Knowledge (XXG)

Schulze method

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924: 3024:# Input: d, the number of voters who prefer candidate i to candidate j. # Output: p, the strength of the strongest path from candidate i to candidate j. for i from 1 to C for j from 1 to C if i ≠ j then if d > d then p := d else p := 0 for i from 1 to C for j from 1 to C if i ≠ j then for k from 1 to C if i ≠ k and j ≠ k then p := max (p, min (p, p)) 2209: 2195: 2181: 2167: 2145: 2128: 2114: 2100: 2078: 2064: 2047: 2033: 2011: 1997: 1983: 1966: 1944: 1930: 1916: 1902: 1379: 59: 899: 1083: 911: 1847:. An arrow from the node representing a candidate X to the one representing a candidate Y is labelled with d. To avoid cluttering the diagram, an arrow has only been drawn from X to Y when d > d (i.e. the table cells with light green background), omitting the one in the opposite direction (the table cells with light red background). 5145:
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. 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,
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Otherwise, draw a square box around the Schwartz set in the upper left corner. It can be described as the minimal "winner's circle" of candidates who do not lose to anyone outside the circle. Note that to the right of the box there is no red, which means it is a winner's circle, and note that within
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Make the results table, called the "matrix of pairwise preferences", such as used above in the example. Then, every positive number is a pairwise win for the candidate on that row (and marked green), ties are zeroes, and losses are negative (marked red). Order the candidates by how long they last in
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One example of computing the strongest path strength is p = 33: the strongest path from B to D is the direct path (B, D) which has strength 33. But when computing p, 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)
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In Highest median, Ranked Pairs, and Schulze voting, there is always a regret-free, semi-honest ballot for any voter, holding all other ballots constant and assuming they know enough about how others will vote. Under such circumstances, there is always at least one way for a voter to participate
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If there is still no candidate with no red on their line, something needs to be compromised on; every candidate lost some race, and the loss we tolerate the best is the one where the loser obtained the most votes. So, take the red cell with the highest number (if going by margins, the least
1113:. The strength of a single-step beatpath from Alice to Bob is just the number of voters who rank Alice over Bob. For a longer beatpath, consisting of multiple "beats", the strength of a beatpath is as strong as its weakest link (i.e. the beat with the smallest number of winning votes). 3055:
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 represents either the number of voters who strictly prefer A to B (A>B), or the
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This method can also be used to calculate a result, if the table is remade in such a way that one can conveniently and reliably rearrange the order of the candidates on both the row and the column, with the same order used on both at all times.
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We say Alice has a "beatpath-win" over Bob if her strongest beatpath to Bob is stronger than all of Bob's beatpaths to Alice. The winner is the candidate who has a beatpath-win over every other candidate.
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A randomly chosen ballot determines winner. This and closely related methods are of mathematical interest and included here to demonstrate that even unreasonable methods can pass voting method criteria.
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Majority Judgment fails the mutual majority criterion, but satisfies the criterion if the majority ranks the mutually favored set above a given absolute grade and all others below that grade.
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The cells for d have a light green background if d > d, otherwise the background is light red. There is no undisputed winner by only looking at the pairwise differences here.
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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
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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
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Majority Judgment may elect a candidate uniquely least-preferred by over half of voters, but it never elects the candidate uniquely bottom-rated by over half of voters.
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the winner of the Schulze method. This method is equivalent to the others described here, but the presentation is optimized for the significance of steps being
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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 underlined.
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Where a winner is randomly chosen from the candidates, sortition is included to demonstrate that even non-voting methods can pass some criteria.
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A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm.
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Approval voting, score voting, and majority judgment satisfy IIA if it is assumed that voters rate candidates independently using their own
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Tideman, T. Nicolaus, "Independence of clones as a criterion for voting rules", Social Choice and Welfare vol 4 #3 (1987), pp. 185–206.
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The Schulze method was developed by Markus Schulze in 1997. It was first discussed in public mailing lists in 1997–1998 and in 2000.
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defeats Bob, and Bob beats Charlie, then Alice "indirectly" defeats Charlie; this kind of indirect win is called a 'beatpath'.
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Although ties in the Schulze ranking are unlikely, they are possible. Schulze's original paper recommended breaking ties by
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So we get straight to the second drop (E's loss to C by 3 votes), and that shows us the winner, E, with its clear row.
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Here is a margins table made from the above example. Note the change of order used for demonstration purposes.
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beats Bob, and Bob beats Charlie, then Alice (indirectly) beats Charlie; this kind of indirect win is called a
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A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method
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A new monotonic, clone-independent, reversal symmetric, and Condorcet-consistent single-winner election method
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Since the Schulze method satisfies the Condorcet criterion, it automatically fails the following criteria:
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with all the candidates as nodes; label the edges with the number of votes supporting the winner.
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with equal ratings allowed. There are two common (equivalent) descriptions of Schulze's method.
877: 7283: 6303:[Some considerations on which group Volt Europe will join in the European Parliament]. 8029: 7938: 7895: 7815: 7737: 7660: 7645: 7603: 7459: 7454: 7440: 6870: 6348: 5919:[The raw result of the primary election] (in Swedish). 19 January 2010. Archived from 5711:", Social Choice and Welfare, volume 36, number 2, page 267–303, 2011. Preliminary version in 5667:", Social Choice and Welfare, volume 36, number 2, page 267–303, 2011. Preliminary version in 5479: 4401: 4085: 3929: 3545: 834: 804: 726: 663: 497: 224: 199: 182: 50: 7435: 7019: 5991: 5819: 5812: 5664: 2947: 8070: 7702: 7558: 7543: 7449: 7326: 6305: 4665: 4507: 3699: 3583: 3576: 2208: 2194: 2180: 2166: 2144: 2127: 2113: 2099: 2077: 2063: 2046: 2032: 2010: 1996: 1982: 1965: 1943: 1929: 1915: 1901: 1125: 1013: 972: 915: 872: 763: 751: 465: 341: 167: 161: 143: 132: 127: 115: 76: 38: 17: 7212: 6360: 5346:
Graduate Student Organization at the State University of New York: Computer Science (GSOCS)
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The following table compares the Schulze method with other single-winner election methods:
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The Schulze winner can also be constructed iteratively, using a defeat-dropping method:
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the box there is no reordering possible that would produce a smaller winner's circle.
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than candidate D. Continuing in this way, the result is that the Schulze ranking is
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Now the output of the Schulze method can be determined. For example, when comparing
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in February chose this method for their first special election held in March 2018.
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Operating Procedures of the Address Council of the Address Supporting Organization
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The first drop (A's loss to E by 1 vote) does not help shrink the Schwartz set.
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The pairwise preferences have to be computed first. For example, when comparing
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of candidates is the strength of the strongest pairwise win of a candidate A ∉
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also exists. The Schulze method is used by several organizations including
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for unbinding internal opinion polls. In 2010/2011, the Pirate Parties of
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the Schulze order reverses a larger majority than the Ranked Pairs order.
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without grading any less-preferred candidate above any more-preferred one.
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of (voters with A>B) minus (voters with B>A). But no matter how the
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Associated Student Government at the Computer Sciences Department of the
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negative), make it green—or any color other than red—and go back step 2.
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Knight Foundation awards $ 5000 to best created-on-the-spot projects
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through their use of the WeGovNow platform, which in turn uses the
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s are defined, the Schulze ranking has no cycles, and assuming the
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The winner is the only candidate left at the end of the procedure.
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Likewise, since the Schulze method is not a dictatorship and is a
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Constitutional Amendment: Condorcet/Clone Proof SSD Voting Method
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Collective Decisions and Voting: The Potential for Public Choice
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Mathematics of Social Choice: Voting, Compensation, and Division
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Markus Schulze proved that this definition of a beatpath-win is
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Check if any candidates are tied (and if so, break the ties by
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A sample ballot asking voters to order candidates by preference
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11 of the 16 regional sections and the federal section of the
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Organizations which currently use the Schulze method include:
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In 2011, Schulze published the method in the academic journal
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If there is a candidate with no red on their line, they win.
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Ridefinizione della lista di San Cesareo con Metodo Schulze
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h24 notizie - portale indipendente di news dalla provincia
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Constitutional voting, definition of cumulative preference
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2017 Golden Geek Awards - Nominations Open, February 2018
6135:"National Congress 2011 Results – Pirate Party Australia" 6546:
2016 Golden Geek Awards - Nominations Open, January 2017
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2014 Golden Geek Awards - Nominations Open, January 2015
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2013 Golden Geek Awards - Nominations Open, January 2014
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Club der Ehemaligen der Deutschen SchülerAkademien e. V.
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The main difference between the Schulze method and the
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2018 Golden Geek Awards - Nominations Open, March 2019
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2015 Golden Geek Awards - Nominations Open, March 2016
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Election of the Annodex Association committee for 2007
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for all referendums. It is also used by the cities of
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In the following example 45 voters rank 5 candidates.
7366:[Result of Arbitration Committee Elections]. 7311:[Knowledge (XXG):Parliament/Decisionmaking]. 7117:
Free Culture Student Board Elected Using Selectricity
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Campobasso. Comunali, scattano le primarie a 5 Stelle
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The Schulze method satisfies the following criteria:
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developed by Markus Schulze. It is also known as the
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The AEGEEan - AEGEE's online magazine - AEGEE-Europe
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Internet Corporation for Assigned Names and Numbers
975: 7260:"Wikipédia:Prise de décision/Choix dans les votes" 2992: 2928: 2880: 2788: 2681: 2629: 2577: 2525: 2473: 2435: 2399: 2363: 2327: 2291: 1813: 1761: 1709: 1657: 1605: 1567: 1531: 1495: 1459: 1423: 1367: 1326: 1019:Schulze's method is based on the idea of breaking 5391:Institute of Electrical and Electronics Engineers 3101:Cut away every part of the table outside the box. 3086:as a human goes through it, not for computation. 1023:by using indirect victories. The idea is that if 6299:The Board of Directors of Volt Europe in Spain. 5086: 5084: 5401:through their use of the HotCRP decision tool. 1855:of a path is the strength of its weakest link. 6411:"Hillegass-Parker House Bylaws § 5. Elections" 5703: 5701: 5699: 5697: 5343:Flemish Society of Engineering Students Leuven 7528: 6869:. Berlin: Interaktive Demokratie e. V. 2014. 5725: 5723: 5721: 5695: 5693: 5691: 5689: 5687: 5685: 5683: 5681: 5679: 5677: 3652:Local Independence of Irrelevant Alternatives 946: 8: 7985:Independence of Smith-dominated alternatives 6578:Family Affair Voting Scheme - Schulze Method 5525:League of Professional System Administrators 3531:Independence of Smith-dominated alternatives 1102:The idea behind Schulze's method is that if 7020:"OpenStack Election — OpenStack Governance" 5862:"Un any d'aprofundiment democràtic a Silla" 3669:Comparison of single-winner voting systems 1375:. The full set of pairwise preferences is: 7722: 7535: 7521: 7513: 7008:ONNX Steering Committee election guideline 6002:) adopted this method for their primaries. 5188:The Schulze method is used by the city of 3667: 1151:If there is more than one candidate left: 953: 939: 29: 7363:Девятнадцатые выборы арбитров, второй тур 7155:Minutes of the 2018 Annual Sverok Meeting 5731:Properties of Preferential Election Rules 5415:Berufsverband der Kinder- und Jugendärzte 2949: 2897: 2813: 2721: 2659: 2607: 2555: 2503: 2451: 2413: 2377: 2341: 2305: 2269: 1851:which has strength min(30, 28) = 28. The 1791: 1739: 1687: 1635: 1583: 1545: 1509: 1473: 1437: 1401: 1339: 1298: 6693:"CIVS Election Results: GnuPG Logo Vote" 6650:Democratic election of the server admins 6170:Article III.3.4 of the Statutory Rules ( 5073: 5071: 5069: 3359: 3235: 3111: 2256: 1860: 1388: 1184: 1109:Every beatpath is assigned a particular 7980:Independence of irrelevant alternatives 7758:Sequential proportional approval voting 7132:"[IAEP] Election status update" 7104:Bylaws of the Students for Free Culture 6729:Article 6 Section 2 of the Constitution 6388:. Gso.cs.binghamton.edu. Archived from 5834:Hortanoticias, Redacción (2016-02-23). 5656: 5456:European Democratic Education Community 4984: 4978: 3638:Independence of irrelevant alternatives 45: 1168:Delete the edge closest to being tied. 7475:Arizonans for Condorcet Ranked Voting 6945:Wahlen zum Neo-2-Freeze: Formalitäten 6783:Rules of Procedures for Online Voting 6361:Référendum sur la réforme du thurnage 2929:{\displaystyle E>A>C>B>D} 1161:Eliminate all candidates outside the 7: 7168:"2007 TopCoder Collegiate Challenge" 7089:Squeak Oversight Board Election 2010 6957:Hinweise zur Stimmabgabe, March 2010 6227:"Verslag ledenraadpleging 4 januari" 5860:Silla, ~ El Cresol de (2016-05-26). 5737:, issue 3, pages 8–15, December 1994 5127:method can be seen in this example: 3078:There is another alternative way to 3051:Ties and alternative implementations 1385:labeled with pairwise preferences d 1128:, providing a full extension of the 7790:Indirect single transferable voting 6930:Voting for more than just either-or 6610:Constitution for the Debian Project 5905:"Dags att kandidera till riksdagen" 5788:Schulze Method - Simpler Definition 5395:Association for Computing Machinery 5324:Student government and associations 2796:, for the Schulze method candidate 7213:"/v/GAs - Pairwise voting results" 5130:Suppose the MinMax score of a set 25: 6214:Rules adopted on 18 December 2011 5471:Free Hardware Foundation of Italy 5371:Associated Student Government at 5365:Associated Student Government at 5339:École normale supérieure de Paris 5337:Associated Student Government at 2258:Strengths of the strongest paths 6866:The Principles of LiquidFeedback 6589:Steering and Technical committee 6473:Ajith, Van Atta win ASG election 6326:"The Schulze Method – Agora 101" 6225:Pontier, Matthijs (2015-01-11). 5330:AEGEE – European Students' Forum 5230:Democratic Socialists of America 2881:{\displaystyle (31=)p>p(=24)} 2789:{\displaystyle (28=)p>p(=25)} 971: 922: 909: 897: 845:McKelvey–Schofield chaos theorem 491:Semi-proportional representation 123:First preference plurality (FPP) 8160:Single-winner electoral systems 7284:"Pages liées à Méthode Schulze" 6446:Kingman adopts Condorcet voting 6251:Pankerl, Florian (2010-09-18). 6087:. November 2013. Archived from 1390:Matrix of pairwise preferences 7901:Mixed ballot transferable vote 6415:Hillegass-Parker House website 3643:The Schulze method also fails 2987: 2975: 2966: 2954: 2875: 2866: 2863: 2851: 2842: 2830: 2824: 2815: 2783: 2774: 2771: 2759: 2750: 2738: 2732: 2723: 2676: 2664: 2624: 2612: 2572: 2560: 2520: 2508: 2468: 2456: 2430: 2418: 2394: 2382: 2358: 2346: 2322: 2310: 2286: 2274: 1808: 1796: 1756: 1744: 1704: 1692: 1652: 1640: 1600: 1588: 1562: 1550: 1526: 1514: 1490: 1478: 1454: 1442: 1418: 1406: 1356: 1344: 1315: 1303: 883:Harsanyi's utilitarian theorem 840:Moulin's impossibility theorem 805:Conflicting majorities paradox 27:Single-winner electoral system 1: 7482:Command line application and 7193:"Ubuntu IRC Council Position" 7043:Mark, Atwood (May 25, 2016). 6891:"Madisonium Bylaws - Adopted" 6759:"A club by any other name..." 5177:Wikimedia's Board of Trustees 3573:Woodall's plurality criterion 3486:Satisfied and failed criteria 3068:s are unique it has no ties. 3047:is the number of candidates. 3000:for every other candidate X. 709:Frustrated majorities paradox 8102:Comparison of voting systems 7944:Satisfaction approval voting 7929:Single non-transferable vote 7748:Proportional approval voting 7471:by the Public Software Group 7401:The Schulze Method of Voting 7370:(in Russian). Archived from 6829:"Kumoricon – Mascot Contest" 6762:Kanawha Valley Scrabble Club 6695:. 2013-10-03. Archived from 6563:article 7(e)(iii)(2) of the 6309:(in Spanish). Archived from 6272:article IV section 3 of the 6045:Macaro, Mirko (2015-03-03). 5564:Open Neural Network Exchange 5501:Kanawha Valley Scrabble Club 5379:University of Kaiserslautern 878:Condorcet dominance theorems 818:Social and collective choice 18:Schwartz sequential dropping 8155:Monotonic Condorcet methods 7708:Graduated majority judgment 7191:Bell, Alan (May 17, 2012). 6324:Hajdu, Tekla (2017-09-24). 6231:Piratenpartij Noord Holland 5774:Tiebreakers, Subcycle Rules 5216:Schulze was adopted by the 5202:London Borough of Southwark 3020:illustrates the algorithm. 1070:prior to their adoption of 1036:proportional representation 544:By mechanism of combination 315:Proportional representation 8176: 7960:Condorcet winner criterion 7651:First-past-the-post voting 7508:Implementation in Python 3 7503:Implementation in Python 2 7433:Christoph Börgers (2009), 7113:, article V, section 1.1.1 7065:"Committee Elections 2012" 6386:"User Voting Instructions" 5994:) and the Pirate Party of 4982: 3611:Invulnerability to burying 2808:. Another example is that 1063: 1012:. The Schulze method is a 742:Multiple districts paradox 473:Fractional approval voting 461:Interactive representation 8115: 8107:Voting systems by country 8010:Mutual majority criterion 7965:Condorcet loser criterion 7911:Vote linkage mixed system 7823:Largest remainders method 7550: 6973:"2009 Director Elections" 6616:Debian Voting Information 5781:Maybe Schulze is decisive 5587:Students for Free Culture 5160:Social Choice and Welfare 5007:is incompatible with the 3536:Mutual majority criterion 3521:Condorcet loser criterion 1078:Description of the method 1006:ranked-choice voting rule 689:Paradoxes and pathologies 538:Mixed-member proportional 533:Mixed-member majoritarian 528:By results of combination 419:Approval-based committees 8000:Majority loser criterion 7886:Additional member system 7844:Hagenbach-Bischoff quota 7763:Single transferable vote 7688:Positional voting system 7624:Minimax Condorcet method 7582:Combined approval voting 7362: 7331:(August 2009), and here 7024:governance.openstack.org 6811:, Kubernetes, 2022-09-24 6717:Haskell Logo Competition 5917:"Råresultat primärvalet" 5760:Condorect sub-cycle rule 5433:Cloud Foundry Foundation 5138:against a candidate B ∈ 3582:Symmetric-completion if 3511:Majority loser criterion 3022: 3014:Floyd–Warshall algorithm 1040:single transferable vote 868:Condorcet's jury theorem 669:Double simultaneous vote 644:Rural–urban proportional 639:Dual-member proportional 601: 590: 557:Parallel (superposition) 449:Fractional social choice 436:Expanding approvals rule 265: 250: 235: 166: 155: 131: 8025:Resolvability criterion 8015:Participation criterion 7990:Later-no-harm criterion 7806:Highest averages method 7458:, Burlington: Ashgate, 7309:"ויקיפדיה:פרלמנט/הכרעה" 7266:(in French), 2019-08-22 6911:(in German). Metalab.at 6740:section 9.4.7.3 of the 6632:. Eudec.org. 2009-11-15 6459:article 9.4.5.h of the 5940:Pirate Party of Germany 5813:Disambiguation of 4.1.5 5367:Northwestern University 5359:Associated Students of 5222:Pirate Party of Germany 3557:Resolvability criterion 2993:{\displaystyle p\geq p} 2172:E-(31)-D-(28)-C-(29)-B- 1132:to any set of ballots. 1042:(STV) variant known as 795:Tyranny of the majority 572:Fusion (majority bonus) 389:Quota-remainder methods 8066:First-preference votes 8005:Monotonicity criterion 7975:Independence of clones 7678:Simple majoritarianism 7498:Implementation in Ruby 7493:Implementation in Java 7172:community.topcoder.com 6991:"Online Voting Policy" 6960:Ergebnisse, March 2010 6188:Píratar (2013-10-23). 6014:"DSA Special Election" 5373:University of Freiburg 5361:Minerva Schools at KGI 5350:Hillegass Parker House 5218:Pirate Party of Sweden 5180: 3541:Independence of clones 3501:Monotonicity criterion 3113:Initial results table 2994: 2940:wins. In other words, 2930: 2882: 2790: 2683: 2631: 2579: 2527: 2475: 2437: 2401: 2365: 2329: 2293: 2212: 2198: 2184: 2170: 2148: 2131: 2117: 2103: 2081: 2067: 2050: 2036: 2014: 2000: 1986: 1969: 1947: 1933: 1919: 1905: 1815: 1763: 1711: 1659: 1607: 1569: 1533: 1497: 1461: 1425: 1386: 1369: 1328: 1163:majority-preferred set 1090:Schulze's method uses 1087: 1066:. It was also used by 1062:political parties and 929:Mathematics portal 835:Majority impossibility 824:Impossibility theorems 620:Negative vote transfer 441:Method of equal shares 62: 7970:Consistency criterion 7891:Alternative vote plus 7656:Instant-runoff voting 6781:section 3.4.1 of the 6070:article 25(5) of the 5174: 5005:Condorcet's criterion 2995: 2931: 2883: 2791: 2684: 2632: 2580: 2528: 2476: 2438: 2402: 2366: 2330: 2294: 2211: 2197: 2183: 2169: 2147: 2130: 2116: 2102: 2080: 2066: 2049: 2035: 2013: 1999: 1985: 1968: 1946: 1932: 1918: 1904: 1816: 1764: 1712: 1660: 1608: 1570: 1534: 1498: 1462: 1426: 1381: 1370: 1329: 1136:Iterative description 1085: 732:Best-is-worst paradox 721:Pathological response 456:Direct representation 109:Single-winner methods 61: 8040:Seats-to-votes ratio 7811:Webster/Sainte-Laguë 7245:2011 Board Elections 7239:2009 Board Elections 7233:2008 Board Elections 6808:Kubernetes Community 5980:Tempelhof-Schöneberg 5923:on 24 December 2012. 5899:on 24 December 2012. 5729:Douglas R. Woodall, 5498:(ICANN) (until 2023) 3760:No favorite betrayal 2948: 2896: 2888:, so candidate E is 2812: 2720: 2658: 2606: 2554: 2502: 2450: 2412: 2376: 2340: 2304: 2268: 1790: 1738: 1686: 1634: 1582: 1544: 1508: 1472: 1436: 1400: 1368:{\displaystyle d=25} 1338: 1327:{\displaystyle d=20} 1297: 1269:pairwise, there are 1191:Order of preference 1098:Beatpath explanation 916:Economics portal 863:Median voter theorem 82:Comparative politics 8020:Plurality criterion 7619:Kemeny–Young method 7217:vidyagaemawards.com 7136:lists.sugarlabs.org 6851:article 8.3 of the 6630:"Guidance Document" 6439:Condorcet elections 5964:Steglitz-Zehlendorf 5893:"Inför primärvalen" 5437:County Highpointers 5410:Annodex Association 4929:Tideman alternative 3670: 3516:Condorcet criterion 3362: 3361:Second drop, final 3238: 3114: 3010:widest path problem 2259: 1863: 1391: 904:Politics portal 615:Vote linkage system 586:Seat linkage system 173:Ranked-choice (RCV) 8061:Election threshold 7995:Majority criterion 7671:Supplementary vote 7428:Accurate Democracy 7407:The Schulze Method 7109:2013-03-18 at the 6950:2011-07-27 at the 6655:2015-10-02 at the 6372:article 57 of the 6313:on 20 August 2024. 6190:"Schulze aðferðin" 6141:. 18 November 2011 6139:pirateparty.org.au 6108:article 12 of the 5866:El Cresol de Silla 5389:It is used by the 5237:Five Star Movement 5181: 5175:Sample ballot for 3668: 3633:implies it fails: 3562:Polynomial runtime 3506:Majority criterion 3491:Satisfied criteria 3360: 3236: 3112: 3028:This algorithm is 2990: 2926: 2878: 2786: 2679: 2627: 2575: 2523: 2471: 2433: 2397: 2361: 2325: 2289: 2257: 2213: 2199: 2185: 2171: 2149: 2132: 2118: 2104: 2082: 2068: 2051: 2037: 2015: 2001: 1987: 1970: 1948: 1934: 1920: 1906: 1861: 1811: 1759: 1707: 1655: 1603: 1565: 1529: 1493: 1457: 1421: 1389: 1387: 1365: 1324: 1285:voters who prefer 1273:voters who prefer 1088: 800:Discursive dilemma 759:Lesser evil voting 634:Supermixed systems 337:Largest remainders 195:Round-robin voting 63: 8150:Electoral systems 8132: 8131: 8030:Reversal symmetry 7939:Cumulative voting 7921:Semi-proportional 7896:Mixed single vote 7862: 7861: 7738:Mixed single vote 7646:Exhaustive ballot 7609:Copeland's method 7604:Condorcet methods 7544:Electoral systems 7403:by Markus Schulze 7328:(May 2009), here 6876:978-3-00-044795-2 6681:Project:Elections 6484:§6 and §7 of its 6012:Chumich, Andrew. 5840:Hortanoticias.com 5707:Markus Schulze, " 5663:Markus Schulze, " 5612:Vidya Gaem Awards 5510:Knight Foundation 5480:GNU Privacy Guard 5475:Gentoo Foundation 5310:the United States 5212:Political parties 5198:San Donà di Piave 5116: 5115: 3546:Reversal symmetry 3479: 3478: 3355: 3354: 3231: 3230: 3084:visually apparent 2706: 2705: 2682:{\displaystyle p} 2630:{\displaystyle p} 2578:{\displaystyle p} 2526:{\displaystyle p} 2474:{\displaystyle p} 2436:{\displaystyle p} 2400:{\displaystyle p} 2364:{\displaystyle p} 2328:{\displaystyle p} 2292:{\displaystyle p} 2255: 2254: 1838: 1837: 1814:{\displaystyle d} 1762:{\displaystyle d} 1710:{\displaystyle d} 1658:{\displaystyle d} 1606:{\displaystyle d} 1568:{\displaystyle d} 1532:{\displaystyle d} 1496:{\displaystyle d} 1460:{\displaystyle d} 1424:{\displaystyle d} 1259: 1258: 963: 962: 850:Gibbard's theorem 790:Dominance paradox 727:Perverse response 431:Phragmen's method 297:Majority judgment 225:Positional voting 183:Condorcet methods 51:electoral systems 16:(Redirected from 8167: 8071:Liquid democracy 7723: 7703:Two-round system 7614:Dodgson's method 7537: 7530: 7523: 7514: 7450:Nicolaus Tideman 7420: 7388: 7382: 7376: 7375: 7358: 7352: 7341: 7335: 7334:(December 2009). 7323: 7317: 7316: 7313:he.wikipedia.org 7305: 7299: 7298: 7296: 7295: 7288:fr.wikipedia.org 7280: 7274: 7273: 7272: 7271: 7256: 7250: 7227: 7221: 7220: 7209: 7203: 7202: 7200: 7199: 7188: 7182: 7181: 7179: 7178: 7164: 7158: 7152: 7146: 7145: 7143: 7142: 7128: 7122: 7098: 7092: 7086: 7080: 7079: 7077: 7076: 7061: 7055: 7054: 7052: 7051: 7040: 7034: 7033: 7031: 7030: 7016: 7010: 7005: 6999: 6998: 6995:openembedded.org 6987: 6981: 6980: 6969: 6963: 6939: 6933: 6928:David Chandler, 6926: 6920: 6919: 6917: 6916: 6905: 6899: 6898: 6887: 6881: 6880: 6861: 6855: 6849: 6843: 6842: 6840: 6839: 6825: 6819: 6818: 6817: 6816: 6803: 6797: 6791: 6785: 6779: 6773: 6772: 6770: 6769: 6755: 6749: 6738: 6732: 6726: 6720: 6714: 6708: 6707: 6705: 6704: 6689: 6683: 6678: 6672: 6671:, September 2011 6666: 6660: 6647: 6641: 6640: 6638: 6637: 6626: 6620: 6598: 6592: 6586: 6580: 6574: 6568: 6561: 6555: 6532: 6526: 6519: 6513: 6507: 6501: 6495: 6489: 6482: 6476: 6470: 6464: 6457: 6451: 6432: 6426: 6425: 6423: 6421: 6407: 6401: 6400: 6398: 6397: 6382: 6376: 6370: 6364: 6358: 6352: 6346: 6340: 6339: 6337: 6336: 6321: 6315: 6314: 6296: 6290: 6283: 6277: 6270: 6264: 6263: 6261: 6260: 6248: 6242: 6241: 6239: 6238: 6222: 6216: 6211: 6205: 6204: 6202: 6201: 6185: 6179: 6168: 6162: 6156: 6150: 6149: 6147: 6146: 6131: 6125: 6119: 6113: 6106: 6100: 6099: 6097: 6096: 6081: 6075: 6068: 6062: 6061: 6059: 6058: 6042: 6036: 6030: 6024: 6023: 6021: 6020: 6009: 6003: 5936: 5927: 5924: 5912: 5911:on 23 July 2014. 5900: 5886: 5877: 5876: 5874: 5873: 5857: 5851: 5850: 5848: 5847: 5831: 5825: 5806: 5800: 5793:Markus Schulze, 5790:, September 1998 5779:Markus Schulze, 5772:Markus Schulze, 5758:Markus Schulze, 5753: 5747: 5744: 5738: 5727: 5716: 5715:, 17:9-19, 2003. 5705: 5672: 5671:, 17:9-19, 2003. 5661: 5423: 5314:SustainableUnion 5220:(2009), and the 5109: 5106: 5100: 5097: 5091: 5088: 5079: 5075: 5064: 5061: 5055: 5052: 5046: 5039: 5028: 5025:sincere favorite 5002: 4826: 4797: 4753: 4648: 4562: 4441: 4416: 4280: 4270: 4254: 4250: 3872:Appr­ovals 3851: 3762: 3756: 3750: 3733:Clone­proof 3729: 3719: 3713: 3702: 3700:Condorcet winner 3671: 3659:Comparison table 3650:'s criterion of 3363: 3239: 3115: 3016:. The following 2999: 2997: 2996: 2991: 2943: 2939: 2935: 2933: 2932: 2927: 2887: 2885: 2884: 2879: 2807: 2799: 2795: 2793: 2792: 2787: 2715: 2711: 2688: 2686: 2685: 2680: 2636: 2634: 2633: 2628: 2584: 2582: 2581: 2576: 2532: 2530: 2529: 2524: 2480: 2478: 2477: 2472: 2442: 2440: 2439: 2434: 2406: 2404: 2403: 2398: 2370: 2368: 2367: 2362: 2334: 2332: 2331: 2326: 2298: 2296: 2295: 2290: 2260: 2105:D-(28)-C-(29)-B- 2016:B-(33)-D-(28)-C- 1949:A-(30)-D-(28)-C- 1864: 1862:Strongest paths 1820: 1818: 1817: 1812: 1768: 1766: 1765: 1760: 1716: 1714: 1713: 1708: 1664: 1662: 1661: 1656: 1612: 1610: 1609: 1604: 1574: 1572: 1571: 1566: 1538: 1536: 1535: 1530: 1502: 1500: 1499: 1494: 1466: 1464: 1463: 1458: 1430: 1428: 1427: 1422: 1392: 1374: 1372: 1371: 1366: 1333: 1331: 1330: 1325: 1292: 1288: 1284: 1280: 1276: 1272: 1268: 1264: 1188:Number of voters 1185: 1126:Condorcet method 1014:Condorcet method 1000: 999: 996: 995: 992: 989: 986: 983: 980: 977: 955: 948: 941: 927: 926: 914: 913: 902: 901: 857:Positive results 752:Strategic voting 649:Majority jackpot 606: 595: 466:Liquid democracy 342:National remnant 332:Highest averages 269: 254: 239: 171: 162:Alternative vote 160: 144:Partisan primary 136: 77:Mechanism design 30: 21: 8175: 8174: 8170: 8169: 8168: 8166: 8165: 8164: 8135: 8134: 8133: 8128: 8111: 8090: 8044: 8035:Smith criterion 7948: 7915: 7876:Parallel voting 7858: 7854:Imperiali quota 7827: 7794: 7712: 7666:Contingent vote 7629:Nanson's method 7587:Unified primary 7577:Approval voting 7563: 7546: 7541: 7418: 7397: 7392: 7391: 7383: 7379: 7364: 7360: 7359: 7355: 7342: 7338: 7324: 7320: 7307: 7306: 7302: 7293: 7291: 7282: 7281: 7277: 7269: 7267: 7258: 7257: 7253: 7228: 7224: 7211: 7210: 7206: 7197: 7195: 7190: 7189: 7185: 7176: 7174: 7166: 7165: 7161: 7157:, November 2018 7153: 7149: 7140: 7138: 7130: 7129: 7125: 7119:, February 2008 7111:Wayback Machine 7099: 7095: 7087: 7083: 7074: 7072: 7071:. 10 April 2012 7063: 7062: 7058: 7049: 7047: 7042: 7041: 7037: 7028: 7026: 7018: 7017: 7013: 7006: 7002: 6989: 6988: 6984: 6977:noisebridge.net 6971: 6970: 6966: 6954:, February 2010 6952:Wayback Machine 6940: 6936: 6927: 6923: 6914: 6912: 6907: 6906: 6902: 6889: 6888: 6884: 6877: 6863: 6862: 6858: 6850: 6846: 6837: 6835: 6827: 6826: 6822: 6814: 6812: 6805: 6804: 6800: 6792: 6788: 6780: 6776: 6767: 6765: 6757: 6756: 6752: 6744:(archived from 6739: 6735: 6731:, February 2021 6727: 6723: 6715: 6711: 6702: 6700: 6691: 6690: 6686: 6679: 6675: 6667: 6663: 6657:Wayback Machine 6648: 6644: 6635: 6633: 6628: 6627: 6623: 6599: 6595: 6591:, November 2021 6587: 6583: 6575: 6571: 6562: 6558: 6533: 6529: 6520: 6516: 6512:, February 2007 6508: 6504: 6496: 6492: 6483: 6479: 6471: 6467: 6463:, November 2017 6458: 6454: 6433: 6429: 6419: 6417: 6409: 6408: 6404: 6395: 6393: 6384: 6383: 6379: 6374:statutory rules 6371: 6367: 6359: 6355: 6347: 6343: 6334: 6332: 6323: 6322: 6318: 6298: 6297: 6293: 6285:§10 III of its 6284: 6280: 6271: 6267: 6258: 6256: 6250: 6249: 6245: 6236: 6234: 6224: 6223: 6219: 6212: 6208: 6199: 6197: 6187: 6186: 6182: 6169: 6165: 6157: 6153: 6144: 6142: 6133: 6132: 6128: 6124:, February 2014 6120: 6116: 6107: 6103: 6094: 6092: 6083: 6082: 6078: 6069: 6065: 6056: 6054: 6044: 6043: 6039: 6035:, February 2014 6031: 6027: 6018: 6016: 6011: 6010: 6006: 5937: 5930: 5915: 5903: 5891: 5887: 5880: 5871: 5869: 5859: 5858: 5854: 5845: 5843: 5833: 5832: 5828: 5822:, December 2000 5815:, November 2000 5811:Anthony Towns, 5807: 5803: 5797:, November 1998 5767:Party List P.S. 5765:Mike Ossipoff, 5754: 5750: 5745: 5741: 5728: 5719: 5706: 5675: 5662: 5658: 5653: 5648: 5623:Knowledge (XXG) 5451:EuroBillTracker 5417: 5387: 5326: 5298:the Netherlands 5228:chapter of the 5214: 5208:decision tool. 5186: 5169: 5152: 5120: 5118: 5117: 5112: 5107: 5103: 5098: 5094: 5089: 5082: 5076: 5067: 5062: 5058: 5053: 5049: 5040: 5031: 5003: 4986: 3766: 3706:Condorcet loser 3695:Mutual majority 3681: 3679: 3678: 3676: 3661: 3631:Arrow's Theorem 3594: 3592:Failed criteria 3589: 3526:Smith criterion 3493: 3488: 3053: 3026: 3025: 3006: 2946: 2945: 2941: 2937: 2894: 2893: 2810: 2809: 2805: 2804:than candidate 2797: 2718: 2717: 2713: 2709: 2656: 2655: 2604: 2603: 2552: 2551: 2500: 2499: 2448: 2447: 2410: 2409: 2374: 2373: 2338: 2337: 2302: 2301: 2266: 2265: 2251: 2248: 1872: 1869: 1788: 1787: 1736: 1735: 1684: 1683: 1632: 1631: 1580: 1579: 1542: 1541: 1506: 1505: 1470: 1469: 1434: 1433: 1398: 1397: 1336: 1335: 1295: 1294: 1290: 1286: 1282: 1278: 1274: 1270: 1266: 1262: 1180: 1138: 1100: 1080: 1010:beatpath method 974: 970: 959: 921: 920: 908: 896: 888: 887: 854: 830:Arrow's theorem 820: 810: 809: 778: 748: 737:No-show paradox 718: 704:Cloning paradox 694:Spoiler effects 691: 681: 680: 655: 542: 525: 515: 514: 487: 478:Maximal lottery 445: 426:Thiele's method 415: 385: 317: 307: 306: 292:Approval voting 280:Cardinal voting 276: 221: 215:Maximal lottery 179: 111: 101: 28: 23: 22: 15: 12: 11: 5: 8173: 8171: 8163: 8162: 8157: 8152: 8147: 8137: 8136: 8130: 8129: 8116: 8113: 8112: 8110: 8109: 8104: 8098: 8096: 8092: 8091: 8089: 8088: 8083: 8078: 8073: 8068: 8063: 8058: 8052: 8050: 8046: 8045: 8043: 8042: 8037: 8032: 8027: 8022: 8017: 8012: 8007: 8002: 7997: 7992: 7987: 7982: 7977: 7972: 7967: 7962: 7956: 7954: 7950: 7949: 7947: 7946: 7941: 7936: 7934:Limited voting 7931: 7925: 7923: 7917: 7916: 7914: 7913: 7908: 7903: 7898: 7893: 7888: 7883: 7878: 7872: 7870: 7864: 7863: 7860: 7859: 7857: 7856: 7851: 7846: 7841: 7835: 7833: 7829: 7828: 7826: 7825: 7820: 7819: 7818: 7813: 7802: 7800: 7796: 7795: 7793: 7792: 7787: 7782: 7781: 7780: 7775: 7770: 7760: 7755: 7750: 7745: 7740: 7735: 7729: 7727: 7720: 7714: 7713: 7711: 7710: 7705: 7700: 7695: 7690: 7685: 7680: 7675: 7674: 7673: 7668: 7663: 7661:Coombs' method 7653: 7648: 7643: 7642: 7641: 7639:Schulze method 7636: 7631: 7626: 7621: 7616: 7611: 7601: 7599:Bucklin voting 7596: 7591: 7590: 7589: 7584: 7573: 7571: 7565: 7564: 7551: 7548: 7547: 7542: 7540: 7539: 7532: 7525: 7517: 7511: 7510: 7505: 7500: 7495: 7490: 7477: 7472: 7466: 7447: 7431: 7425: 7423:Bernhard Nebel 7413: 7404: 7396: 7395:External links 7393: 7390: 7389: 7377: 7374:on 2015-02-22. 7353: 7336: 7325:See e.g. here 7318: 7300: 7275: 7251: 7249: 7248: 7242: 7236: 7222: 7204: 7183: 7159: 7147: 7123: 7121: 7120: 7114: 7093: 7081: 7056: 7035: 7011: 7000: 6982: 6964: 6962: 6961: 6958: 6955: 6934: 6921: 6900: 6882: 6875: 6856: 6844: 6820: 6798: 6786: 6774: 6750: 6733: 6721: 6709: 6684: 6673: 6661: 6642: 6621: 6619: 6618: 6613: 6607: 6593: 6581: 6569: 6556: 6554: 6553: 6550: 6547: 6544: 6541: 6538: 6527: 6525:, October 2013 6514: 6502: 6490: 6477: 6465: 6452: 6450: 6449: 6442: 6427: 6402: 6377: 6365: 6353: 6351:, January 2021 6349:Voting Details 6341: 6316: 6291: 6278: 6265: 6243: 6217: 6206: 6196:(in Icelandic) 6180: 6163: 6158:§6(10) of the 6151: 6126: 6114: 6112:, January 2015 6101: 6076: 6074:, October 2013 6063: 6037: 6025: 6004: 5944:LiquidFeedback 5928: 5926: 5925: 5913: 5901: 5878: 5852: 5826: 5824: 5823: 5818:Norman Petry, 5816: 5801: 5799: 5798: 5795:Schulze Method 5791: 5786:Norman Petry, 5784: 5783:, August 1998 5777: 5770: 5763: 5762:, October 1997 5748: 5739: 5735:Voting Matters 5717: 5713:Voting Matters 5673: 5669:Voting Matters 5655: 5654: 5652: 5649: 5647: 5646: 5620: 5614: 5609: 5604: 5599: 5594: 5589: 5584: 5579: 5574: 5571: 5566: 5561: 5556: 5551: 5546: 5541: 5536: 5533: 5531:LiquidFeedback 5528: 5522: 5517: 5512: 5507: 5502: 5499: 5493: 5488: 5483: 5477: 5472: 5469: 5464: 5459: 5453: 5448: 5443: 5438: 5435: 5430: 5425: 5412: 5406: 5386: 5383: 5382: 5381: 5375: 5369: 5363: 5357: 5352: 5347: 5344: 5341: 5335: 5332: 5325: 5322: 5321: 5320: 5315: 5312: 5266:Pirate Parties 5263: 5249:Monte Compatri 5213: 5210: 5206:LiquidFeedback 5185: 5182: 5168: 5165: 5151: 5148: 5114: 5113: 5111: 5110: 5101: 5092: 5080: 5065: 5056: 5047: 5043:absolute scale 5029: 4983: 4981: 4977: 4976: 4975:Ran­king 4973: 4970: 4967: 4964: 4961: 4958: 4955: 4952: 4949: 4946: 4943: 4940: 4937: 4934: 4931: 4925: 4924: 4921: 4918: 4915: 4912: 4909: 4906: 4903: 4900: 4897: 4894: 4891: 4888: 4885: 4882: 4879: 4873: 4872: 4869: 4866: 4863: 4860: 4857: 4854: 4851: 4848: 4845: 4842: 4839: 4836: 4833: 4830: 4827: 4820: 4819: 4816: 4813: 4810: 4807: 4804: 4801: 4798: 4794: 4791: 4788: 4785: 4782: 4779: 4776: 4773: 4767: 4766: 4765:Ran­king 4763: 4760: 4757: 4754: 4750: 4747: 4744: 4741: 4738: 4735: 4732: 4729: 4726: 4723: 4720: 4714: 4713: 4710: 4707: 4704: 4701: 4698: 4695: 4692: 4689: 4686: 4683: 4680: 4677: 4674: 4671: 4668: 4662: 4661: 4660:Ran­king 4658: 4655: 4652: 4649: 4645: 4642: 4639: 4636: 4633: 4630: 4627: 4624: 4621: 4618: 4615: 4609: 4608: 4605: 4602: 4599: 4596: 4593: 4590: 4587: 4584: 4581: 4578: 4575: 4572: 4569: 4566: 4563: 4556: 4555: 4552: 4549: 4546: 4543: 4540: 4537: 4534: 4531: 4528: 4525: 4522: 4519: 4516: 4513: 4510: 4504: 4503: 4502:Ran­king 4500: 4497: 4494: 4491: 4488: 4485: 4482: 4479: 4476: 4473: 4470: 4467: 4464: 4461: 4458: 4452: 4451: 4450:Ran­king 4448: 4445: 4442: 4438: 4435: 4432: 4429: 4426: 4423: 4420: 4417: 4413: 4410: 4407: 4404: 4398: 4397: 4396:Ran­king 4394: 4391: 4388: 4385: 4382: 4379: 4376: 4373: 4370: 4367: 4364: 4361: 4358: 4355: 4352: 4346: 4345: 4344:Ran­king 4342: 4339: 4336: 4333: 4330: 4327: 4324: 4321: 4318: 4315: 4312: 4309: 4306: 4303: 4300: 4298:Instant-runoff 4294: 4293: 4290: 4287: 4284: 4281: 4277: 4274: 4271: 4267: 4264: 4261: 4258: 4255: 4251: 4247: 4244: 4242:Highest median 4238: 4237: 4236:Ran­king 4234: 4231: 4228: 4225: 4222: 4219: 4216: 4213: 4210: 4207: 4204: 4201: 4198: 4195: 4192: 4186: 4185: 4184:Ran­king 4182: 4179: 4176: 4173: 4170: 4167: 4164: 4161: 4158: 4155: 4152: 4149: 4146: 4143: 4140: 4134: 4133: 4132:Ran­king 4130: 4127: 4124: 4121: 4118: 4115: 4112: 4109: 4106: 4103: 4100: 4097: 4094: 4091: 4088: 4082: 4081: 4080:Ran­king 4078: 4075: 4072: 4069: 4066: 4063: 4060: 4057: 4054: 4051: 4048: 4045: 4042: 4039: 4036: 4030: 4029: 4028:Ran­king 4026: 4023: 4020: 4017: 4014: 4011: 4008: 4005: 4002: 3999: 3996: 3993: 3990: 3987: 3984: 3978: 3977: 3976:Ran­king 3974: 3971: 3968: 3965: 3962: 3959: 3956: 3953: 3950: 3947: 3944: 3941: 3938: 3935: 3932: 3926: 3925: 3924:Ran­king 3922: 3919: 3916: 3913: 3910: 3907: 3904: 3901: 3898: 3895: 3892: 3889: 3886: 3883: 3880: 3874: 3873: 3870: 3867: 3864: 3861: 3858: 3855: 3852: 3848: 3845: 3842: 3839: 3836: 3833: 3830: 3827: 3821: 3820: 3817: 3814: 3811: 3808: 3805: 3802: 3799: 3796: 3793: 3790: 3787: 3784: 3781: 3778: 3775: 3773:Anti-plurality 3769: 3768: 3763: 3757: 3751: 3745: 3740: 3738:Mono­tone 3735: 3730: 3720: 3714: 3708: 3703: 3697: 3692: 3690:Majority loser 3687: 3682: 3677: 3674: 3666: 3665: 3660: 3657: 3656: 3655: 3641: 3640: 3619: 3618: 3613: 3608: 3603: 3593: 3590: 3588: 3587: 3586:are used for d 3580: 3579:are used for d 3570: 3567: 3564: 3559: 3554: 3553:Mono-add-plump 3551: 3548: 3543: 3538: 3533: 3528: 3523: 3518: 3513: 3508: 3503: 3497: 3492: 3489: 3487: 3484: 3477: 3476: 3474: 3471: 3468: 3465: 3462: 3458: 3457: 3454: 3452: 3449: 3446: 3443: 3439: 3438: 3435: 3432: 3430: 3427: 3424: 3420: 3419: 3416: 3413: 3410: 3408: 3405: 3401: 3400: 3397: 3394: 3391: 3388: 3386: 3382: 3381: 3378: 3375: 3372: 3369: 3366: 3353: 3352: 3350: 3347: 3344: 3341: 3338: 3334: 3333: 3330: 3328: 3325: 3322: 3319: 3315: 3314: 3311: 3308: 3306: 3303: 3300: 3296: 3295: 3292: 3289: 3286: 3284: 3281: 3277: 3276: 3273: 3270: 3267: 3264: 3262: 3258: 3257: 3254: 3251: 3248: 3245: 3242: 3229: 3228: 3226: 3223: 3220: 3217: 3214: 3210: 3209: 3206: 3204: 3201: 3198: 3195: 3191: 3190: 3187: 3184: 3182: 3179: 3176: 3172: 3171: 3168: 3165: 3162: 3160: 3157: 3153: 3152: 3149: 3146: 3143: 3140: 3138: 3134: 3133: 3130: 3127: 3124: 3121: 3118: 3107: 3106: 3102: 3099: 3095: 3092: 3052: 3049: 3023: 3005: 3004:Implementation 3002: 2989: 2986: 2983: 2980: 2977: 2974: 2971: 2968: 2965: 2962: 2959: 2956: 2953: 2925: 2922: 2919: 2916: 2913: 2910: 2907: 2904: 2901: 2877: 2874: 2871: 2868: 2865: 2862: 2859: 2856: 2853: 2850: 2847: 2844: 2841: 2838: 2835: 2832: 2829: 2826: 2823: 2820: 2817: 2785: 2782: 2779: 2776: 2773: 2770: 2767: 2764: 2761: 2758: 2755: 2752: 2749: 2746: 2743: 2740: 2737: 2734: 2731: 2728: 2725: 2704: 2703: 2701: 2698: 2695: 2692: 2689: 2678: 2675: 2672: 2669: 2666: 2663: 2652: 2651: 2648: 2646: 2643: 2640: 2637: 2626: 2623: 2620: 2617: 2614: 2611: 2600: 2599: 2596: 2593: 2591: 2588: 2585: 2574: 2571: 2568: 2565: 2562: 2559: 2548: 2547: 2544: 2541: 2538: 2536: 2533: 2522: 2519: 2516: 2513: 2510: 2507: 2496: 2495: 2492: 2489: 2486: 2483: 2481: 2470: 2467: 2464: 2461: 2458: 2455: 2444: 2443: 2432: 2429: 2426: 2423: 2420: 2417: 2407: 2396: 2393: 2390: 2387: 2384: 2381: 2371: 2360: 2357: 2354: 2351: 2348: 2345: 2335: 2324: 2321: 2318: 2315: 2312: 2309: 2299: 2288: 2285: 2282: 2279: 2276: 2273: 2263: 2253: 2252: 2249: 2246: 2244: 2241: 2238: 2235: 2232: 2229: 2226: 2225: 2222: 2219: 2205: 2191: 2177: 2163: 2159: 2158: 2155: 2141: 2138: 2124: 2110: 2096: 2092: 2091: 2088: 2074: 2060: 2057: 2043: 2029: 2025: 2024: 2021: 2007: 1993: 1979: 1976: 1962: 1958: 1957: 1954: 1940: 1926: 1912: 1898: 1895: 1891: 1890: 1888: 1885: 1882: 1879: 1876: 1873: 1870: 1867: 1845:directed graph 1836: 1835: 1833: 1830: 1827: 1824: 1821: 1810: 1807: 1804: 1801: 1798: 1795: 1784: 1783: 1780: 1778: 1775: 1772: 1769: 1758: 1755: 1752: 1749: 1746: 1743: 1732: 1731: 1728: 1725: 1723: 1720: 1717: 1706: 1703: 1700: 1697: 1694: 1691: 1680: 1679: 1676: 1673: 1670: 1668: 1665: 1654: 1651: 1648: 1645: 1642: 1639: 1628: 1627: 1624: 1621: 1618: 1615: 1613: 1602: 1599: 1596: 1593: 1590: 1587: 1576: 1575: 1564: 1561: 1558: 1555: 1552: 1549: 1539: 1528: 1525: 1522: 1519: 1516: 1513: 1503: 1492: 1489: 1486: 1483: 1480: 1477: 1467: 1456: 1453: 1450: 1447: 1444: 1441: 1431: 1420: 1417: 1414: 1411: 1408: 1405: 1395: 1383:Directed graph 1364: 1361: 1358: 1355: 1352: 1349: 1346: 1343: 1323: 1320: 1317: 1314: 1311: 1308: 1305: 1302: 1257: 1256: 1253: 1249: 1248: 1245: 1241: 1240: 1237: 1233: 1232: 1229: 1225: 1224: 1221: 1217: 1216: 1213: 1209: 1208: 1205: 1201: 1200: 1197: 1193: 1192: 1189: 1179: 1176: 1172: 1171: 1170: 1169: 1166: 1159: 1149: 1146:directed graph 1137: 1134: 1099: 1096: 1092:ranked ballots 1079: 1076: 967:Schulze method 961: 960: 958: 957: 950: 943: 935: 932: 931: 919: 918: 906: 893: 890: 889: 886: 885: 880: 875: 870: 865: 853: 852: 847: 842: 837: 832: 821: 816: 815: 812: 811: 808: 807: 802: 797: 792: 777: 776: 774:Turkey-raising 771: 766: 761: 747: 746: 745: 744: 734: 729: 717: 716: 714:Center squeeze 711: 706: 701: 699:Spoiler effect 692: 687: 686: 683: 682: 679: 678: 673: 672: 671: 658:By ballot type 654: 653: 652: 651: 646: 641: 631: 630: 629: 628: 627: 622: 612: 611: 610: 599: 576: 575: 574: 569: 564: 559: 541: 540: 535: 526: 521: 520: 517: 516: 513: 512: 510:Limited voting 507: 506: 505: 486: 485: 480: 475: 470: 469: 468: 463: 444: 443: 438: 433: 428: 414: 413: 408: 403: 398: 384: 383: 382: 381: 379:Localized list 376: 371: 366: 361: 351: 350: 349: 347:Biproportional 344: 339: 334: 318: 313: 312: 309: 308: 305: 304: 299: 294: 289: 275: 274: 259: 244: 220: 219: 218: 217: 212: 207: 202: 192: 178: 177: 176: 175: 164: 151:Instant-runoff 148: 147: 146: 138:Jungle primary 125: 114:Single vote - 112: 107: 106: 103: 102: 100: 99: 89: 84: 79: 74: 68: 65: 64: 54: 53: 43: 42: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 8172: 8161: 8158: 8156: 8153: 8151: 8148: 8146: 8143: 8142: 8140: 8127: 8126: 8121: 8120: 8114: 8108: 8105: 8103: 8100: 8099: 8097: 8093: 8087: 8084: 8082: 8079: 8077: 8074: 8072: 8069: 8067: 8064: 8062: 8059: 8057: 8054: 8053: 8051: 8047: 8041: 8038: 8036: 8033: 8031: 8028: 8026: 8023: 8021: 8018: 8016: 8013: 8011: 8008: 8006: 8003: 8001: 7998: 7996: 7993: 7991: 7988: 7986: 7983: 7981: 7978: 7976: 7973: 7971: 7968: 7966: 7963: 7961: 7958: 7957: 7955: 7951: 7945: 7942: 7940: 7937: 7935: 7932: 7930: 7927: 7926: 7924: 7922: 7918: 7912: 7909: 7907: 7904: 7902: 7899: 7897: 7894: 7892: 7889: 7887: 7884: 7882: 7879: 7877: 7874: 7873: 7871: 7869: 7865: 7855: 7852: 7850: 7847: 7845: 7842: 7840: 7837: 7836: 7834: 7830: 7824: 7821: 7817: 7814: 7812: 7809: 7808: 7807: 7804: 7803: 7801: 7797: 7791: 7788: 7786: 7783: 7779: 7776: 7774: 7771: 7769: 7766: 7765: 7764: 7761: 7759: 7756: 7754: 7751: 7749: 7746: 7744: 7741: 7739: 7736: 7734: 7731: 7730: 7728: 7724: 7721: 7719: 7715: 7709: 7706: 7704: 7701: 7699: 7696: 7694: 7691: 7689: 7686: 7684: 7681: 7679: 7676: 7672: 7669: 7667: 7664: 7662: 7659: 7658: 7657: 7654: 7652: 7649: 7647: 7644: 7640: 7637: 7635: 7632: 7630: 7627: 7625: 7622: 7620: 7617: 7615: 7612: 7610: 7607: 7606: 7605: 7602: 7600: 7597: 7595: 7592: 7588: 7585: 7583: 7580: 7579: 7578: 7575: 7574: 7572: 7570: 7569:Single-winner 7566: 7562: 7560: 7556: 7549: 7545: 7538: 7533: 7531: 7526: 7524: 7519: 7518: 7515: 7509: 7506: 7504: 7501: 7499: 7496: 7494: 7491: 7488: 7485: 7481: 7480:Condorcet PHP 7478: 7476: 7473: 7470: 7467: 7465: 7464:0-7546-4717-X 7461: 7457: 7456: 7451: 7448: 7446: 7445:0-89871-695-0 7442: 7438: 7437: 7432: 7430:by Rob Loring 7429: 7426: 7424: 7417: 7414: 7412: 7408: 7405: 7402: 7399: 7398: 7394: 7387: 7381: 7378: 7373: 7369: 7365: 7357: 7354: 7350: 7346: 7340: 7337: 7333: 7330: 7327: 7322: 7319: 7314: 7310: 7304: 7301: 7289: 7285: 7279: 7276: 7265: 7261: 7255: 7252: 7246: 7243: 7241:, August 2009 7240: 7237: 7234: 7231: 7230: 7226: 7223: 7218: 7214: 7208: 7205: 7194: 7187: 7184: 7173: 7169: 7163: 7160: 7156: 7151: 7148: 7137: 7133: 7127: 7124: 7118: 7115: 7112: 7108: 7105: 7102: 7101: 7097: 7094: 7090: 7085: 7082: 7070: 7066: 7060: 7057: 7046: 7039: 7036: 7025: 7021: 7015: 7012: 7009: 7004: 7001: 6996: 6992: 6986: 6983: 6978: 6974: 6968: 6965: 6959: 6956: 6953: 6949: 6946: 6943: 6942: 6938: 6935: 6931: 6925: 6922: 6910: 6904: 6901: 6896: 6892: 6886: 6883: 6878: 6872: 6868: 6867: 6860: 6857: 6854: 6848: 6845: 6834: 6830: 6824: 6821: 6810: 6809: 6802: 6799: 6795: 6790: 6787: 6784: 6778: 6775: 6763: 6760: 6754: 6751: 6747: 6743: 6737: 6734: 6730: 6725: 6722: 6718: 6713: 6710: 6699:on 2013-10-03 6698: 6694: 6688: 6685: 6682: 6677: 6674: 6670: 6665: 6662: 6658: 6654: 6651: 6646: 6643: 6631: 6625: 6622: 6617: 6614: 6612:, appendix A6 6611: 6608: 6605: 6602: 6601: 6597: 6594: 6590: 6585: 6582: 6579: 6576:Adam Helman, 6573: 6570: 6566: 6560: 6557: 6551: 6548: 6545: 6542: 6539: 6536: 6535: 6531: 6528: 6524: 6518: 6515: 6511: 6506: 6503: 6500: 6497:§6(6) of the 6494: 6491: 6487: 6481: 6478: 6474: 6469: 6466: 6462: 6456: 6453: 6447: 6444:Ka-Ping Yee, 6443: 6440: 6437:Ka-Ping Yee, 6436: 6435: 6431: 6428: 6416: 6412: 6406: 6403: 6392:on 2013-09-09 6391: 6387: 6381: 6378: 6375: 6369: 6366: 6362: 6357: 6354: 6350: 6345: 6342: 6331: 6327: 6320: 6317: 6312: 6308: 6307: 6302: 6295: 6292: 6288: 6282: 6279: 6275: 6269: 6266: 6254: 6247: 6244: 6232: 6228: 6221: 6218: 6215: 6210: 6207: 6195: 6191: 6184: 6181: 6177: 6173: 6167: 6164: 6161: 6155: 6152: 6140: 6136: 6130: 6127: 6123: 6118: 6115: 6111: 6105: 6102: 6091:on 2015-04-02 6090: 6086: 6080: 6077: 6073: 6067: 6064: 6052: 6048: 6041: 6038: 6034: 6029: 6026: 6015: 6008: 6005: 6001: 5997: 5993: 5989: 5985: 5981: 5977: 5973: 5969: 5965: 5961: 5957: 5953: 5949: 5945: 5941: 5935: 5933: 5929: 5922: 5918: 5914: 5910: 5906: 5902: 5898: 5894: 5890: 5889: 5885: 5883: 5879: 5867: 5863: 5856: 5853: 5841: 5837: 5830: 5827: 5821: 5817: 5814: 5810: 5809: 5805: 5802: 5796: 5792: 5789: 5785: 5782: 5778: 5776:, August 1998 5775: 5771: 5768: 5764: 5761: 5757: 5756: 5752: 5749: 5743: 5740: 5736: 5732: 5726: 5724: 5722: 5718: 5714: 5710: 5704: 5702: 5700: 5698: 5696: 5694: 5692: 5690: 5688: 5686: 5684: 5682: 5680: 5678: 5674: 5670: 5666: 5660: 5657: 5650: 5644: 5640: 5636: 5632: 5628: 5624: 5621: 5618: 5615: 5613: 5610: 5608: 5605: 5603: 5600: 5598: 5595: 5593: 5590: 5588: 5585: 5583: 5580: 5578: 5575: 5572: 5570: 5567: 5565: 5562: 5560: 5557: 5555: 5552: 5550: 5547: 5545: 5542: 5540: 5537: 5534: 5532: 5529: 5526: 5523: 5521: 5518: 5516: 5513: 5511: 5508: 5506: 5503: 5500: 5497: 5494: 5492: 5489: 5487: 5484: 5481: 5478: 5476: 5473: 5470: 5468: 5465: 5463: 5460: 5457: 5454: 5452: 5449: 5447: 5444: 5442: 5439: 5436: 5434: 5431: 5429: 5428:BoardGameGeek 5426: 5421: 5416: 5413: 5411: 5408: 5407: 5405: 5402: 5400: 5396: 5392: 5385:Organizations 5384: 5380: 5376: 5374: 5370: 5368: 5364: 5362: 5358: 5356: 5353: 5351: 5348: 5345: 5342: 5340: 5336: 5333: 5331: 5328: 5327: 5323: 5319: 5316: 5313: 5311: 5307: 5303: 5299: 5295: 5291: 5287: 5283: 5279: 5275: 5271: 5267: 5264: 5262: 5258: 5254: 5250: 5246: 5242: 5238: 5235: 5234: 5233: 5231: 5227: 5223: 5219: 5211: 5209: 5207: 5203: 5199: 5195: 5191: 5183: 5178: 5173: 5166: 5164: 5162: 5161: 5155: 5149: 5147: 5143: 5141: 5137: 5133: 5128: 5126: 5121: 5105: 5102: 5096: 5093: 5087: 5085: 5081: 5074: 5072: 5070: 5066: 5060: 5057: 5051: 5048: 5044: 5038: 5036: 5034: 5030: 5026: 5022: 5021:later-no-help 5018: 5017:later-no-harm 5014: 5013:participation 5010: 5006: 5001: 4999: 4997: 4995: 4993: 4991: 4989: 4985: 4979: 4974: 4971: 4968: 4965: 4962: 4959: 4956: 4953: 4950: 4947: 4944: 4941: 4938: 4935: 4932: 4930: 4927: 4926: 4922: 4919: 4916: 4913: 4910: 4907: 4904: 4901: 4898: 4895: 4892: 4889: 4886: 4883: 4880: 4878: 4875: 4874: 4870: 4867: 4864: 4861: 4858: 4855: 4852: 4849: 4846: 4843: 4840: 4837: 4834: 4831: 4828: 4825: 4822: 4821: 4817: 4814: 4811: 4808: 4805: 4802: 4799: 4795: 4792: 4789: 4786: 4783: 4780: 4777: 4774: 4772: 4769: 4768: 4764: 4761: 4758: 4755: 4751: 4748: 4745: 4742: 4739: 4736: 4733: 4730: 4727: 4724: 4721: 4719: 4716: 4715: 4711: 4708: 4705: 4702: 4699: 4696: 4693: 4690: 4687: 4684: 4681: 4678: 4675: 4672: 4669: 4667: 4664: 4663: 4659: 4656: 4653: 4650: 4646: 4643: 4640: 4637: 4634: 4631: 4628: 4625: 4622: 4619: 4616: 4614: 4611: 4610: 4606: 4603: 4600: 4597: 4594: 4591: 4588: 4585: 4582: 4579: 4576: 4573: 4570: 4567: 4564: 4561: 4560:Random ballot 4558: 4557: 4553: 4550: 4547: 4544: 4541: 4538: 4535: 4532: 4529: 4526: 4523: 4520: 4517: 4514: 4511: 4509: 4506: 4505: 4501: 4498: 4495: 4492: 4489: 4486: 4483: 4480: 4477: 4474: 4471: 4468: 4465: 4462: 4459: 4457: 4454: 4453: 4449: 4446: 4443: 4439: 4436: 4433: 4430: 4427: 4424: 4421: 4418: 4414: 4411: 4408: 4405: 4403: 4400: 4399: 4395: 4392: 4389: 4386: 4383: 4380: 4377: 4374: 4371: 4368: 4365: 4362: 4359: 4356: 4353: 4351: 4348: 4347: 4343: 4340: 4337: 4334: 4331: 4328: 4325: 4322: 4319: 4316: 4313: 4310: 4307: 4304: 4301: 4299: 4296: 4295: 4291: 4288: 4285: 4282: 4278: 4275: 4272: 4268: 4265: 4262: 4259: 4256: 4252: 4248: 4245: 4243: 4240: 4239: 4235: 4232: 4229: 4226: 4223: 4220: 4217: 4214: 4211: 4208: 4205: 4202: 4199: 4196: 4193: 4191: 4188: 4187: 4183: 4180: 4177: 4174: 4171: 4168: 4165: 4162: 4159: 4156: 4153: 4150: 4147: 4144: 4141: 4139: 4136: 4135: 4131: 4128: 4125: 4122: 4119: 4116: 4113: 4110: 4107: 4104: 4101: 4098: 4095: 4092: 4089: 4087: 4084: 4083: 4079: 4076: 4073: 4070: 4067: 4064: 4061: 4058: 4055: 4052: 4049: 4046: 4043: 4040: 4037: 4035: 4032: 4031: 4027: 4024: 4021: 4018: 4015: 4012: 4009: 4006: 4003: 4000: 3997: 3994: 3991: 3988: 3985: 3983: 3980: 3979: 3975: 3972: 3969: 3966: 3963: 3960: 3957: 3954: 3951: 3948: 3945: 3942: 3939: 3936: 3933: 3931: 3928: 3927: 3923: 3920: 3917: 3914: 3911: 3908: 3905: 3902: 3899: 3896: 3893: 3890: 3887: 3884: 3881: 3879: 3876: 3875: 3871: 3868: 3865: 3862: 3859: 3856: 3853: 3849: 3846: 3843: 3840: 3837: 3834: 3831: 3828: 3826: 3823: 3822: 3818: 3815: 3812: 3809: 3806: 3803: 3800: 3797: 3794: 3791: 3788: 3785: 3782: 3779: 3776: 3774: 3771: 3770: 3764: 3761: 3758: 3755: 3754:Later-no-help 3752: 3749: 3748:Later-no-harm 3746: 3744: 3743:Participation 3741: 3739: 3736: 3734: 3731: 3728: 3724: 3721: 3718: 3715: 3712: 3709: 3707: 3704: 3701: 3698: 3696: 3693: 3691: 3688: 3686: 3683: 3673: 3672: 3664: 3658: 3653: 3649: 3646: 3645: 3644: 3639: 3636: 3635: 3634: 3632: 3628: 3624: 3623:ranked voting 3617: 3616:Later-no-harm 3614: 3612: 3609: 3607: 3604: 3602: 3601:Participation 3599: 3598: 3597: 3591: 3585: 3581: 3578: 3577:winning votes 3574: 3571: 3568: 3565: 3563: 3560: 3558: 3555: 3552: 3549: 3547: 3544: 3542: 3539: 3537: 3534: 3532: 3529: 3527: 3524: 3522: 3519: 3517: 3514: 3512: 3509: 3507: 3504: 3502: 3499: 3498: 3496: 3490: 3485: 3483: 3475: 3472: 3469: 3466: 3463: 3460: 3459: 3455: 3453: 3450: 3447: 3444: 3441: 3440: 3436: 3433: 3431: 3428: 3425: 3422: 3421: 3417: 3414: 3411: 3409: 3406: 3403: 3402: 3398: 3395: 3392: 3389: 3387: 3384: 3383: 3379: 3376: 3373: 3370: 3367: 3365: 3364: 3358: 3351: 3348: 3345: 3342: 3339: 3336: 3335: 3331: 3329: 3326: 3323: 3320: 3317: 3316: 3312: 3309: 3307: 3304: 3301: 3298: 3297: 3293: 3290: 3287: 3285: 3282: 3279: 3278: 3274: 3271: 3268: 3265: 3263: 3260: 3259: 3255: 3252: 3249: 3246: 3243: 3241: 3240: 3234: 3227: 3224: 3221: 3218: 3215: 3212: 3211: 3207: 3205: 3202: 3199: 3196: 3193: 3192: 3188: 3185: 3183: 3180: 3177: 3174: 3173: 3169: 3166: 3163: 3161: 3158: 3155: 3154: 3150: 3147: 3144: 3141: 3139: 3136: 3135: 3131: 3128: 3125: 3122: 3119: 3117: 3116: 3110: 3103: 3100: 3096: 3093: 3089: 3088: 3087: 3085: 3081: 3076: 3074: 3073:random ballot 3069: 3067: 3063: 3059: 3050: 3048: 3046: 3042: 3040: 3035: 3031: 3021: 3019: 3015: 3011: 3003: 3001: 2984: 2981: 2978: 2972: 2969: 2963: 2960: 2957: 2951: 2923: 2920: 2917: 2914: 2911: 2908: 2905: 2902: 2899: 2891: 2872: 2869: 2860: 2857: 2854: 2848: 2845: 2839: 2836: 2833: 2827: 2821: 2818: 2803: 2780: 2777: 2768: 2765: 2762: 2756: 2753: 2747: 2744: 2741: 2735: 2729: 2726: 2702: 2699: 2696: 2693: 2690: 2673: 2670: 2667: 2661: 2654: 2653: 2649: 2647: 2644: 2641: 2638: 2621: 2618: 2615: 2609: 2602: 2601: 2597: 2594: 2592: 2589: 2586: 2569: 2566: 2563: 2557: 2550: 2549: 2545: 2542: 2539: 2537: 2534: 2517: 2514: 2511: 2505: 2498: 2497: 2493: 2490: 2487: 2484: 2482: 2465: 2462: 2459: 2453: 2446: 2445: 2427: 2424: 2421: 2415: 2408: 2391: 2388: 2385: 2379: 2372: 2355: 2352: 2349: 2343: 2336: 2319: 2316: 2313: 2307: 2300: 2283: 2280: 2277: 2271: 2264: 2262: 2261: 2245: 2242: 2239: 2236: 2233: 2230: 2228: 2227: 2223: 2220: 2217: 2210: 2206: 2203: 2196: 2192: 2189: 2182: 2178: 2175: 2168: 2164: 2161: 2160: 2156: 2153: 2146: 2142: 2139: 2136: 2129: 2125: 2122: 2115: 2111: 2108: 2101: 2097: 2094: 2093: 2089: 2086: 2079: 2075: 2072: 2065: 2061: 2058: 2055: 2048: 2044: 2041: 2034: 2030: 2027: 2026: 2022: 2019: 2012: 2008: 2005: 1998: 1994: 1991: 1984: 1980: 1977: 1974: 1967: 1963: 1960: 1959: 1955: 1952: 1945: 1941: 1938: 1931: 1927: 1924: 1917: 1913: 1910: 1903: 1899: 1896: 1893: 1892: 1889: 1886: 1883: 1880: 1877: 1874: 1866: 1865: 1859: 1856: 1854: 1848: 1846: 1841: 1834: 1831: 1828: 1825: 1822: 1805: 1802: 1799: 1793: 1786: 1785: 1781: 1779: 1776: 1773: 1770: 1753: 1750: 1747: 1741: 1734: 1733: 1729: 1726: 1724: 1721: 1718: 1701: 1698: 1695: 1689: 1682: 1681: 1677: 1674: 1671: 1669: 1666: 1649: 1646: 1643: 1637: 1630: 1629: 1625: 1622: 1619: 1616: 1614: 1597: 1594: 1591: 1585: 1578: 1577: 1559: 1556: 1553: 1547: 1540: 1523: 1520: 1517: 1511: 1504: 1487: 1484: 1481: 1475: 1468: 1451: 1448: 1445: 1439: 1432: 1415: 1412: 1409: 1403: 1396: 1394: 1393: 1384: 1380: 1376: 1362: 1359: 1353: 1350: 1347: 1341: 1321: 1318: 1312: 1309: 1306: 1300: 1254: 1251: 1250: 1246: 1243: 1242: 1238: 1235: 1234: 1230: 1227: 1226: 1222: 1219: 1218: 1214: 1211: 1210: 1206: 1203: 1202: 1198: 1195: 1194: 1190: 1187: 1186: 1183: 1177: 1175: 1167: 1164: 1160: 1157: 1156:random ballot 1153: 1152: 1150: 1147: 1143: 1142: 1141: 1135: 1133: 1131: 1130:majority rule 1127: 1123: 1118: 1114: 1112: 1107: 1105: 1097: 1095: 1093: 1084: 1077: 1075: 1073: 1069: 1065: 1061: 1057: 1053: 1049: 1045: 1041: 1037: 1032: 1030: 1026: 1022: 1017: 1015: 1011: 1007: 1004: 1003:single winner 998: 968: 956: 951: 949: 944: 942: 937: 936: 934: 933: 930: 925: 917: 912: 907: 905: 900: 895: 894: 892: 891: 884: 881: 879: 876: 874: 873:May's theorem 871: 869: 866: 864: 861: 860: 859: 858: 851: 848: 846: 843: 841: 838: 836: 833: 831: 828: 827: 826: 825: 819: 814: 813: 806: 803: 801: 798: 796: 793: 791: 788: 787: 786: 785: 784: 783:majority rule 781:Paradoxes of 775: 772: 770: 767: 765: 762: 760: 757: 756: 755: 754: 753: 743: 740: 739: 738: 735: 733: 730: 728: 725: 724: 723: 722: 715: 712: 710: 707: 705: 702: 700: 697: 696: 695: 690: 685: 684: 677: 674: 670: 667: 666: 665: 662: 661: 660: 659: 650: 647: 645: 642: 640: 637: 636: 635: 632: 626: 623: 621: 618: 617: 616: 613: 609: 604: 600: 598: 593: 589: 588: 587: 584: 583: 582: 581: 577: 573: 570: 568: 565: 563: 560: 558: 555: 554: 553: 552: 547: 546: 545: 539: 536: 534: 531: 530: 529: 524: 523:Mixed systems 519: 518: 511: 508: 504: 501: 500: 499: 496: 495: 494: 493: 492: 484: 483:Random ballot 481: 479: 476: 474: 471: 467: 464: 462: 459: 458: 457: 454: 453: 452: 451: 450: 442: 439: 437: 434: 432: 429: 427: 424: 423: 422: 421: 420: 412: 409: 407: 404: 402: 399: 397: 394: 393: 392: 391: 390: 380: 377: 375: 372: 370: 367: 365: 362: 360: 357: 356: 355: 352: 348: 345: 343: 340: 338: 335: 333: 330: 329: 328: 327:Apportionment 325: 324: 323: 322: 316: 311: 310: 303: 300: 298: 295: 293: 290: 288: 285: 284: 283: 282: 281: 272: 268: 263: 262:Antiplurality 260: 257: 253: 248: 245: 242: 238: 233: 230: 229: 228: 227: 226: 216: 213: 211: 208: 206: 203: 201: 198: 197: 196: 193: 191: 190:Condorcet-IRV 188: 187: 186: 185: 184: 174: 169: 165: 163: 158: 154: 153: 152: 149: 145: 142: 141: 139: 134: 129: 126: 124: 121: 120: 119: 117: 110: 105: 104: 97: 93: 90: 88: 85: 83: 80: 78: 75: 73: 72:Social choice 70: 69: 67: 66: 60: 56: 55: 52: 48: 47:Social choice 44: 40: 36: 32: 31: 19: 8123: 8117: 7733:Mixed-member 7718:Proportional 7693:Score voting 7638: 7634:Ranked pairs 7553:Part of the 7552: 7453: 7434: 7416:Spieltheorie 7380: 7372:the original 7367: 7356: 7339: 7321: 7315:(in Hebrew). 7312: 7303: 7292:. Retrieved 7287: 7278: 7268:, retrieved 7263: 7254: 7225: 7216: 7207: 7196:. Retrieved 7186: 7175:. Retrieved 7171: 7162: 7150: 7139:. Retrieved 7135: 7126: 7096: 7091:, March 2010 7084: 7073:. Retrieved 7068: 7059: 7048:. Retrieved 7038: 7027:. Retrieved 7023: 7014: 7003: 6994: 6985: 6976: 6967: 6937: 6924: 6913:. Retrieved 6903: 6894: 6885: 6865: 6859: 6847: 6836:. Retrieved 6832: 6823: 6813:, retrieved 6807: 6801: 6789: 6777: 6766:. Retrieved 6764:. 2009-04-02 6761: 6753: 6736: 6724: 6719:, March 2009 6712: 6701:. Retrieved 6697:the original 6687: 6676: 6669:Voters Guide 6664: 6645: 6634:. Retrieved 6624: 6596: 6584: 6572: 6559: 6530: 6517: 6505: 6493: 6480: 6475:, April 2013 6468: 6455: 6448:, April 2005 6441:, March 2005 6430: 6418:. Retrieved 6414: 6405: 6394:. Retrieved 6390:the original 6380: 6368: 6356: 6344: 6333:. Retrieved 6329: 6319: 6311:the original 6304: 6294: 6281: 6268: 6257:. Retrieved 6246: 6235:. Retrieved 6230: 6220: 6209: 6198:. Retrieved 6193: 6183: 6166: 6154: 6143:. Retrieved 6138: 6129: 6117: 6104: 6093:. Retrieved 6089:the original 6079: 6066: 6055:. Retrieved 6053:(in Italian) 6050: 6040: 6028: 6017:. Retrieved 6007: 5921:the original 5909:the original 5897:the original 5870:. Retrieved 5868:(in Catalan) 5865: 5855: 5844:. Retrieved 5842:(in Spanish) 5839: 5829: 5804: 5751: 5742: 5734: 5712: 5668: 5659: 5559:OpenEmbedded 5403: 5388: 5355:Kingman Hall 5226:Boise, Idaho 5224:(2010). The 5215: 5187: 5158: 5156: 5153: 5144: 5139: 5135: 5131: 5129: 5125:ranked pairs 5122: 5119: 5104: 5095: 5059: 5050: 4980:Table Notes 4717: 4712:Single mark 4613:Ranked pairs 4607:Single mark 4554:Single mark 4350:Kemeny–Young 3819:Single mark 3662: 3648:Peyton Young 3642: 3625:system (not 3620: 3595: 3494: 3480: 3356: 3232: 3108: 3091:elimination. 3083: 3079: 3077: 3070: 3065: 3061: 3057: 3054: 3044: 3038: 3034:running time 3027: 3007: 2889: 2801: 2707: 2215: 2201: 2187: 2173: 2151: 2134: 2120: 2106: 2084: 2070: 2053: 2039: 2017: 2003: 1989: 1972: 1950: 1936: 1922: 1908: 1857: 1852: 1849: 1842: 1839: 1260: 1181: 1173: 1139: 1119: 1115: 1110: 1108: 1101: 1089: 1072:score voting 1060:Pirate Party 1033: 1028: 1018: 1009: 966: 964: 856: 855: 822: 780: 779: 764:Exaggeration 750: 749: 720: 719: 693: 657: 656: 625:Mixed ballot 580:Compensatory 578: 551:compensatory 548: 543: 527: 489: 488: 447: 446: 417: 416: 387: 386: 374:List-free PR 319: 287:Score voting 278: 277: 223: 222: 210:Ranked pairs 204: 181: 180: 113: 8076:Spoilt vote 7839:Droop quota 7778:Schulze STV 7753:Rural–urban 7698:STAR voting 7594:Borda count 7419:(in German) 7411:Hubert Bray 7290:(in French) 7247:, June 2011 7235:, June 2008 6909:"Wahlmodus" 6895:Google Docs 6796:, June 2009 6748:2023-06-06) 6659:, July 2010 6606:, June 2003 6521:§9a of the 6363:, June 2021 6289:, June 2013 6276:, July 2012 6255:(in German) 5998:(in 2012) ( 5990:(in 2011) ( 5972:Lichtenberg 5769:, July 1998 5554:Noisebridge 5418: [ 5318:Volt Europe 5306:Switzerland 5261:San Cesareo 5200:and by the 5009:consistency 3606:Consistency 3569:MinMax sets 3550:Mono-append 3237:First drop 3080:demonstrate 2944:wins since 1064:many others 1044:Schulze STV 1021:cyclic ties 664:Single vote 567:Conditional 562:Coexistence 411:Quota Borda 401:Schulze STV 359:Closed list 302:STAR voting 247:Borda count 8139:Categories 8095:Comparison 7849:Hare quota 7799:Allocation 7785:Spare vote 7773:Hare-Clark 7743:Party-list 7294:2022-09-24 7270:2022-09-24 7198:2022-09-24 7177:2022-09-24 7141:2022-09-24 7075:2022-09-24 7050:2022-09-24 7029:2022-09-24 6915:2010-05-08 6838:2022-09-24 6815:2022-09-24 6768:2022-09-24 6703:2022-09-24 6636:2010-05-08 6567:, May 2021 6488:, May 2014 6396:2010-05-08 6335:2022-09-24 6259:2022-09-24 6237:2022-09-24 6233:(in Dutch) 6200:2022-09-24 6145:2022-09-24 6095:2022-09-24 6057:2022-09-24 6019:2018-02-25 5996:Regensburg 5942:are using 5872:2022-09-24 5846:2022-09-24 5592:Sugar Labs 5573:OpenSwitch 5535:Madisonium 5515:Kubernetes 5253:Montemurlo 5241:Campobasso 5184:Government 4638:LIIA Only 4375:LIIA Only 3018:pseudocode 1283:8+2+7+8=25 1271:5+5+3+7=20 1122:transitive 769:Truncation 498:Cumulative 321:Party-list 96:By country 87:Comparison 8086:Unseating 8081:Sortition 7683:Plurality 7559:Economics 7469:preftools 7264:Wikipédia 6833:Kumoricon 6420:4 October 5635:Hungarian 5617:Wikimedia 5569:OpenStack 5520:Kumoricon 5467:Free Geek 5397:, and by 5393:, by the 5270:Australia 5179:elections 5027:criteria. 4824:Sortition 4508:Plurality 3717:Smith-IIA 3675:Criterion 3030:efficient 2970:≥ 2716:, since 2674:∗ 2622:∗ 2570:∗ 2518:∗ 2466:∗ 2422:∗ 2386:∗ 2350:∗ 2314:∗ 2278:∗ 2200:E-(31)-D- 2190:-C-(29)-B 2186:E-(31)-D- 2150:D-(28)-C- 2123:-C-(29)-B 2073:-B-(33)-D 2038:C-(29)-B- 1988:B-(33)-D- 1921:A-(30)-D- 1911:-C-(29)-B 1907:A-(30)-D- 1806:∗ 1754:∗ 1702:∗ 1650:∗ 1598:∗ 1554:∗ 1518:∗ 1482:∗ 1446:∗ 1410:∗ 1068:Wikimedia 676:Dual-vote 369:Panachage 364:Open list 354:List type 232:Plurality 128:Two-round 116:plurality 39:Economics 7953:Criteria 7906:Scorporo 7555:politics 7452:(2006), 7439:, SIAM, 7368:kalan.cc 7107:Archived 6948:Archived 6653:Archived 5948:Neukölln 5602:TopCoder 5505:KDE e.V. 5491:Homebrew 4138:Copeland 3825:Approval 3685:Majority 3566:prudence 3032:and has 1853:strength 1111:strength 1029:beatpath 396:Hare STV 35:Politics 33:A joint 8125:Project 7816:D'Hondt 7768:CPO-STV 7726:Systems 7487:library 6565:charter 6461:charter 6194:Píratar 5978:), and 5643:Persian 5639:Russian 5539:Metalab 5527:(LOPSA) 5486:Haskell 5482:(GnuPG) 5458:(EUDEC) 5290:Iceland 5286:Germany 5278:Belgium 5274:Austria 5257:Pescara 5150:History 4923:Scores 4818:Scores 4718:Schulze 4402:Minimax 4292:Scores 4190:Dodgson 4034:Bucklin 3878:Baldwin 3765:Ballot 3584:margins 1178:Example 1144:Draw a 1001:) is a 406:CPO-STV 256:Baldwin 205:Schulze 200:Minimax 118:methods 8145:Debian 8119:Portal 8056:Ballot 7832:Quotas 7561:series 7462:  7443:  7069:rllmuk 6873:  6853:bylaws 6746:source 6523:bylaws 6499:bylaws 6486:bylaws 6306:Medium 6287:bylaws 6274:bylaws 6172:french 6160:bylaws 6110:bylaws 6072:bylaws 5988:Berlin 5641:, and 5631:Hebrew 5627:French 5619:(2008) 5607:Ubuntu 5597:Sverok 5582:Squeak 5577:RLLMUK 5462:FFmpeg 5446:Debian 5424:(BVKJ) 5399:USENIX 5308:, and 5302:Sweden 5282:Brazil 5259:, and 5023:, and 4666:Runoff 4456:Nanson 4086:Coombs 3680:Method 3058:margin 3043:where 2936:, and 2890:better 2802:better 1281:, and 1255:EBADC 1247:DCEBA 1239:CBADE 1231:CAEBD 1223:CABED 1215:BEDAC 1207:ADECB 1199:ACBED 1056:Gentoo 1052:Ubuntu 1048:Debian 271:Coombs 41:series 8049:Other 7868:Mixed 7229:See: 7100:See: 6941:See: 6600:See: 6534:See: 6434:See: 6176:dutch 5956:Mitte 5888:See: 5808:See: 5755:See: 5651:Notes 5422:] 5294:Italy 5245:Fondi 5194:Turin 5190:Silla 5167:Usage 4871:None 4771:Score 3982:Borda 3930:Black 3767:type 3711:Smith 3627:rated 1293:. So 1104:Alice 1025:Alice 608:'MMP' 597:'AMS' 7557:and 7460:ISBN 7441:ISBN 7386:here 7384:See 7349:here 7347:and 7345:here 7343:See 6871:ISBN 6422:2015 6000:link 5992:link 5984:link 5976:link 5968:link 5960:link 5952:link 5441:Dapr 5196:and 4957:Yes 4951:Yes 4948:Yes 4945:Yes 4942:Yes 4939:Yes 4936:Yes 4933:Yes 4908:Yes 4893:Yes 4884:Yes 4877:STAR 4868:Yes 4865:Yes 4862:Yes 4859:Yes 4856:Yes 4850:Yes 4815:Yes 4812:Yes 4806:Yes 4803:Yes 4800:Yes 4749:Yes 4746:Yes 4740:Yes 4737:Yes 4734:Yes 4731:Yes 4728:Yes 4725:Yes 4722:Yes 4706:Yes 4703:Yes 4682:Yes 4673:Yes 4670:Yes 4644:Yes 4641:Yes 4635:Yes 4632:Yes 4629:Yes 4626:Yes 4623:Yes 4620:Yes 4617:Yes 4604:Yes 4601:Yes 4598:Yes 4595:Yes 4592:Yes 4589:Yes 4586:Yes 4548:Yes 4545:Yes 4542:Yes 4539:Yes 4512:Yes 4475:Yes 4472:Yes 4469:Yes 4466:Yes 4463:Yes 4460:Yes 4434:Yes 4406:Yes 4381:Yes 4372:Yes 4369:Yes 4366:Yes 4363:Yes 4360:Yes 4357:Yes 4354:Yes 4338:Yes 4335:Yes 4326:Yes 4314:Yes 4308:Yes 4305:Yes 4302:Yes 4289:Yes 4286:Yes 4276:Yes 4273:Yes 4246:Yes 4203:Yes 4194:Yes 4169:Yes 4160:Yes 4157:Yes 4154:Yes 4151:Yes 4148:Yes 4145:Yes 4142:Yes 4129:Yes 4102:Yes 4096:Yes 4093:Yes 4090:Yes 4074:Yes 4065:Yes 4044:Yes 4041:Yes 4038:Yes 4022:Yes 4016:Yes 4013:Yes 3998:Yes 3989:Yes 3961:Yes 3946:Yes 3943:Yes 3937:Yes 3934:Yes 3897:Yes 3894:Yes 3891:Yes 3888:Yes 3885:Yes 3882:Yes 3869:Yes 3866:Yes 3860:Yes 3857:Yes 3854:Yes 3829:Yes 3816:Yes 3807:Yes 3804:Yes 3780:Yes 3727:LIIA 3437:−11 3313:−11 3189:−11 2921:> 2915:> 2909:> 2903:> 2846:> 2754:> 2712:and 2247:From 2216:(31) 2202:(28) 2188:(28) 2174:(25) 2152:(24) 2135:(28) 2121:(28) 2107:(25) 2085:(24) 2071:(29) 2054:(29) 2040:(25) 2018:(24) 2004:(33) 1990:(28) 1973:(25) 1951:(24) 1937:(30) 1923:(28) 1909:(28) 1871:From 1334:and 1265:and 1038:, a 1034:For 965:The 549:Non- 503:SNTV 92:List 49:and 37:and 7881:MMP 7484:PHP 7421:by 7409:by 5970:), 5962:), 5954:), 5625:in 5549:Neo 5544:MTV 5268:of 5239:of 4972:No 4969:No 4966:No 4963:No 4960:No 4954:No 4920:No 4917:No 4914:No 4911:No 4905:No 4902:No 4899:No 4896:No 4890:No 4887:No 4881:No 4853:No 4847:No 4844:No 4841:No 4838:No 4835:No 4832:No 4829:No 4809:No 4796:Yes 4793:No 4790:No 4787:No 4784:No 4781:No 4778:No 4775:No 4762:No 4759:No 4756:No 4743:No 4709:No 4700:No 4697:No 4694:No 4691:No 4688:No 4685:No 4679:No 4676:No 4657:No 4654:No 4651:No 4583:No 4580:No 4577:No 4574:No 4571:No 4568:No 4565:No 4551:No 4536:No 4533:No 4530:No 4527:No 4524:No 4521:No 4518:No 4515:No 4499:No 4496:No 4493:No 4490:No 4487:No 4484:No 4481:No 4478:No 4447:No 4444:No 4437:No 4431:No 4428:No 4425:No 4422:No 4419:No 4415:Yes 4412:No 4409:No 4393:No 4390:No 4387:No 4384:No 4378:No 4341:No 4332:No 4329:No 4323:No 4320:No 4317:No 4311:No 4283:No 4269:Yes 4266:No 4263:No 4260:No 4257:No 4249:Yes 4233:No 4230:No 4227:No 4224:No 4221:No 4218:No 4215:No 4212:No 4209:No 4206:No 4200:No 4197:No 4181:No 4178:No 4175:No 4172:No 4166:No 4163:No 4126:No 4123:No 4120:No 4117:No 4114:No 4111:No 4108:No 4105:No 4099:No 4077:No 4071:No 4068:No 4062:No 4059:No 4056:No 4053:No 4050:No 4047:No 4025:No 4019:No 4010:No 4007:No 4004:No 4001:No 3995:No 3992:No 3986:No 3973:No 3970:No 3967:No 3964:No 3958:No 3955:No 3952:No 3949:No 3940:No 3921:No 3918:No 3915:No 3912:No 3909:No 3906:No 3903:No 3900:No 3863:No 3850:Yes 3847:No 3844:No 3841:No 3838:No 3835:No 3832:No 3813:No 3810:No 3801:No 3798:No 3795:No 3792:No 3789:No 3786:No 3783:No 3777:No 3723:IIA 3629:), 3575:if 3473:−21 3467:−15 3464:−17 3456:21 3451:−13 3418:15 3399:17 3349:−21 3343:−15 3340:−17 3332:21 3327:−13 3294:15 3275:17 3225:−21 3219:−15 3216:−17 3208:21 3203:−13 3170:15 3151:17 2800:is 2650:24 2598:24 2546:24 2494:24 2154:-E 2087:-E 2020:-E 1953:-E 1782:14 1730:24 1678:18 1626:22 1289:to 1277:to 267:el. 252:el. 241:IRV 237:el. 8141:: 8122:— 7286:. 7262:, 7215:. 7170:. 7134:. 7067:. 7022:. 6993:. 6975:. 6893:. 6831:. 6413:. 6328:. 6229:. 6192:. 6174:, 6137:. 6049:. 5931:^ 5881:^ 5864:. 5838:. 5733:, 5720:^ 5676:^ 5637:, 5633:, 5629:, 5420:de 5304:, 5300:, 5296:, 5292:, 5288:, 5284:, 5280:, 5276:, 5272:, 5255:, 5251:, 5247:, 5243:, 5163:. 5083:^ 5068:^ 5032:^ 5019:, 5015:, 5011:, 4987:^ 4752:No 4647:No 4440:No 4279:No 4253:No 3470:11 3461:D 3445:−9 3442:B 3434:13 3429:−7 3423:C 3415:−5 3407:−1 3404:A 3393:−3 3385:E 3380:D 3346:11 3337:D 3321:−9 3318:B 3310:13 3305:−7 3299:C 3291:−5 3283:−1 3280:A 3269:−3 3261:E 3256:D 3222:11 3213:D 3197:−9 3194:B 3186:13 3181:−7 3175:C 3167:−5 3159:−1 3156:A 3145:−3 3137:E 3132:D 3075:. 3037:O( 2873:24 2819:31 2781:25 2727:28 2700:31 2697:28 2694:28 2691:25 2645:28 2642:28 2639:25 2595:29 2590:29 2587:25 2543:33 2540:28 2535:25 2491:30 2488:28 2485:28 2250:To 2243:E 2224:E 2221:— 2218:-D 2214:E- 2204:-C 2176:-A 2162:E 2157:D 2137:-C 2133:D- 2119:D- 2109:-A 2095:D 2090:C 2083:C- 2069:C- 2056:-B 2052:C- 2042:-A 2028:C 2023:B 2006:-D 2002:B- 1992:-C 1975:-A 1971:B- 1961:B 1956:A 1939:-D 1935:A- 1925:-C 1894:A 1887:E 1868:To 1832:31 1829:21 1826:27 1823:23 1777:28 1774:12 1771:15 1727:17 1722:29 1719:19 1675:33 1672:16 1667:25 1623:30 1620:26 1617:20 1363:25 1322:20 1158:). 1074:. 1058:, 1054:, 1050:, 1031:. 603:NZ 592:UK 168:US 157:UK 140:) 133:US 7536:e 7529:t 7522:v 7351:. 7297:. 7219:. 7201:. 7180:. 7144:. 7078:. 7053:. 7032:. 6997:. 6979:. 6918:. 6897:. 6879:. 6841:. 6771:. 6706:. 6639:. 6424:. 6399:. 6338:. 6262:. 6240:. 6203:. 6178:) 6148:. 6098:. 6060:. 6022:. 5982:( 5974:( 5966:( 5958:( 5950:( 5875:. 5849:. 5645:. 5140:X 5136:X 5132:X 3725:/ 3654:. 3448:5 3426:3 3412:7 3396:9 3390:1 3377:B 3374:C 3371:A 3368:E 3324:5 3302:3 3288:7 3272:9 3266:1 3253:B 3250:C 3247:A 3244:E 3200:5 3178:3 3164:7 3148:9 3142:1 3129:B 3126:C 3123:A 3120:E 3066:d 3062:d 3045:C 3041:) 3039:C 2988:] 2985:E 2982:, 2979:X 2976:[ 2973:p 2967:] 2964:X 2961:, 2958:E 2955:[ 2952:p 2942:E 2938:E 2924:D 2918:B 2912:C 2906:A 2900:E 2876:) 2870:= 2867:( 2864:] 2861:E 2858:, 2855:D 2852:[ 2849:p 2843:] 2840:D 2837:, 2834:E 2831:[ 2828:p 2825:) 2822:= 2816:( 2806:B 2798:A 2784:) 2778:= 2775:( 2772:] 2769:A 2766:, 2763:B 2760:[ 2757:p 2751:] 2748:B 2745:, 2742:A 2739:[ 2736:p 2733:) 2730:= 2724:( 2714:B 2710:A 2677:] 2671:, 2668:E 2665:[ 2662:p 2625:] 2619:, 2616:D 2613:[ 2610:p 2573:] 2567:, 2564:C 2561:[ 2558:p 2521:] 2515:, 2512:B 2509:[ 2506:p 2469:] 2463:, 2460:A 2457:[ 2454:p 2431:] 2428:E 2425:, 2419:[ 2416:p 2395:] 2392:D 2389:, 2383:[ 2380:p 2359:] 2356:C 2353:, 2347:[ 2344:p 2323:] 2320:B 2317:, 2311:[ 2308:p 2287:] 2284:A 2281:, 2275:[ 2272:p 2240:D 2237:C 2234:B 2231:A 2140:— 2059:— 1978:— 1897:— 1884:D 1881:C 1878:B 1875:A 1809:] 1803:, 1800:E 1797:[ 1794:d 1757:] 1751:, 1748:D 1745:[ 1742:d 1705:] 1699:, 1696:C 1693:[ 1690:d 1653:] 1647:, 1644:B 1641:[ 1638:d 1601:] 1595:, 1592:A 1589:[ 1586:d 1563:] 1560:E 1557:, 1551:[ 1548:d 1527:] 1524:D 1521:, 1515:[ 1512:d 1491:] 1488:C 1485:, 1479:[ 1476:d 1455:] 1452:B 1449:, 1443:[ 1440:d 1419:] 1416:A 1413:, 1407:[ 1404:d 1360:= 1357:] 1354:A 1351:, 1348:B 1345:[ 1342:d 1319:= 1316:] 1313:B 1310:, 1307:A 1304:[ 1301:d 1291:A 1287:B 1279:B 1275:A 1267:B 1263:A 1252:8 1244:7 1236:2 1228:7 1220:3 1212:8 1204:5 1196:5 1165:. 997:/ 994:ə 991:s 988:t 985:l 982:ʊ 979:ʃ 976:ˈ 973:/ 969:( 954:e 947:t 940:v 605:: 594:: 273:) 264:( 258:) 249:( 243:) 234:( 170:: 159:: 135:: 130:( 98:) 94:( 20:)

Index

Schwartz sequential dropping
Politics
Economics
Social choice
electoral systems

Social choice
Mechanism design
Comparative politics
Comparison
List
By country
Single-winner methods
plurality
First preference plurality (FPP)
Two-round
US
Jungle primary
Partisan primary
Instant-runoff
UK
Alternative vote
US
Ranked-choice (RCV)
Condorcet methods
Condorcet-IRV
Round-robin voting
Minimax
Schulze
Ranked pairs

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