]'s criterion [[Independence of irrelevant alternatives#Local independence|Local Independence of Irrelevant Alternatives]].
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| === Comparison table ===
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| The following table compares the Schulze method with other [[Ranked voting systems|preferential]] [[single-winner voting system|single-winner election methods]]: | |
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| {| class="wikitable" style="text-align:center"
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| |-
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| | style="width:8%;" |
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| | style="width:3%;" | [[Monotonicity criterion|Monotonic]]
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| | style="width:3%;" | [[Condorcet criterion|Condorcet]]
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| | style="width:3%;" | [[Majority criterion|Majority]]
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| | style="width:3%;" | [[Condorcet loser criterion|Condorcet loser]]
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| | style="width:3%;" | [[Majority loser criterion|Majority loser]]
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| | style="width:3%;" | [[Mutual majority criterion|Mutual majority]]
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| | style="width:3%;" | [[Smith criterion|Smith]]
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| | style="width:3%;" | [[Independence of Smith-dominated alternatives|ISDA]]
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| | style="width:3%;" | [[Independence of irrelevant alternatives#Local independence|LIIA]]
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| | style="width:3%;" | [[Independence of clones criterion|Clone independence]]
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| | style="width:3%;" | [[Reversal symmetry]]
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| | style="width:3%;" | [[Polynomial time]]
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| | style="width:3%;" | [[Participation criterion|Participation]], [[consistency criterion|Consistency]]
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| | style="width:3%;" | [[Resolvability criterion|Resolvability]]
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| |-
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| ! Schulze
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| | {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{no}} || {{yes}} || {{yes}} || {{yes}} || {{no}} || {{yes}}
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| |-
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| ! [[Ranked Pairs]]
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| | {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{no}} || {{yes}}
| |
| |-
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| ! [[Copeland's method|Copeland]]
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| | {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{no}} || {{no}} || {{yes}} || {{yes}} || {{no}} || {{no}}
| |
| |-
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| ! [[Kemeny–Young method|Kemeny-Young]]
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| | {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{no}} || {{yes}} || {{no}} || {{no}} || {{yes}}
| |
| |-
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| ! [[Nanson's method|Nanson]]
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| | {{no}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{yes}} || {{no}} || {{yes}}
| |
| |-
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| ! [[Nanson's method#Baldwin method|Baldwin]]
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| | {{no}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{no}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{no}} || {{yes}}
| |
| |-
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| ! [[Instant-runoff voting]]
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| | {{no}} || {{no}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{no}} || {{yes}} || {{no}} || {{yes}}
| |
| |-
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| ! [[Borda count|Borda]]
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| | {{yes}} || {{no}} || {{no}} || {{yes}} || {{yes}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{yes}} || {{yes}} || {{yes}}
| |
| |-
| |
| ! [[Bucklin voting|Bucklin]]
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| | {{yes}} || {{no}} || {{yes}} || {{no}} || {{yes}} || {{yes}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{no}} || {{yes}}
| |
| |-
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| ! [[Coombs' method|Coombs]]
| |
| | {{no}} || {{no}} || {{yes}} || {{yes}} || {{yes}} || {{yes}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{no}} || {{yes}}
| |
| |-
| |
| ! [[Minimax Condorcet|MiniMax]]
| |
| | {{yes}} || {{yes}} || {{yes}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{no}} || {{yes}}
| |
| |-
| |
| ! [[Plurality voting system|Plurality]]
| |
| | {{yes}} || {{no}} || {{yes}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{yes}} || {{yes}}
| |
| |-
| |
| ! [[Anti-plurality voting|Anti-plurality]]
| |
| | {{yes}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{yes}} || {{yes}}
| |
| |-
| |
| ! [[Contingent vote|Contingent voting]]
| |
| | {{no}} || {{no}} || {{yes}} || {{yes}} || {{yes}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{no}} || {{yes}}
| |
| |-
| |
| ! [[Sri Lankan contingent vote|Sri Lankan contingent voting]]
| |
| | {{no}} || {{no}} || {{yes}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{no}} || {{yes}}
| |
| |-
| |
| ! [[Supplementary vote|Supplementary voting]]
| |
| | {{no}} || {{no}} || {{yes}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{yes}} || {{no}} || {{yes}}
| |
| |-
| |
| ! [[Dodgson's method|Dodgson]]
| |
| | {{no}} || {{yes}} || {{yes}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{no}} || {{yes}}
| |
| |}
| |
| | |
| The main difference between the Schulze method and the [[ranked pairs]] method can be seen in this example:
| |
|
| |
| Suppose the MinMax score of a set '''X''' of candidates is the strength of the strongest pairwise win of a candidate A ∉ '''X''' against a candidate B ∈ '''X'''. Then the Schulze method, but not Ranked Pairs, guarantees that the winner is always a candidate of the set with minimum MinMax score.<ref name=schulze2011 />{{rp|§4.8}} So, in some sense, the Schulze method minimizes the largest majority that has to be reversed when determining the winner.
| |
|
| |
| On the other hand, Ranked Pairs minimizes the largest majority that has to be reversed to determine the order of finish, in the minlexmax sense.
| |
| <ref>Tideman, T. Nicolaus, "Independence of clones as a criterion for voting rules," Social Choice and Welfare vol 4 #3 (1987), pp 185-206.
| |
| </ref>
| |
| In other words, when Ranked Pairs and the Schulze method produce different orders of finish, for the majorities on which the two orders of finish disagree, the Schulze order reverses a larger majority than the Ranked Pairs order.
| |
| | |
| == History ==
| |
| The Schulze method was developed by Markus Schulze in 1997. It was first discussed in public mailing lists in 1997–1998<ref>See:
| |
| * Markus Schulze, [http://lists.electorama.com/pipermail/election-methods-electorama.com/1997-October/001570.html Condorect sub-cycle rule], October 1997 (In this message, the Schulze method is mistakenly believed to be identical to the [[ranked pairs]] method.)
| |
| * Mike Ossipoff, [http://groups.yahoo.com/group/election-methods-list/message/467 Party List P.S.], July 1998
| |
| * Markus Schulze, [http://groups.yahoo.com/group/election-methods-list/message/673 Tiebreakers, Subcycle Rules], August 1998
| |
| * Markus Schulze, [http://groups.yahoo.com/group/election-methods-list/message/845 Maybe Schulze is decisive], August 1998
| |
| * Norman Petry, [http://groups.yahoo.com/group/election-methods-list/message/867 Schulze Method - Simpler Definition], September 1998
| |
| * Markus Schulze, [http://groups.yahoo.com/group/election-methods-list/message/2291 Schulze Method], November 1998</ref> and in 2000.<ref>See:
| |
| * [[Anthony Towns]], [http://lists.debian.org/debian-vote/2000/11/msg00121.html Disambiguation of 4.1.5], November 2000
| |
| * Norman Petry, [http://lists.debian.org/debian-vote/2000/12/msg00045.html Constitutional voting, definition of cumulative preference], December 2000</ref> Subsequently, Schulze method users included [[Software in the Public Interest]] (2003),<ref name=SPI>[http://www.spi-inc.org/corporate/resolutions/2003/2003-01-06.wta.1/ Process for adding new board members], January 2003</ref> [[Debian]] (2003),<ref name=Debian>See:
| |
| * [http://www.debian.org/vote/2003/vote_0002 Constitutional Amendment: Condorcet/Clone Proof SSD Voting Method], June 2003
| |
| * [http://www.debian.org/devel/constitution Constitution for the Debian Project], appendix A6
| |
| * [http://www.debian.org/vote/ Debian Voting Information]</ref> [[Gentoo Linux|Gentoo]] (2005),<ref name=Gentoo>See:
| |
| * [http://www.gentoo.org/foundation/en/ Gentoo Foundation Charter]
| |
| * Aron Griffis, [http://article.gmane.org/gmane.linux.gentoo.nfp/252/match=Condorcet+Schwartz+drop+dropped 2005 Gentoo Trustees Election Results], May 2005
| |
| * Lars Weiler, [http://article.gmane.org/gmane.linux.gentoo.weekly-news/121/match=Condorcet Gentoo Weekly Newsletter 23 May 2005]
| |
| * Daniel Drake, [http://article.gmane.org/gmane.linux.gentoo.devel/28603/match=Condorcet+Cloneproof+Schwartz+Sequential+Dropping Gentoo metastructure reform poll is open], June 2005
| |
| * Grant Goodyear, [http://article.gmane.org/gmane.linux.gentoo.devel/42260/match=Schulze+method Results now more official], September 2006
| |
| * [http://dev.gentoo.org/~fox2mike/elections/council/2007/council2007-results 2007 Gentoo Council Election Results], September 2007
| |
| * [http://www.gentoo.org/proj/en/elections/council/2008/council-2008-results.txt 2008 Gentoo Council Election Results], June 2008
| |
| * [http://www.gentoo.org/proj/en/elections/council/2008/council-200811-results.txt 2008 Gentoo Council Election Results], November 2008
| |
| * [http://www.gentoo.org/proj/en/elections/council/2009/council-200906-results.txt 2009 Gentoo Council Election Results], June 2009
| |
| * [http://www.gentoo.org/proj/en/elections/council/2009/council-200912-results.txt 2009 Gentoo Council Election Results], December 2009
| |
| * [http://www.gentoo.org/proj/en/elections/council/2010/council-201006-results.txt 2010 Gentoo Council Election Results], June 2010</ref> [[TopCoder]] (2005),<ref name=TopCoder>See:
| |
| * [http://www.topcoder.com/tc?module=Static&d1=tournaments&d2=tco06&d3=logo_rules 2006 TopCoder Open Logo Design Contest], November 2005
| |
| * [http://www.topcoder.com/tc?module=Static&d1=tournaments&d2=tccc06&d3=logo_rules 2006 TopCoder Collegiate Challenge Logo Design Contest], June 2006
| |
| * [http://studio.topcoder.com/?module=ViewContestDetails&ct=2030 2007 TopCoder High School Tournament Logo], September 2006
| |
| * [http://studio.topcoder.com/?module=ViewContestDetails&ct=2046 2007 TopCoder Arena Skin Contest], November 2006
| |
| * [http://studio.topcoder.com/?module=ViewContestDetails&ct=2047 2007 TopCoder Open Logo Contest], January 2007
| |
| * [http://studio.topcoder.com/?module=ViewContestDetails&ct=2050 2007 TopCoder Open Web Design Contest], January 2007
| |
| * [http://studio.topcoder.com/?module=ViewContestDetails&ct=2122 2007 TopCoder Collegiate Challenge T-Shirt Design Contest], September 2007
| |
| * [http://studio.topcoder.com/?module=ViewContestDetails&ct=2127 2008 TopCoder Open Logo Design Contest], September 2007
| |
| * [http://studio.topcoder.com/?module=ViewContestDetails&ct=2133 2008 TopCoder Open Web Site Design Contest], October 2007
| |
| * [http://studio.topcoder.com/?module=ViewContestDetails&ct=2183 2008 TopCoder Open T-Shirt Design Contest], March 2008</ref> [[Wikimedia Foundation|Wikimedia]] (2008),<ref name=Wikimedia>See:
| |
| * Jesse Plamondon-Willard, [[mailarchive:foundation-l/2008-May/043134.html|Board election to use preference voting]], May 2008
| |
| * Mark Ryan, [[mailarchive:foundation-l/2008-June/044361.html|2008 Wikimedia Board Election results]], June 2008
| |
| * [[m:Board elections/2008/Results/en|2008 Board Elections]], June 2008
| |
| * [[m:Board elections/2009/Results/en|2009 Board Elections]], August 2009</ref> [[KDE]] (2008),<ref name=KDE>section 3.4.1 of the [http://ev.kde.org/rules/online_voting.php Rules of Procedures for Online Voting]</ref> the [[Free Software Foundation Europe]] (2008),<ref name=FSFE>See:
| |
| * article 6 section 3 of the [http://www.fsfeurope.org/about/legal/Constitution.en.pdf constitution]
| |
| * [http://www.fsfeurope.org/news/2009/news-20090301-01.en.html Fellowship vote for General Assembly seats], March 2009
| |
| * [http://fsfe.org/news/2009/news-20090601-01.en.html And the winner of the election for FSFE's Fellowship GA seat is ...], June 2009</ref> the [[Pirate Party (Sweden)|Pirate Party of Sweden]] (2009),<ref name=PiratePartySweden>See:
| |
| * [http://forum.piratpartiet.se/FindPost174988.aspx Inför primärvalen], October 2009
| |
| * [http://forum.piratpartiet.se/FindPost176567.aspx Dags att kandidera till riksdagen], October 2009
| |
| * [http://forum.piratpartiet.se/FindPost193877.aspx Råresultat primärvalet], January 2010</ref> and the [[Pirate Party Germany|Pirate Party of Germany]] (2010).<ref name=PiratePartyGermany>11 of the 16 regional sections and the federal section of the [[Pirate Party Germany|Pirate Party of Germany]] are using [http://liquidfeedback.org/ LiquidFeedback] for unbinding internal opinion polls. In 2010/2011, the Pirate Parties of [[Neukölln]] ([http://wiki.piratenpartei.de/BE:Neuk%C3%B6lln/Gebietsversammlungen/2010.3/Protokoll link]), [[Mitte]] ([http://berlin.piratenpartei.de/2011/01/18/kandidaten-der-piraten-in-mitte-aufgestellt/ link]), [[Steglitz-Zehlendorf]] ([http://wiki.piratenpartei.de/wiki/images/d/da/BE_Gebietsversammlung_Steglitz_Zehlendorf_2011_01_20_Protokoll.pdf link]), [[Lichtenberg]] ([http://piraten-lichtenberg.de/?p=205 link]), and [[Tempelhof-Schöneberg]] ([http://wiki.piratenpartei.de/BE:Gebietsversammlungen/Tempelhof-Schoeneberg/Protokoll_2011.1 link]) adopted the Schulze method for its primaries. Furthermore, the Pirate Party of [[Berlin]] (in 2011) ([http://wiki.piratenpartei.de/BE:Parteitag/2011.1/Protokoll link]) and the Pirate Party of [[Regensburg]] (in 2012) ([http://wiki.piratenpartei.de/BY:Regensburg/Gr%C3%BCndung/Gesch%C3%A4ftsordnung#Anlage_A link]) adopted this method for their primaries.</ref> In the French Wikipedia, the Schulze method was one of two multi-candidate methods approved by a majority in 2005,<ref name=FrenchWikipedia>[[:fr:Wikipédia:Prise de décision/Choix dans les votes#B - Proposition n°7 : Méthode Condorcet|Choix dans les votes]]</ref> and it has been used several times.<ref>[[:fr:Spécial:Pages liées/Méthode Schulze]]</ref>
| |
| | |
| In 2011, Schulze published the method in the academic journal ''Social Choice and Welfare.''<ref name="schulze2011">Markus Schulze, [http://www.springerlink.com/content/y5451n4908227162/?p=78c7a3edd3f64751ac9c2afc8aa6fad2&pi=0 A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method], Social Choice and Welfare, volume 36, number 2, page 267–303, 2011. Preliminary version in ''Voting Matters'', 17:9-19, 2003.</ref>
| |
| | |
| == Users ==
| |
| [[Image:Voting2.png|thumb|right|sample ballot for [[Wikimedia Foundation|Wikimedia's Board of Trustees]] elections]]
| |
| | |
| The Schulze method is not currently used in parliamentary elections. However, it has been used for parliamentary primaries in the Swedish [[Pirate Party (Sweden)|Pirate Party]]. It is also starting to receive support in other public organizations. Organizations which currently use the Schulze method are:
| |
| | |
| {{Colbegin|2}}
| |
| * [[Alternative for Germany]] <ref>§12(4), §12(15), and §14(3) of the [https://www.alternativefuer.de/pdf/Bundessatzung-Parteibeschluss.pdf bylaws], April 2013</ref>
| |
| * [[Annodex|Annodex Association]] <ref>[http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?id=E_50cfc592ae8f13d9 Election of the Annodex Association committee for 2007], February 2007</ref>
| |
| * [[Northwestern University|Associated Student Government at Northwestern University]] <ref>[http://www.northbynorthwestern.com/story/ajith-van-atta-win-asg-election/ Ajith, Van Atta win ASG election], April 2013</ref>
| |
| * [[:de:Berufsverband der Kinder- und Jugendärzte|Berufsverband der Kinder- und Jugendärzte (BVKJ)]] <ref>§9a of the [http://www.kinderaerzte-im-netz.de/bvkj/contentkin/psfile/pdf/56/BVKJ_Satzu4e2d51acd5583.pdf bylaws], October 2013</ref>
| |
| * Blitzed <ref>[http://wiki.blitzed.org/Condorcet_method_for_admin_voting Condorcet method for admin voting], January 2005</ref>
| |
| * [[BoardGameGeek]] <ref>See:
| |
| * [http://www.boardgamegeek.com/article/1751580 Important notice for Golden Geek voters], September 2007
| |
| * [http://www.boardgamegeek.com/article/2582330 Golden Geek Awards 2008 - Nominations Open], August 2008
| |
| * [http://www.boardgamegeek.com/article/3840078 Golden Geek Awards 2009 - Nominations Open], August 2009
| |
| * [http://www.boardgamegeek.com/article/5492260 Golden Geek Awards 2010 - Nominations Open], September 2010
| |
| * [http://boardgamegeek.com/thread/694044 Golden Geek Awards 2011 - Nominations Open], September 2011</ref>
| |
| * [[Apache Cassandra|Cassandra]] <ref>[http://article.gmane.org/gmane.comp.db.cassandra.devel/424/match=condorcet+schwartz+sequential+dropping+beatpath Project Logo], October 2009</ref>
| |
| * Codex Alpe Adria <ref>{{cite web|url=http://0xAA.org/competitions/ |title=Codex Alpe Adria Competitions |publisher=0xaa.org |date=2010-01-24 |accessdate=2010-05-08}}</ref>
| |
| * Collective Agency <ref>[http://collectiveagency.co/2012/03/21/civics-meeting-minutes-32012/ Civics Meeting Minutes], March 2012</ref>
| |
| * [[University of South Florida|College of Marine Science]] <ref>{{cite web|url=http://www.marine.usf.edu/fellowships/Guidelines-and-Application-2012-2013.doc |title=Fellowship Guidelines |format=PDF |date= |accessdate=2011-06-01}}</ref>
| |
| * [[University of York|Computer Science Departmental Society for York University (HackSoc)]] <ref>[http://www.hacksoc.org/HackSocElections.pdf Report on HackSoc Elections], December 2008</ref>
| |
| * County Highpointers <ref>Adam Helman, [http://www.cohp.org/records/votes/family_affair_voting_scheme.html Family Affair Voting Scheme - Schulze Method]</ref>
| |
| * [[Debian]] <ref name=Debian/>
| |
| * Demokratische Bildung Berlin <ref>appendix 1 of the [http://www.demokratische-schule-x.de/media/DBB_Satzung_Stand_August_2010.pdf constitution]</ref>
| |
| * [[EuroBillTracker]] <ref>See:
| |
| * [http://forum.eurobilltracker.eu/viewtopic.php?t=4920&highlight=condorcet+beatpath+ssd Candidate cities for EBTM05], December 2004
| |
| * [http://forum.eurobilltracker.eu/viewtopic.php?t=4921&highlight=condorcet Meeting location preferences], December 2004
| |
| * [http://forum.eurobilltracker.eu/viewtopic.php?t=9353&highlight=condorcet+beatpath Date for EBTM07 Berlin], January 2007
| |
| * [http://forum.eurobilltracker.eu/viewtopic.php?t=10564&highlight=condorcet+beatpath Vote the date of the Summer EBTM08 in Ljubljana], January 2008
| |
| * [http://forum.eurobilltracker.com/viewtopic.php?f=26&t=17919&start=15#p714947 New Logo for EBT], August 2009</ref>
| |
| * [[European Democratic Education Conference|European Democratic Education Conference (EUDEC)]] <ref>{{cite web|url=http://www.eudec.org/Guidance%20Document |title=Guidance Document |publisher=Eudec.org |date=2009-11-15 |accessdate=2010-05-08}}</ref>
| |
| * Fair Trade Northwest <ref>article XI section 2 of the [http://fairtradenorthwest.org/FTNW%20Bylaws.pdf bylaws]</ref>
| |
| * [[FFmpeg]] <ref>[http://article.gmane.org/gmane.comp.video.ffmpeg.devel/113026/match=%22schulze%20method%22+%22Cloneproof%20schwartz%20sequential%20droping%22+Condorcet Democratic election of the server admins], July 2010</ref>
| |
| * [[Five Star Movement]] of [[Monte Compatri]] <ref>article 25(5) of the [http://www.5stellemontecompatri.it/wp-content/uploads/2013/11/REGOLAMENTO-M5S-Montecompatri1.doc bylaws], October 2013</ref> and [[Montemurlo]] <ref>[http://www.montemurlo5stelle.net/2013/11/2-step-comunarie-di-montemurlo.html 2° Step Comunarie di Montemurlo], November 2013</ref>
| |
| * Flemish Student Society of Leuven <ref>article 51 of the [http://www.vtk.be/page/file/ef87370c1d5798758d1730a14f7410d96783301e/ statutory rules]</ref>
| |
| * [[Free Geek]] <ref>[http://wiki.freegeek.org/images/7/7a/Voters_guide.pdf Voters Guide], September 2011</ref>
| |
| * Free Hardware Foundation of Italy <ref>See:
| |
| * [http://fhf.it/notizie/nuovo-consiglio-nella-fhf Eletto il nuovo Consiglio nella Free Hardware Foundation], June 2008
| |
| * [http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?id=E_5b6e434828ec547b Poll Results], June 2008</ref>
| |
| * [[Free Software Foundation Europe|Free Software Foundation Europe (FSFE)]] <ref name=FSFE/>
| |
| * [[Gentoo Linux|Gentoo Foundation]] <ref name=Gentoo/>
| |
| * [[GNU Privacy Guard|GNU Privacy Guard (GnuPG)]] <ref>[http://logo-contest.gnupg.org/results.html GnuPG Logo Vote], November 2006</ref>
| |
| * Gothenburg Hacker Space (GHS) <ref>§14 of the [http://gbg.hackerspace.se/site/om-ghs/stadgar/ bylaws]</ref>
| |
| * Graduate Student Organization at the State University of New York: Computer Science (GSOCS) <ref>{{cite web|url=http://gso.cs.binghamton.edu/index.php/Voting |title=User Voting Instructions |publisher=Gso.cs.binghamton.edu |date= |accessdate=2010-05-08}}</ref>
| |
| * [[Haskell (programming language)|Haskell]] <ref>[http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?num_winners=1&id=E_d21b0256a4fd5ed7&algorithm=beatpath Haskell Logo Competition], March 2009</ref>
| |
| * [http://ithacagenerator.org/ Ithaca Generator] <ref>article VI section 10 of the [http://ithacagenerator.org/alternate-membership-terms/bylaws/ bylaws], November 2012</ref>
| |
| * Kanawha Valley Scrabble Club <ref>[http://wvscrabble.blogspot.com/2009/04/club-by-any-other-name.html A club by any other name ...], April 2009</ref>
| |
| * [[KDE|KDE e.V.]] <ref name=KDE/>
| |
| * [[Kingman Hall]] <ref>See:
| |
| * Ka-Ping Yee, [http://www.livejournal.com/users/zestyping/102718.html Condorcet elections], March 2005
| |
| * Ka-Ping Yee, [http://www.livejournal.com/users/zestyping/111588.html Kingman adopts Condorcet voting], April 2005</ref>
| |
| * [[John S. and James L. Knight Foundation|Knight Foundation]] <ref>[http://civic.mit.edu/blog/andrew/knight-foundation-awards-5000-to-best-created-on-the-spot-projects Knight Foundation awards $5000 to best created-on-the-spot projects], June 2009</ref>
| |
| * [[Kubuntu]] <ref>[http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?id=E_31619806caaf95b5 Kubuntu Council 2013], May 2013</ref>
| |
| * [[Kumoricon]] <ref>See:
| |
| * [http://www.kumoricon.org/forums/index.php?topic=2599.45 Mascot 2007 contest], July 2006
| |
| * [http://www.kumoricon.org/forums/index.php?topic=4497.0 Mascot 2008 and cover 2007 contests], May 2007
| |
| * [http://www.kumoricon.org/forums/index.php?topic=6653.0 Mascot 2009 and program cover 2008 contests], April 2008
| |
| * [http://www.kumoricon.org/forums/index.php?topic=10048.0 Mascot 2010 and program cover 2009 contests], May 2009
| |
| * [http://www.kumoricon.org/forums/index.php?topic=12955.0 Mascot 2011 and book cover 2010 contests], May 2010
| |
| * [http://www.kumoricon.org/forums/index.php?topic=15340.0 Mascot 2012 and book cover 2011 contests], May 2011</ref>
| |
| * [[League of Professional System Administrators|League of Professional System Administrators (LOPSA)]] <ref>article 8.3 of the [http://governance.lopsa.org/LOPSA_Bylaws bylaws]</ref>
| |
| * [http://www.libre-entreprise.org/ Libre-Entreprise] <ref>See:
| |
| * [http://www.libre-entreprise.org/index.php/Election:DateReunionSolutionLinux2006 Choix de date pour la réunion Libre-entreprise durant le Salon Solution Linux 2006], January 2006
| |
| * [http://www.libre-entreprise.org/index.php/Election:EntreeLibricks Entrée de Libricks dans le réseau Libre-entreprise], February 2008</ref>
| |
| * [[LiquidFeedback]] <ref>{{cite web|title=Concepts|url=http://liquidfeedback.org/|work=Home page of LiquidFeedback|publisher=Interactive Democracy|accessdate=26 December 2012}}</ref>
| |
| * [[Cinelerra|Lumiera/Cinelerra]] <ref>[http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?id=E_7df51370797b45d6 Lumiera Logo Contest], January 2009</ref>
| |
| * Mathematical Knowledge Management Interest Group (MKM-IG) <ref>The MKM-IG uses [http://condorcet-dd.sourceforge.net/ Condorcet with dual dropping]. That means: The Schulze ranking and the [[ranked pairs]] ranking are calculated and the winner is the top-ranked candidate of that of these two rankings that has the better Kemeny score. See:
| |
| * MKM-IG Charter
| |
| * [[Michael Kohlhase]], [http://lists.jacobs-university.de/pipermail/projects-mkm-ig/2004-November/000041.html MKM-IG Trustees Election Details & Ballot], November 2004
| |
| * Andrew A. Adams, [http://lists.jacobs-university.de/pipermail/projects-mkm-ig/2005-December/000072.html MKM-IG Trustees Election 2005], December 2005
| |
| * Lionel Elie Mamane, [http://lists.jacobs-university.de/pipermail/projects-mkm-ig/2007-August/000406.html Elections 2007: Ballot], August 2007</ref>
| |
| * [[Metalab]] <ref>{{cite web|url=http://metalab.at/wiki/Generalversammlung_2007/Wahlmodus |title=Wahlmodus |language={{de icon}} |publisher=Metalab.at |date= |accessdate=2010-05-08}}</ref>
| |
| * [[MTV|Music Television (MTV)]] <ref>[[Benjamin Mako Hill]], [http://www.oscon.com/oscon2008/public/schedule/detail/3230 Voting Machinery for the Masses], July 2008</ref>
| |
| * [[:de:Neo (Tastaturbelegung)|Neo]] <ref>See:
| |
| * [http://wiki.neo-layout.org/wiki/Neo-2-Freeze/Wahl?version=10#a7.Wahlverfahren Wahlen zum Neo-2-Freeze: Formalitäten], February 2010
| |
| * [http://wiki.neo-layout.org/wiki/Neo-2-Freeze/Wahl/Stimmabgabe?version=11 Hinweise zur Stimmabgabe], March 2010
| |
| * [http://wiki.neo-layout.org/wiki/Neo-2-Freeze/Wahl/Ergebnisse?version=9 Ergebnisse], March 2010</ref>
| |
| * [[Noisebridge]] <ref>[https://www.noisebridge.net/index.php?title=2009_Director_Elections&oldid=8951 2009 Director Elections]</ref>
| |
| * North Shore Cyclists (NSC) <ref>[http://www.nscyc.org/JerseyWinner NSC Jersey election], [http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?id=E_6c53f2bddb068673 NSC Jersey vote], September 2007</ref>
| |
| * [[OpenEmbedded]] <ref>[http://www.openembedded.org/index.php/Online_Voting_Policy Online Voting Policy]</ref>
| |
| * [[OpenStack]] <ref>See:
| |
| * [http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?id=E_f35052f9f6d58f36&rkey=4603fbf32e182e6c 2010 OpenStack Community Election], November 2010
| |
| * [http://www.openstack.org/blog/2012/02/openstack-governance-elections-spring-2012/ OpenStack Governance Elections Spring 2012], February 2012</ref>
| |
| * [http://www.parkscholars.org/index.php Park Alumni Society (PAS)] <ref>{{cite web|url=http://www.parkscholars.org/voting.php |title=Voting Procedures |publisher=Parkscholars.org |date= |accessdate=2010-05-08}}</ref>
| |
| * [[Pirate Party Australia]] <ref>[http://pirateparty.org.au/2011/11/18/national-congress-2011-results/ National Congress 2011 Results], November 2011</ref>
| |
| * [[Pirate Party of Austria]] <ref>§6(10) of the [http://wiki.piratenpartei.at/wiki/Satzung bylaws]</ref>
| |
| * [[Pirate Party Belgium|Pirate Party of Belgium]] <ref>[http://piratetimes.net/the-belgian-pirate-party-announces-top-candidates-for-the-european-electionsthe-belgian-pirate-party-announces-top-candidates-for-the-european-elections/ The Belgian Pirate Party Announces Top Candidates for the European Elections], January 2014</ref>
| |
| * [[Pirate Party of Brazil]]
| |
| * [[Pirate Party (France)|Pirate Party of France]] <ref>§11.2.E of the [http://partipirate.org/ri.pdf statutory rules]</ref>
| |
| * [[Pirate Party Germany|Pirate Party of Germany]] <ref name=PiratePartyGermany/>
| |
| * [[Pirate Party Iceland]] <ref>article 7.5 of the [http://www.piratar.is/um-pirata/log-felagsins/ bylaws]</ref>
| |
| * [[Italian Pirate Party|Pirate Party of Italy]] <ref>[http://www.partito-pirata.it/statute/ Rules adopted on 18 December 2011]</ref>
| |
| * [[Mexican Pirate wikiParty|Pirate Party of Mexico]] <ref>[http://wikipartido.mx/Timon-war/faces/votacionydebate/votacion/votResultados.xhtml?vid=1 Vote Result for Name Definition]</ref>
| |
| * [[Pirate Party of the Netherlands]] <ref>[https://www.piratenpartij.nl/blog/argure/help-mee-met-het-nieuwe-piratenpartij-logo Help mee met het nieuwe Piratenpartij-logo!], August 2013</ref>
| |
| * [[Pirate Party of New Zealand]] <ref>[http://pirateparty.org.nz/wiki/23_January_2011_meeting_minutes 23 January 2011 meeting minutes]</ref>
| |
| * [[Pirate Party (Sweden)|Pirate Party of Sweden]] <ref name=PiratePartySweden/>
| |
| * [[Pirate Party of Switzerland]] <ref>[http://blog.florian-pankerl.de/?p=444 Piratenversammlung der Piratenpartei Schweiz], September 2010</ref>
| |
| * [[Pirate Party (United States)|Pirate Party of the United States]] <ref>Article IV Section 4 of the [http://www.pirate-party.us/wiki/Pirate_National_Committee_%28PNC%29/Constitution constitution]</ref>
| |
| * Pitcher Plant of the Month
| |
| * Pittsburgh Ultimate <ref>[http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?id=E_89773564141f0859 2006 Community for Pittsburgh Ultimate Board Election], September 2006</ref>
| |
| * [[RLLMUK]] <ref>[http://www.rllmukforum.com/index.php?/topic/260622-committee-elections-2012/ Committee Elections], April 2012</ref>
| |
| * RPMrepo <ref>[http://rpmrepo.org/driesverachtert/LogoVoting LogoVoting], December 2007</ref>
| |
| * [[Sender Policy Framework|Sender Policy Framework (SPF)]] <ref>See:
| |
| * [http://www.openspf.org/Council_Election SPF Council Election Procedures]
| |
| * [http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?id=E_1fd503d126aaa609 2006 SPF Council Election], January 2006
| |
| * [http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?id=E_8e5a1ca7f86a5d5d 2007 SPF Council Election], January 2007</ref>
| |
| * [[Software in the Public Interest|Software in the Public Interest (SPI)]] <ref name=SPI/>
| |
| * [[Squeak]] <ref>[http://www.cs.cornell.edu/w8/~andru/cgi-perl/civs/results.pl?num_winners=7&id=E_716d8c257e6cf36b&algorithm=beatpath Squeak Oversight Board Election 2010], March 2010</ref>
| |
| * [[Students for Free Culture]] <ref>See:
| |
| * [http://wiki.freeculture.org/Bylaws Bylaws of the Students for Free Culture], article V, section 1.1.1
| |
| * [http://blog.selectricity.org/?p=4 Free Culture Student Board Elected Using Selectricity], February 2008</ref>
| |
| * [[Sugar Labs]] <ref>[http://lists.sugarlabs.org/archive/iaep/2009-September/008620.html Election status update], September 2009</ref>
| |
| * SustainableUnion <ref>§10 III of its [http://sustainableunion.yolasite.com/resources/130614_Satzung_sud_fBayern.pdf bylaws], June 2013</ref>
| |
| * [[Sverok]] <ref>[http://www.sverok.se/wp-content/uploads/2010/11/Protokoll-Riksm%C3%B6te-20102.pdf Minutes of the 2010 Annual Sverok Meeting], November 2010</ref>
| |
| * [[TestPAC]] <ref>article VI section 6 of the [http://testpacpleaseignore.org/official-test-pac-bylaws/ bylaws]</ref>
| |
| * [[TopCoder]] <ref name=TopCoder/>
| |
| * [[Ubuntu (operating system)|Ubuntu]] <ref>[https://lists.ubuntu.com/archives/ubuntu-irc/2012-May/001538.html Ubuntu IRC Council Position], May 2012</ref>
| |
| * University of British Columbia Math Club <ref>See [http://twitter.com/alox/status/11353642881 this mail].</ref>
| |
| * [[Vidya Gaem Awards]] <ref>[http://2012.vidyagaemawards.com/voting/results/pairwise Pairwise Voting Results]</ref>
| |
| * [[Wikipedia]] in [[French Wikipedia|French]],<ref name=FrenchWikipedia/> [[Hebrew Wikipedia|Hebrew]],<ref>See e.g. [http://he.wikipedia.org/w/index.php?title=ויקיפדיה:פרלמנט&oldid=7014412 here] (May 2009), [http://he.wikipedia.org/w/index.php?title=ויקיפדיה:סדנה_לגרפיקה/סמליל&oldid=7388447 here] (August 2009), and [http://he.wikipedia.org/w/index.php?title=ויקיפדיה:סדנה_לגרפיקה/100,000/הצבעה&oldid=8057743 here] (December 2009).</ref> [[Hungarian Wikipedia|Hungarian]],<ref>See [[:hu:Wikipédia:Szavazás/Az „Arbitrációs Bizottság” magyar neve|here]] and [[:hu:Sablonvita:Bővebben/Szavazás#A szavazás módja|here]].</ref> and [[Russian Wikipedia|Russian]].<ref>See:
| |
| * [[tools:~kalan/arb7/schulze|Result of 2007 Arbitration Committee Elections]]
| |
| * [[tools:~kalan/arb8/schulze|Result of 2008 Arbitration Committee Elections]]
| |
| * [[tools:~kalan/arb9/schulze|Result of 2009 Arbitration Committee Elections]]
| |
| * [[tools:~kalan/arb10/schulze|Result of 2010 Arbitration Committee Elections]]</ref>
| |
| {{Colend}}
| |
| | |
| == Notes ==
| |
| {{reflist|2}}
| |
| {{refbegin}}
| |
| {{refend}}
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| | |
| == External links ==
| |
| {{Commons}}
| |
| * {{official website|http://m-schulze.9mail.de/}}
| |
| * [http://www.dsi.unifi.it/~PP2009/talks/Talks_giovedi/Talks_giovedi/grabmeier.pdf Condorcet Computations] by Johannes Grabmeier
| |
| * [http://www.informatik.uni-freiburg.de/~ki/teaching/ss09/gametheory/spieltheorie.pdf Spieltheorie] {{de icon}} by [[Bernhard Nebel]]
| |
| * [http://accuratedemocracy.com/voting_rules.htm Accurate Democracy] by Rob Loring
| |
| * Christoph Börgers (2009), ''[http://books.google.com/books?id=dccBaphP1G4C&pg=PA37 Mathematics of Social Choice: Voting, Compensation, and Division]'', SIAM, ISBN 0-89871-695-0
| |
| * [[Nicolaus Tideman]] (2006), ''[http://books.google.com/books?id=RN5q_LuByUoC&pg=PA228 Collective Decisions and Voting: The Potential for Public Choice]'', Burlington: Ashgate, ISBN 0-7546-4717-X
| |
| * [http://www.public-software-group.org/preftools preftools] by the Public Software Group
| |
| * [http://www.azsos.gov/election/2008/general/ballotmeasuretext/I-21-2008.pdf Arizonans for Condorcet Ranked Voting]
| |
| * [http://ballotpedia.org/wiki/index.php?title=Arizona_Competitive_Elections_Reform_Act_%282008%29]
| |
| * [http://www.ballot-access.org/2008/04/29/arizona-high-school-student-files-paperwork-for-initiatives-for-irv-and-easier-ballot-access/]
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| [[Category:Articles with example pseudocode]]
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| [[Category:Debian]]
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| [[Category:Electoral reform]]
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| [[Category:Electoral systems]]
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| [[Category:Monotonic Condorcet methods]]
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| [[Category:Single-winner electoral systems]]
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| [[Category:Voting systems]]
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| {{Link GA|pl}}
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