1642:
913:
48:
888:
900:
1546:
In this summary matrix, the largest ranking score equals the sum of the counts in the upper-right, triangular half of the matrix (shown here in bold, with a green background). No other possible ranking can have a summary matrix that yields a higher sum of numbers in the upper-right, triangular half.
1550:
In this summary matrix, the sum of the numbers in the lower-left, triangular half of the matrix (shown here with a red background) are a minimum. The academic papers by John Kemeny and Peyton Young refer to finding this minimum sum, which is called the Kemeny score, and which is based on how many
4654:
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
977:
This method assigns a score for each possible sequence, where each sequence considers which choice might be most popular, which choice might be second-most popular, which choice might be third-most popular, and so on down to which choice might be least-popular. The sequence that has the highest
1082:
These preferences can be expressed in a tally table. A tally table, which arranges all the pairwise counts in three columns, is useful for counting (tallying) ballot preferences and calculating ranking scores. The center column tracks when a voter indicates more than one choice at the same
1414:
After the overall ranking has been calculated, the pairwise comparison counts can be arranged in a summary matrix, as shown below, in which the choices appear in the winning order from most popular (top and left) to least popular (bottom and right). This matrix layout does not include the
1038:
In order to demonstrate how an individual preference order is converted into a tally table, it is worth considering the following example. Suppose that a single voter has a choice among four candidates (i.e. Elliot, Meredith, Roland, and Selden) and has the following preference order:
3106:
sometimes allowed the computation of full rankings for votes on as many as 40 candidates in seconds. However, certain 40-candidate 5-voter Kemeny elections generated at random were not solvable on a 3 GHz
Pentium computer in a useful time bound in 2006.
1207:
Now suppose that multiple voters had voted on those four candidates. After all ballots have been counted, the same type of tally table can be used to summarize all the preferences of all the voters. Here is an example for a case that has 100 voters:
1336:
After the tally table has been completed, each possible ranking of choices is examined in turn, and its ranking score is calculated by adding the appropriate number from each row of the tally table. For example, the possible ranking:
1023:
The ranking that has the largest score is identified as the overall ranking. (If more than one ranking has the same largest score, all these possible rankings are tied, and typically the overall ranking involves one or more ties.)
5222: — A website that calculates Kemeny–Young results, and gives further explanation and examples of the concept. It also calculates the winner according to plurality, Borda count, instant-runoff and other voting methods.
3228:
In the papers by John Kemeny and Peyton Young, the Kemeny scores use counts of how many voters oppose, rather than support, each pairwise preference, but the smallest such score identifies the same overall ranking.
3212:
approach to preference aggregation: he supposed that there was an objectively 'correct', but unknown preference order over the alternatives, and voters receive noisy signals of this true preference order (cf.
1012:
on which voters rank choices according to their order of preference. A voter is allowed to rank more than one choice at the same preference level. Unranked choices are usually interpreted as least-preferred.
2057:
The ranking score for the possible ranking of
Memphis first, Nashville second, Chattanooga third, and Knoxville fourth equals (the unit-less number) 345, which is the sum of the following annotated numbers.
1354:
satisfies the preferences Elliot > Roland, Elliot > Meredith, Elliot > Selden, Roland > Meredith, Roland > Selden, and
Meredith > Selden. The respective scores, taken from the table, are
2816:
Identifies the overall order of preference for all the choices. The method does this for all possible sets of voter preferences and always produces the same result for the same set of voter preferences.
4676:
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.
1386:
After the scores for every possible ranking have been calculated, the ranking that has the largest score can be identified, and becomes the overall ranking. In this case, the overall ranking is:
2733:
are involved, the Kemeny–Young method only produces a tie at a preference level when the number of voters with one preference exactly matches the number of voters with the opposite preference.
4640:
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.
1406:
If there are cycles or ties, more than one possible ranking can have the same largest score. Cycles are resolved by producing a single overall ranking where some of the choices are tied.
3002:
If all the ballots are divided into separate races and choice X is identified as the most popular in every such race, then choice X is the most popular when all the ballots are combined.
1016:
Kemeny–Young calculations are usually done in two steps. The first step is to create a matrix or table that counts pairwise voter preferences. The second step is to test all possible
3042:
Offering a larger number of similar choices, instead of offering only a single such choice, does not change the probability that one of these choices is identified as most popular.
2718:
In this arrangement the largest ranking score (393) equals the sum of the counts in bold, which are in the upper-right, triangular half of the matrix (with a green background).
5172: — A website that calculates Kemeny–Young results. For comparison, it also calculates the winner according to plurality, Condorcet, Borda count, and other voting methods.
2892:
If all the ballots are divided into separate races and the overall ranking for the separate races are the same, then the same ranking occurs when all the ballots are combined.
941:
5247:
4631:
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.
3179:
978:
score is the winning sequence, and the first choice in the winning sequence is the most popular choice. (As explained below, ties can occur at any ranking level.)
5196: — Command-line program for fast calculation of Kemeny-Young results, as source code and compiled binaries for Windows and Linux. Open source, except uses
3140:
1630:
4985:; Fomin, Fedor V.; Koster, Arie M. C. A.; Kratsch, Dieter; Thilikos, Dimitrios M. (2012), "A note on exact algorithms for vertex ordering problems on graphs",
3185:
for computing a Kemeny-Young ranking, and there also exists a parameterized subexponential-time algorithm with running time O(2) for computing such a ranking.
4717:
5697:
3293:
2871:
5465:
4622:. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates.
632:
3208:
and the so-called quasi-Condorcet criterion. It can also be characterized using consistency and a monotonicity property. In other papers, Young adopted an
3095:
An algorithm for computing a Kemeny-Young ranking in time polynomial in the number of candidates is not known, and unlikely to exist since the problem is
1020:, calculate a score for each such ranking, and compare the scores. Each ranking score equals the sum of the pairwise counts that apply to that ranking.
5178: — C++ program, available on GitHub under the MIT license, that calculates VoteFair ranking results, which include Condorcet-Kemeny calculations.
2752:
There are voter preferences that can yield every possible overall order-of-preference result, including ties at any combination of preference levels.
5593:
5445:
664:
526:
521:
5692:
5470:
3303:
3299:
2927:
2726:
In all cases that do not result in an exact tie, the Kemeny–Young method identifies a most-popular choice, second-most popular choice, and so on.
934:
627:
2844:
If voters increase a choice's preference level, the ranking result either does not change or the promoted choice increases in overall popularity.
2525:
The largest ranking score is 393, and this score is associated with the following possible ranking, so this ranking is also the overall ranking:
4685:
Where a winner is randomly chosen from the candidates, sortition is included to demonstrate that even non-voting methods can pass some criteria.
5455:
5240:
4667:
A variant of
Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm.
309:
2862:, which is the smallest nonempty set of choices such that every member of the set is pairwise preferred to every choice not in the Smith set.
5050:
4618:
Approval voting, score voting, and majority judgment satisfy IIA if it is assumed that voters rate candidates independently using their own
833:
5862:
5819:
3182:
84:
5502:
4956:
4862:
Bachmeier, Georg; Brandt, Felix; Geist, Christian; Harrenstein, Paul; Kardel, Keyvan; Peters, Dominik; Seedig, Hans Georg (2019-11-01).
927:
2582:
The summary matrix below arranges the pairwise counts in order from most popular (top and left) to least popular (bottom and right):
5233:
5153:
4838:
2830:
Any pairwise preference expressed by every voter results in the preferred choice being ranked higher than the less-preferred choice.
1623:
5837:
3225:
himself was aware of the Kemeny-Young rule and its maximum-likelihood interpretation, but was unable to clearly express his ideas.
828:
5687:
5633:
3037:
2906:
If the preferences on every ballot are inverted, then the previously most popular choice must not remain the most popular choice.
2747:
818:
568:
539:
479:
5485:
5216: — Tutorial that uses a simple formulation as integer program and is adaptable to other languages with bindings to lpsolve.
5814:
550:
75:
2988:
Ranking an additional choice (that was otherwise unranked) cannot displace a choice from being identified as the most popular.
5613:
613:
3118:. As such, many methods for the computation of feedback arc sets can be applied to this problem, including a variant of the
255:
240:
225:
3084:
An algorithm is known to determine the winner using this method in a runtime that is polynomial in the number of choices.
5656:
5641:
5460:
3218:
2780:
If a majority of voters strictly prefer choice X to every other choice, then choice X is identified as the most popular.
1616:
871:
491:
414:
335:
5707:
5430:
5420:
5281:
3204:
and Arthur
Levenglick axiomatically characterized the method, showing that it is the unique neutral method satisfying
2775:
303:
285:
126:
3214:
856:
3016:
The optimal voting strategy for an individual should always include giving their favorite candidate maximum support.
5857:
5672:
5363:
4714:
4601:
4505:
3011:
747:
730:
697:
677:
461:
449:
419:
220:
178:
111:
2974:
Adding ballots that rank choice X over choice Y never cause choice Y, instead of choice X, to become most popular.
555:
5722:
5677:
5623:
5535:
3271:
3217:.) Using a simple probabilistic model for these noisy signals, Young showed that the Kemeny–Young method was the
603:
596:
80:
5712:
5598:
5556:
5475:
5400:
5336:
5294:
3266:
657:
585:
574:
437:
424:
407:
384:
362:
325:
315:
3119:
5737:
5727:
5702:
5518:
5395:
4597:
4589:
3319:
2983:
2969:
1656:
1595:
783:
637:
320:
5213:
3181:, significantly faster for many candidates than the factorial time of testing all rankings. There exists a
5778:
5717:
5580:
5523:
3314:
3309:
2960:
A voter cannot cause a choice to become the most popular by giving the choice an insincerely high ranking.
2880:, adding or withdrawing choice X does not change a result in which choice Y is identified as most popular.
2839:
1675:
812:
692:
622:
429:
5206: — Implements Davenport's algorithm with no other library dependencies. Open source, LGPL licensed.
3110:
The Kemeny–Young method can be formulated as an instance of a more abstract problem, of finding weighted
2575:
If a single winner is needed, the first choice, Nashville, is chosen. (In this example
Nashville is the
5682:
5603:
5368:
4585:
3874:
3349:
3205:
3056:
A voter cannot cause choice X to become the most popular by giving choice Y an insincerely high ranking.
2997:
2932:
Adding or withdrawing choice X does not change a result in which choice Y is identified as most popular.
1583:
720:
560:
444:
250:
229:
161:
139:
4939:"Faster Algorithms for Feedback Arc Set Tournament, Kemeny Rank Aggregation and Betweenness Tournament"
3232:
Since 1991 the method has been promoted under the name "VoteFair popularity ranking" by
Richard Fobes.
912:
778:
4863:
5752:
5321:
3714:
3336:
3222:
1681:
1669:
1028:
851:
838:
806:
70:
1641:
5732:
5326:
5187:
4581:
3926:
3766:
3454:
3103:
2946:
A voter cannot displace a choice from most popular by giving the choice an insincerely low ranking.
2811:
2761:
1652:
1009:
757:
591:
244:
4938:
5773:
5383:
5020:
4982:
4901:
4875:
4844:
3194:
1801:
1663:
991:
967:
917:
788:
399:
183:
5341:
4821:; Brandenburg, Franz J.; Deng, Xiaotie (2005-09-12). Healy, Patrick; Nikolov, Nikola S. (eds.).
4032:
3240:
The following table compares the Kemeny-Young method with other single-winner election methods:
866:
5181:
3145:
5742:
5651:
5608:
5528:
5450:
5373:
5358:
5316:
5197:
5149:
5073:
4893:
4834:
3978:
3662:
3506:
2901:
2825:
1932:
The Kemeny–Young method arranges the pairwise comparison counts in the following tally table:
823:
793:
715:
652:
486:
213:
188:
171:
39:
3031:
these criteria (which means the described criteria do not apply to the Kemeny–Young method):
2921:
these criteria (which means the described criteria do not apply to the Kemeny–Young method):
974:
because if there is a Condorcet winner, it will always be ranked as the most popular choice.
5783:
5415:
5271:
5256:
5065:
5002:
4994:
4965:
4941:, in: Cheong, O., Chwa, K.-Y., and Park, K. (Eds.): ISAAC 2010, Part I, LNCS 6506, pp. 3-14.
4885:
4826:
4808:
C. Dwork, R. Kumar, M. Naor, D. Sivakumar. Rank Aggregation Methods for the Web, WWW10, 2001
4242:
4084:
3276:
3115:
3111:
2789:
2730:
2576:
1573:
1083:
preference level. The above preference order can be expressed as the following tally table:
971:
959:
904:
861:
752:
740:
454:
330:
156:
150:
132:
121:
116:
104:
65:
27:
5016:
5831:
5747:
5588:
5566:
5378:
5299:
5289:
5267:
5012:
4721:
4619:
3401:
3287:
3282:
3079:
3051:
2955:
2941:
2853:
892:
725:
580:
545:
466:
377:
280:
203:
145:
23:
47:
5646:
5351:
5311:
5193:
4294:
3818:
3610:
3125:
963:
762:
702:
687:
498:
367:
342:
193:
1027:
Another way to view the ordering is that it is the one which minimizes the sum of the
887:
5851:
5390:
5069:
5024:
4951:
4818:
4792:
4779:
Giuseppe Munda, "Social multi-criteria evaluation for a sustainable economy", p. 124.
4593:
4136:
3330:
3324:
771:
471:
259:
97:
60:
35:
4922:
4848:
5405:
5346:
5175:
4905:
4347:
4189:
3209:
3201:
3065:
511:
275:
268:
198:
2741:
All Condorcet methods, including the Kemeny–Young method, satisfy these criteria:
4864:"k-Majority digraphs and the hardness of voting with a constant number of voters"
5788:
5551:
5490:
5410:
5306:
4825:. Lecture Notes in Computer Science. Springer Berlin Heidelberg. pp. 1–12.
4453:
3558:
1032:
1017:
389:
347:
290:
235:
4889:
4795:, "Voting schemes for which it can be difficult to tell who won the election",
5561:
5497:
5219:
4998:
5077:
4969:
4897:
5798:
5793:
5207:
4400:
2877:
2859:
2766:
If there is a choice that wins all pairwise contests, then this choice wins.
1648:
357:
352:
4655:
without grading any less-preferred candidate above any more-preferred one.
899:
5618:
5037:
4760:
3261:
608:
5106:
H. P. Young, "Optimal ranking and choice from pairwise comparisons", in
1333:
The sum of the counts in each row must equal the total number of votes.
5480:
5203:
4830:
3096:
394:
5110:
edited by B. Grofman and G. Owen (1986), JAI Press, pp. 113–122.
3070:
The choice identified as most popular is a member of the Schwartz set.
5768:
5190:
supporting multiple Condorcet methods, including Kemeny–Young method.
5007:
2729:
A tie can occur at any preference level. Except in some cases where
970:
counts to identify the most popular choices in an election. It is a
5225:
5135:
H. P. Young, "Group choice and individual judgements", Chapter 9 of
5139:, edited by Dennis Mueller (1997) Cambridge UP., pp.181 –200.
4880:
1378:
giving a total ranking score of 30 + 60 + 60 + 70 + 60 + 40 = 320.
1415:
equal-preference pairwise counts that appear in the tally table:
4577:
4575:
4573:
4571:
4569:
4567:
4565:
5229:
1657:
All voters want the capital to be as close to them as possible.
5184:
2917:
In common with all Condorcet methods, the Kemeny–Young method
4921:
Vincent Conitzer, Andrew Davenport, and Jayant Kalagnanam, "
46:
1666:, the largest city, but far from the others (42% of voters)
1655:. The population is concentrated around four major cities.
5169:
3099:
even if there are just 4 voters (even) or 7 voters (odd).
5148:
Richard Fobes, "The Creative Problem Solver's Toolbox", (
1551:
voters oppose (rather than support) each pairwise order:
4761:
A Consistent Extension of Condorcet's Election Principle
3221:
of the true preference order. Young further argues that
3102:
It has been reported that calculation methods based on
2805:
The Kemeny–Young method also satisfies these criteria:
2794:
A single voter cannot control the outcome in all cases.
4614:
4612:
4610:
3148:
3128:
5807:
5761:
5665:
5632:
5579:
5544:
5511:
5438:
5429:
5280:
5194:
C++ Program for Kemeny-Young Preference Aggregation
1590:(depending on how the second-round tie is handled)
4954:(1964), "A comment on minimum feedback arc sets",
3173:
3134:
5204:C Program for Kemeny-Young Preference Aggregation
4917:
4915:
4663:
4661:
2062:42% (of the voters) prefer Memphis over Nashville
1547:(If it did, that would be the overall ranking.)
3091:Calculation methods and computational complexity
5214:Kemeny-Young Optimal Rank Aggregation in Python
1672:, near the center of the state (26% of voters)
1651:is holding an election on the location of its
5241:
5108:Information pooling and group decision making
5090:H. P. Young, "Condorcet's Theory of Voting",
4923:Improved bounds for computing Kemeny rankings
4713:The numbers in this example are adapted from
3122:that can compute the Kemeny–Young ranking of
1688:The preferences of each region's voters are:
1624:
981:The Kemeny–Young method is also known as the
935:
8:
5698:Independence of Smith-dominated alternatives
4738:John Kemeny, "Mathematics without numbers",
2872:Independence of Smith-dominated alternatives
2737:Satisfied criteria for all Condorcet methods
3246:Comparison of single-winner voting systems
2858:The most popular choice is a member of the
5435:
5248:
5234:
5226:
3244:
1943:Number of votes with indicated preference
1631:
1617:
1219:Number of votes with indicated preference
1094:Number of votes with indicated preference
942:
928:
18:
5137:Perspectives on public choice: a handbook
5006:
4879:
4650:
4648:
4646:
3193:The Kemeny–Young method was developed by
3162:
3147:
3127:
2913:Failed criteria for all Condorcet methods
2082:This table lists all the ranking scores:
1800:This matrix summarizes the corresponding
5049:Can, Burak; Storcken, Ton (2013-03-01).
4734:
4732:
4730:
2584:
2527:
2084:
1934:
1806:
1690:
1553:
1417:
1210:
1085:
1041:
5693:Independence of irrelevant alternatives
5471:Sequential proportional approval voting
4933:
4931:
4868:Journal of Computer and System Sciences
4755:
4753:
4751:
4715:Sample election used in Knowledge (XXG)
4706:
4561:
4555:
2928:Independence of irrelevant alternatives
34:
5038:http://cs.brown.edu/~claire/stoc07.pdf
1684:, far to the northeast (17% of voters)
5119:H. P. Young, "Optimal Voting Rules",
4787:
4785:
2077:83% prefer Chattanooga over Knoxville
2071:68% prefer Nashville over Chattanooga
7:
5097:, no. 2 (1988), pp. 1231–1244.
4799:, Vol. 6, No. 2 (1989), pp. 157–165.
3183:polynomial-time approximation scheme
5503:Indirect single transferable voting
5210:is also open source, LPGL licensed.
4957:IEEE Transactions on Circuit Theory
4791:J. Bartholdi III, C. A. Tovey, and
4765:SIAM Journal on Applied Mathematics
2074:68% prefer Nashville over Knoxville
2065:42% prefer Memphis over Chattanooga
5051:"Update monotone preference rules"
14:
5092:American Political Science Review
2068:42% prefer Memphis over Knoxville
5126:, no.1 (1995), pp. 51–64.
5121:Journal of Economic Perspectives
5070:10.1016/j.mathsocsci.2012.10.004
4759:H. P. Young and A. Levenglick, "
1640:
1035:distance) to the voters' lists.
911:
898:
886:
834:McKelvey–Schofield chaos theorem
480:Semi-proportional representation
112:First preference plurality (FPP)
5036:"How to Rank with Few Errors".
2956:Invulnerability to compromising
1937:
1678:, somewhat east (15% of voters)
1382:Calculating the overall ranking
5614:Mixed ballot transferable vote
4937:Karpinski, M. and Schudy, W.,
3168:
3152:
872:Harsanyi's utilitarian theorem
829:Moulin's impossibility theorem
794:Conflicting majorities paradox
16:Single-winner electoral system
1:
5208:A Ruby binding to the library
3027:The Kemeny–Young method also
2801:Additional satisfied criteria
1403:with a ranking score of 370.
1008:The Kemeny–Young method uses
698:Frustrated majorities paradox
5815:Comparison of voting systems
5657:Satisfaction approval voting
5642:Single non-transferable vote
5461:Proportional approval voting
5058:Mathematical Social Sciences
4770:, no. 2 (1978), pp. 285–300.
3219:maximum likelihood estimator
3052:Invulnerability to push-over
867:Condorcet dominance theorems
807:Social and collective choice
5863:Monotonic Condorcet methods
5421:Graduated majority judgment
5156:), 1993, pp. 223–225.
4987:Theory of Computing Systems
987:VoteFair popularity ranking
533:By mechanism of combination
304:Proportional representation
5879:
5673:Condorcet winner criterion
5364:First-past-the-post voting
4890:10.1016/j.jcss.2019.04.005
4823:Crossings and Permutations
4745:(1959), pp. 577–591.
4559:
3023:Additional failed criteria
3012:Sincere favorite criterion
2942:Invulnerability to burying
2876:If choice X is not in the
2049:
2046:
2043:
2038:
2033:
2030:
2027:
2022:
2017:
2014:
2011:
2006:
2001:
1998:
1995:
1990:
1985:
1982:
1979:
1974:
1969:
1966:
1963:
1958:
1325:
1322:
1319:
1314:
1309:
1306:
1303:
1298:
1293:
1290:
1287:
1282:
1277:
1274:
1271:
1266:
1261:
1258:
1255:
1250:
1245:
1242:
1239:
1234:
1200:
1197:
1194:
1189:
1184:
1181:
1178:
1173:
1168:
1165:
1162:
1157:
1152:
1149:
1146:
1141:
1136:
1133:
1130:
1125:
1120:
1117:
1114:
1109:
731:Multiple districts paradox
462:Fractional approval voting
450:Interactive representation
5828:
5820:Voting systems by country
5723:Mutual majority criterion
5678:Condorcet loser criterion
5624:Vote linkage mixed system
5536:Largest remainders method
5263:
4999:10.1007/s00224-011-9312-0
4797:Social Choice and Welfare
4584:is incompatible with the
3174:{\displaystyle O(n2^{n})}
1942:
1714:
1707:
1700:
1693:
1218:
1213:
1093:
1088:
678:Paradoxes and pathologies
527:Mixed-member proportional
522:Mixed-member majoritarian
517:By results of combination
408:Approval-based committees
5713:Majority loser criterion
5599:Additional member system
5557:Hagenbach-Bischoff quota
5476:Single transferable vote
5401:Positional voting system
5337:Minimax Condorcet method
5295:Combined approval voting
4970:10.1109/tct.1964.1082291
3215:Condorcet's jury theorem
1374:Meredith > Selden: 40
1368:Roland > Meredith: 70
1362:Elliot > Meredith: 60
857:Condorcet's jury theorem
658:Double simultaneous vote
633:Rural–urban proportional
628:Dual-member proportional
590:
579:
546:Parallel (superposition)
438:Fractional social choice
425:Expanding approvals rule
254:
239:
224:
155:
144:
120:
5738:Resolvability criterion
5728:Participation criterion
5703:Later-no-harm criterion
5519:Highest averages method
784:Tyranny of the majority
561:Fusion (majority bonus)
378:Quota-remainder methods
5779:First-preference votes
5718:Monotonicity criterion
5688:Independence of clones
5391:Simple majoritarianism
3175:
3136:
3038:Independence of clones
1371:Roland > Selden: 60
1365:Elliot > Selden: 60
1359:Elliot > Roland: 30
918:Mathematics portal
824:Majority impossibility
813:Impossibility theorems
609:Negative vote transfer
430:Method of equal shares
51:
5683:Consistency criterion
5604:Alternative vote plus
5369:Instant-runoff voting
4582:Condorcet's criterion
3176:
3137:
1584:Instant runoff voting
1029:Kendall tau distances
721:Best-is-worst paradox
710:Pathological response
445:Direct representation
98:Single-winner methods
50:
5753:Seats-to-votes ratio
5524:Webster/Sainte-Laguë
5176:VoteFair_Ranking.cpp
3337:No favorite betrayal
3146:
3126:
2731:circular ambiguities
1010:preferential ballots
905:Economics portal
852:Median voter theorem
71:Comparative politics
5733:Plurality criterion
5332:Kemeny–Young method
4983:Bodlaender, Hans L.
4506:Tideman alternative
3247:
3142:candidates in time
3120:Held–Karp algorithm
3104:integer programming
2812:Unrestricted domain
2762:Condorcet criterion
1802:pairwise comparison
1560:First-place winner
1076:(equal preference)
968:pairwise comparison
956:Kemeny–Young method
893:Politics portal
604:Vote linkage system
575:Seat linkage system
162:Ranked-choice (RCV)
5774:Election threshold
5708:Majority criterion
5384:Supplementary vote
4831:10.1007/11618058_1
4720:2017-03-30 at the
3245:
3171:
3132:
3080:Polynomial runtime
2776:Majority criterion
1938:All possible pairs
1214:All possible pairs
1089:All possible pairs
1074:Meredith or Selden
992:maximum likelihood
789:Discursive dilemma
748:Lesser evil voting
623:Supermixed systems
326:Largest remainders
184:Round-robin voting
52:
5858:Electoral systems
5845:
5844:
5743:Reversal symmetry
5652:Cumulative voting
5634:Semi-proportional
5609:Mixed single vote
5575:
5574:
5451:Mixed single vote
5359:Exhaustive ballot
5322:Copeland's method
5317:Condorcet methods
5257:Electoral systems
5198:Numerical Recipes
4693:
4692:
3135:{\displaystyle n}
3116:tournament graphs
3112:feedback arc sets
2902:Reversal symmetry
2826:Pareto efficiency
2715:
2714:
2572:
2571:
2522:
2521:
2054:
2053:
1951:Equal preference
1929:
1928:
1797:
1796:
1719:
1712:
1705:
1698:
1659:The options are:
1604:
1603:
1544:
1543:
1330:
1329:
1227:Equal preference
1205:
1204:
1102:Equal preference
1080:
1079:
952:
951:
839:Gibbard's theorem
779:Dominance paradox
716:Perverse response
420:Phragmen's method
286:Majority judgment
214:Positional voting
172:Condorcet methods
40:electoral systems
5870:
5784:Liquid democracy
5436:
5416:Two-round system
5327:Dodgson's method
5250:
5243:
5236:
5227:
5157:
5146:
5140:
5133:
5127:
5117:
5111:
5104:
5098:
5088:
5082:
5081:
5055:
5046:
5040:
5034:
5028:
5027:
5010:
4979:
4973:
4972:
4948:
4942:
4935:
4926:
4919:
4910:
4909:
4883:
4859:
4853:
4852:
4815:
4809:
4806:
4800:
4789:
4780:
4777:
4771:
4757:
4746:
4736:
4725:
4711:
4686:
4683:
4677:
4674:
4668:
4665:
4656:
4652:
4641:
4638:
4632:
4629:
4623:
4616:
4605:
4602:sincere favorite
4579:
4403:
4374:
4330:
4225:
4139:
4018:
3993:
3857:
3847:
3831:
3827:
3449:Approvals
3428:
3339:
3333:
3327:
3310:Cloneproof
3306:
3296:
3290:
3279:
3277:Condorcet winner
3248:
3236:Comparison table
3180:
3178:
3177:
3172:
3167:
3166:
3141:
3139:
3138:
3133:
2790:Non-dictatorship
2585:
2577:Condorcet winner
2528:
2085:
2009:Y = Chattanooga
1977:Y = Chattanooga
1954:Prefer Y over X
1948:Prefer X over Y
1940:of choice names
1935:
1807:
1717:
1710:
1703:
1696:
1691:
1644:
1633:
1626:
1619:
1588:Elliot or Selden
1554:
1418:
1230:Prefer Y over X
1224:Prefer X over Y
1216:of choice names
1211:
1105:Prefer Y over X
1099:Prefer X over Y
1091:of choice names
1086:
1042:
972:Condorcet method
960:electoral system
944:
937:
930:
916:
915:
903:
902:
891:
890:
846:Positive results
741:Strategic voting
638:Majority jackpot
595:
584:
455:Liquid democracy
331:National remnant
321:Highest averages
258:
243:
228:
160:
151:Alternative vote
149:
133:Partisan primary
125:
66:Mechanism design
19:
5878:
5877:
5873:
5872:
5871:
5869:
5868:
5867:
5848:
5847:
5846:
5841:
5824:
5803:
5757:
5748:Smith criterion
5661:
5628:
5589:Parallel voting
5571:
5567:Imperiali quota
5540:
5507:
5425:
5379:Contingent vote
5342:Nanson's method
5300:Unified primary
5290:Approval voting
5276:
5259:
5254:
5182:Condorcet Class
5166:
5161:
5160:
5147:
5143:
5134:
5130:
5118:
5114:
5105:
5101:
5089:
5085:
5053:
5048:
5047:
5043:
5035:
5031:
4981:
4980:
4976:
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4949:
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4913:
4861:
4860:
4856:
4841:
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4812:
4807:
4803:
4790:
4783:
4778:
4774:
4758:
4749:
4737:
4728:
4722:Wayback Machine
4712:
4708:
4703:
4697:
4695:
4694:
4689:
4684:
4680:
4675:
4671:
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4659:
4653:
4644:
4639:
4635:
4630:
4626:
4617:
4608:
4580:
4563:
3343:
3283:Condorcet loser
3272:Mutual majority
3258:
3256:
3255:
3253:
3238:
3191:
3158:
3144:
3143:
3124:
3123:
3093:
3025:
2915:
2854:Smith criterion
2803:
2739:
2724:
2722:Characteristics
2717:
2574:
2532:
2524:
2109:
2104:
2099:
2094:
2089:
2081:
2056:
2040:
2039:X = Chattanooga
2024:
2008:
1992:
1976:
1960:
1939:
1931:
1909:
1887:
1865:
1843:
1834:
1827:
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1284:
1268:
1252:
1236:
1215:
1191:
1175:
1159:
1143:
1127:
1111:
1090:
1075:
1046:
1006:
998:median relation
948:
910:
909:
897:
885:
877:
876:
843:
819:Arrow's theorem
809:
799:
798:
767:
737:
726:No-show paradox
707:
693:Cloning paradox
683:Spoiler effects
680:
670:
669:
644:
531:
514:
504:
503:
476:
467:Maximal lottery
434:
415:Thiele's method
404:
374:
306:
296:
295:
281:Approval voting
269:Cardinal voting
265:
210:
204:Maximal lottery
168:
100:
90:
17:
12:
11:
5:
5876:
5874:
5866:
5865:
5860:
5850:
5849:
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5842:
5829:
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5823:
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5809:
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5786:
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5776:
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5765:
5763:
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5750:
5745:
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5735:
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5725:
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5715:
5710:
5705:
5700:
5695:
5690:
5685:
5680:
5675:
5669:
5667:
5663:
5662:
5660:
5659:
5654:
5649:
5647:Limited voting
5644:
5638:
5636:
5630:
5629:
5627:
5626:
5621:
5616:
5611:
5606:
5601:
5596:
5591:
5585:
5583:
5577:
5576:
5573:
5572:
5570:
5569:
5564:
5559:
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5548:
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5542:
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5531:
5526:
5515:
5513:
5509:
5508:
5506:
5505:
5500:
5495:
5494:
5493:
5488:
5483:
5473:
5468:
5463:
5458:
5453:
5448:
5442:
5440:
5433:
5427:
5426:
5424:
5423:
5418:
5413:
5408:
5403:
5398:
5393:
5388:
5387:
5386:
5381:
5376:
5374:Coombs' method
5366:
5361:
5356:
5355:
5354:
5352:Schulze method
5349:
5344:
5339:
5334:
5329:
5324:
5314:
5312:Bucklin voting
5309:
5304:
5303:
5302:
5297:
5286:
5284:
5278:
5277:
5264:
5261:
5260:
5255:
5253:
5252:
5245:
5238:
5230:
5224:
5223:
5217:
5211:
5201:
5191:
5179:
5173:
5165:
5164:External links
5162:
5159:
5158:
5141:
5128:
5112:
5099:
5083:
5064:(2): 136–149.
5041:
5029:
4993:(3): 420–432,
4974:
4964:(2): 296–297,
4943:
4927:
4911:
4854:
4839:
4819:Biedl, Therese
4810:
4801:
4781:
4772:
4747:
4726:
4705:
4704:
4702:
4699:
4691:
4690:
4688:
4687:
4678:
4669:
4657:
4642:
4633:
4624:
4620:absolute scale
4606:
4560:
4558:
4554:
4553:
4552:Ranking
4550:
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4535:
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4529:
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4356:
4353:
4350:
4344:
4343:
4342:Ranking
4340:
4337:
4334:
4331:
4327:
4324:
4321:
4318:
4315:
4312:
4309:
4306:
4303:
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4297:
4291:
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4287:
4284:
4281:
4278:
4275:
4272:
4269:
4266:
4263:
4260:
4257:
4254:
4251:
4248:
4245:
4239:
4238:
4237:Ranking
4235:
4232:
4229:
4226:
4222:
4219:
4216:
4213:
4210:
4207:
4204:
4201:
4198:
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4192:
4186:
4185:
4182:
4179:
4176:
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4170:
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4133:
4132:
4129:
4126:
4123:
4120:
4117:
4114:
4111:
4108:
4105:
4102:
4099:
4096:
4093:
4090:
4087:
4081:
4080:
4079:Ranking
4077:
4074:
4071:
4068:
4065:
4062:
4059:
4056:
4053:
4050:
4047:
4044:
4041:
4038:
4035:
4029:
4028:
4027:Ranking
4025:
4022:
4019:
4015:
4012:
4009:
4006:
4003:
4000:
3997:
3994:
3990:
3987:
3984:
3981:
3975:
3974:
3973:Ranking
3971:
3968:
3965:
3962:
3959:
3956:
3953:
3950:
3947:
3944:
3941:
3938:
3935:
3932:
3929:
3923:
3922:
3921:Ranking
3919:
3916:
3913:
3910:
3907:
3904:
3901:
3898:
3895:
3892:
3889:
3886:
3883:
3880:
3877:
3875:Instant-runoff
3871:
3870:
3867:
3864:
3861:
3858:
3854:
3851:
3848:
3844:
3841:
3838:
3835:
3832:
3828:
3824:
3821:
3819:Highest median
3815:
3814:
3813:Ranking
3811:
3808:
3805:
3802:
3799:
3796:
3793:
3790:
3787:
3784:
3781:
3778:
3775:
3772:
3769:
3763:
3762:
3761:Ranking
3759:
3756:
3753:
3750:
3747:
3744:
3741:
3738:
3735:
3732:
3729:
3726:
3723:
3720:
3717:
3711:
3710:
3709:Ranking
3707:
3704:
3701:
3698:
3695:
3692:
3689:
3686:
3683:
3680:
3677:
3674:
3671:
3668:
3665:
3659:
3658:
3657:Ranking
3655:
3652:
3649:
3646:
3643:
3640:
3637:
3634:
3631:
3628:
3625:
3622:
3619:
3616:
3613:
3607:
3606:
3605:Ranking
3603:
3600:
3597:
3594:
3591:
3588:
3585:
3582:
3579:
3576:
3573:
3570:
3567:
3564:
3561:
3555:
3554:
3553:Ranking
3551:
3548:
3545:
3542:
3539:
3536:
3533:
3530:
3527:
3524:
3521:
3518:
3515:
3512:
3509:
3503:
3502:
3501:Ranking
3499:
3496:
3493:
3490:
3487:
3484:
3481:
3478:
3475:
3472:
3469:
3466:
3463:
3460:
3457:
3451:
3450:
3447:
3444:
3441:
3438:
3435:
3432:
3429:
3425:
3422:
3419:
3416:
3413:
3410:
3407:
3404:
3398:
3397:
3394:
3391:
3388:
3385:
3382:
3379:
3376:
3373:
3370:
3367:
3364:
3361:
3358:
3355:
3352:
3350:Anti-plurality
3346:
3345:
3340:
3334:
3328:
3322:
3317:
3315:Monotone
3312:
3307:
3297:
3291:
3285:
3280:
3274:
3269:
3267:Majority loser
3264:
3259:
3254:
3251:
3243:
3242:
3237:
3234:
3190:
3187:
3170:
3165:
3161:
3157:
3154:
3151:
3131:
3092:
3089:
3088:
3087:
3086:
3085:
3082:
3074:
3073:
3072:
3071:
3068:
3060:
3059:
3058:
3057:
3054:
3046:
3045:
3044:
3043:
3040:
3024:
3021:
3020:
3019:
3018:
3017:
3014:
3006:
3005:
3004:
3003:
3000:
2992:
2991:
2990:
2989:
2986:
2978:
2977:
2976:
2975:
2972:
2964:
2963:
2962:
2961:
2958:
2950:
2949:
2948:
2947:
2944:
2936:
2935:
2934:
2933:
2930:
2914:
2911:
2910:
2909:
2908:
2907:
2904:
2896:
2895:
2894:
2893:
2890:
2884:
2883:
2882:
2881:
2874:
2866:
2865:
2864:
2863:
2856:
2848:
2847:
2846:
2845:
2842:
2834:
2833:
2832:
2831:
2828:
2820:
2819:
2818:
2817:
2814:
2802:
2799:
2798:
2797:
2796:
2795:
2792:
2784:
2783:
2782:
2781:
2778:
2770:
2769:
2768:
2767:
2764:
2756:
2755:
2754:
2753:
2750:
2748:Non-imposition
2738:
2735:
2723:
2720:
2713:
2712:
2709:
2706:
2703:
2700:
2692:
2691:
2686:
2683:
2680:
2677:
2669:
2668:
2663:
2658:
2655:
2652:
2644:
2643:
2638:
2633:
2628:
2625:
2617:
2616:
2609:
2602:
2595:
2588:
2570:
2569:
2566:
2562:
2561:
2558:
2554:
2553:
2550:
2546:
2545:
2542:
2538:
2537:
2534:
2520:
2519:
2516:
2513:
2510:
2507:
2503:
2502:
2499:
2496:
2493:
2490:
2486:
2485:
2482:
2479:
2476:
2473:
2469:
2468:
2465:
2462:
2459:
2456:
2452:
2451:
2448:
2445:
2442:
2439:
2435:
2434:
2431:
2428:
2425:
2422:
2418:
2417:
2414:
2411:
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2405:
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2400:
2397:
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2391:
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2329:
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2320:
2316:
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2312:
2309:
2306:
2303:
2299:
2298:
2295:
2292:
2289:
2286:
2282:
2281:
2278:
2275:
2272:
2269:
2265:
2264:
2261:
2258:
2255:
2252:
2248:
2247:
2244:
2241:
2238:
2235:
2231:
2230:
2227:
2224:
2221:
2218:
2214:
2213:
2210:
2207:
2204:
2201:
2197:
2196:
2193:
2190:
2187:
2184:
2180:
2179:
2176:
2173:
2170:
2167:
2163:
2162:
2159:
2156:
2153:
2150:
2146:
2145:
2142:
2139:
2136:
2133:
2129:
2128:
2125:
2122:
2119:
2116:
2112:
2111:
2106:
2101:
2096:
2091:
2079:
2078:
2075:
2072:
2069:
2066:
2063:
2052:
2051:
2048:
2045:
2042:
2041:Y = Knoxville
2036:
2035:
2032:
2029:
2026:
2025:Y = Knoxville
2020:
2019:
2016:
2013:
2010:
2004:
2003:
2000:
1997:
1994:
1993:Y = Knoxville
1988:
1987:
1984:
1981:
1978:
1972:
1971:
1968:
1965:
1962:
1961:Y = Nashville
1956:
1955:
1952:
1949:
1945:
1944:
1941:
1927:
1926:
1923:
1920:
1917:
1914:
1905:
1904:
1901:
1898:
1895:
1892:
1883:
1882:
1879:
1876:
1873:
1870:
1861:
1860:
1857:
1854:
1851:
1848:
1839:
1838:
1831:
1824:
1817:
1810:
1795:
1794:
1793:
1792:
1789:
1786:
1783:
1776:
1775:
1774:
1771:
1768:
1765:
1758:
1757:
1756:
1753:
1750:
1747:
1740:
1739:
1738:
1735:
1732:
1729:
1721:
1720:
1713:
1706:
1699:
1686:
1685:
1679:
1673:
1667:
1636:
1635:
1628:
1621:
1613:
1612:
1608:
1605:
1602:
1601:
1598:
1592:
1591:
1586:
1580:
1579:
1576:
1570:
1569:
1566:
1562:
1561:
1558:
1542:
1541:
1538:
1535:
1532:
1529:
1521:
1520:
1515:
1512:
1509:
1506:
1498:
1497:
1492:
1487:
1484:
1481:
1473:
1472:
1467:
1462:
1457:
1454:
1446:
1445:
1439:
1433:
1427:
1421:
1411:
1410:Summary matrix
1408:
1401:
1400:
1397:
1394:
1391:
1383:
1380:
1376:
1375:
1372:
1369:
1366:
1363:
1360:
1352:
1351:
1348:
1345:
1342:
1328:
1327:
1324:
1321:
1318:
1312:
1311:
1308:
1305:
1302:
1296:
1295:
1292:
1289:
1286:
1280:
1279:
1276:
1273:
1270:
1264:
1263:
1260:
1257:
1254:
1248:
1247:
1244:
1241:
1238:
1232:
1231:
1228:
1225:
1221:
1220:
1217:
1203:
1202:
1199:
1196:
1193:
1187:
1186:
1183:
1180:
1177:
1171:
1170:
1167:
1164:
1161:
1155:
1154:
1151:
1148:
1145:
1139:
1138:
1135:
1132:
1129:
1123:
1122:
1119:
1116:
1113:
1107:
1106:
1103:
1100:
1096:
1095:
1092:
1078:
1077:
1072:
1068:
1067:
1064:
1060:
1059:
1056:
1052:
1051:
1048:
1005:
1002:
964:ranked ballots
950:
949:
947:
946:
939:
932:
924:
921:
920:
908:
907:
895:
882:
879:
878:
875:
874:
869:
864:
859:
854:
842:
841:
836:
831:
826:
821:
810:
805:
804:
801:
800:
797:
796:
791:
786:
781:
766:
765:
763:Turkey-raising
760:
755:
750:
736:
735:
734:
733:
723:
718:
706:
705:
703:Center squeeze
700:
695:
690:
688:Spoiler effect
681:
676:
675:
672:
671:
668:
667:
662:
661:
660:
647:By ballot type
643:
642:
641:
640:
635:
630:
620:
619:
618:
617:
616:
611:
601:
600:
599:
588:
565:
564:
563:
558:
553:
548:
530:
529:
524:
515:
510:
509:
506:
505:
502:
501:
499:Limited voting
496:
495:
494:
475:
474:
469:
464:
459:
458:
457:
452:
433:
432:
427:
422:
417:
403:
402:
397:
392:
387:
373:
372:
371:
370:
368:Localized list
365:
360:
355:
350:
340:
339:
338:
336:Biproportional
333:
328:
323:
307:
302:
301:
298:
297:
294:
293:
288:
283:
278:
264:
263:
248:
233:
209:
208:
207:
206:
201:
196:
191:
181:
167:
166:
165:
164:
153:
140:Instant-runoff
137:
136:
135:
127:Jungle primary
114:
103:Single vote -
101:
96:
95:
92:
91:
89:
88:
78:
73:
68:
63:
57:
54:
53:
43:
42:
32:
31:
15:
13:
10:
9:
6:
4:
3:
2:
5875:
5864:
5861:
5859:
5856:
5855:
5853:
5840:
5839:
5834:
5833:
5827:
5821:
5818:
5816:
5813:
5812:
5810:
5806:
5800:
5797:
5795:
5792:
5790:
5787:
5785:
5782:
5780:
5777:
5775:
5772:
5770:
5767:
5766:
5764:
5760:
5754:
5751:
5749:
5746:
5744:
5741:
5739:
5736:
5734:
5731:
5729:
5726:
5724:
5721:
5719:
5716:
5714:
5711:
5709:
5706:
5704:
5701:
5699:
5696:
5694:
5691:
5689:
5686:
5684:
5681:
5679:
5676:
5674:
5671:
5670:
5668:
5664:
5658:
5655:
5653:
5650:
5648:
5645:
5643:
5640:
5639:
5637:
5635:
5631:
5625:
5622:
5620:
5617:
5615:
5612:
5610:
5607:
5605:
5602:
5600:
5597:
5595:
5592:
5590:
5587:
5586:
5584:
5582:
5578:
5568:
5565:
5563:
5560:
5558:
5555:
5553:
5550:
5549:
5547:
5543:
5537:
5534:
5530:
5527:
5525:
5522:
5521:
5520:
5517:
5516:
5514:
5510:
5504:
5501:
5499:
5496:
5492:
5489:
5487:
5484:
5482:
5479:
5478:
5477:
5474:
5472:
5469:
5467:
5464:
5462:
5459:
5457:
5454:
5452:
5449:
5447:
5444:
5443:
5441:
5437:
5434:
5432:
5428:
5422:
5419:
5417:
5414:
5412:
5409:
5407:
5404:
5402:
5399:
5397:
5394:
5392:
5389:
5385:
5382:
5380:
5377:
5375:
5372:
5371:
5370:
5367:
5365:
5362:
5360:
5357:
5353:
5350:
5348:
5345:
5343:
5340:
5338:
5335:
5333:
5330:
5328:
5325:
5323:
5320:
5319:
5318:
5315:
5313:
5310:
5308:
5305:
5301:
5298:
5296:
5293:
5292:
5291:
5288:
5287:
5285:
5283:
5282:Single-winner
5279:
5275:
5273:
5269:
5262:
5258:
5251:
5246:
5244:
5239:
5237:
5232:
5231:
5228:
5221:
5218:
5215:
5212:
5209:
5205:
5202:
5199:
5195:
5192:
5189:
5186:
5183:
5180:
5177:
5174:
5171:
5168:
5167:
5163:
5155:
5154:0-9632-2210-4
5151:
5145:
5142:
5138:
5132:
5129:
5125:
5122:
5116:
5113:
5109:
5103:
5100:
5096:
5093:
5087:
5084:
5079:
5075:
5071:
5067:
5063:
5059:
5052:
5045:
5042:
5039:
5033:
5030:
5026:
5022:
5018:
5014:
5009:
5004:
5000:
4996:
4992:
4988:
4984:
4978:
4975:
4971:
4967:
4963:
4959:
4958:
4953:
4947:
4944:
4940:
4934:
4932:
4928:
4924:
4918:
4916:
4912:
4907:
4903:
4899:
4895:
4891:
4887:
4882:
4877:
4873:
4869:
4865:
4858:
4855:
4850:
4846:
4842:
4840:9783540314257
4836:
4832:
4828:
4824:
4820:
4814:
4811:
4805:
4802:
4798:
4794:
4788:
4786:
4782:
4776:
4773:
4769:
4766:
4762:
4756:
4754:
4752:
4748:
4744:
4741:
4735:
4733:
4731:
4727:
4723:
4719:
4716:
4710:
4707:
4700:
4698:
4682:
4679:
4673:
4670:
4664:
4662:
4658:
4651:
4649:
4647:
4643:
4637:
4634:
4628:
4625:
4621:
4615:
4613:
4611:
4607:
4603:
4599:
4598:later-no-help
4595:
4594:later-no-harm
4591:
4590:participation
4587:
4583:
4578:
4576:
4574:
4572:
4570:
4568:
4566:
4562:
4556:
4551:
4548:
4545:
4542:
4539:
4536:
4533:
4530:
4527:
4524:
4521:
4518:
4515:
4512:
4509:
4507:
4504:
4503:
4499:
4496:
4493:
4490:
4487:
4484:
4481:
4478:
4475:
4472:
4469:
4466:
4463:
4460:
4457:
4455:
4452:
4451:
4447:
4444:
4441:
4438:
4435:
4432:
4429:
4426:
4423:
4420:
4417:
4414:
4411:
4408:
4405:
4402:
4399:
4398:
4394:
4391:
4388:
4385:
4382:
4379:
4376:
4372:
4369:
4366:
4363:
4360:
4357:
4354:
4351:
4349:
4346:
4345:
4341:
4338:
4335:
4332:
4328:
4325:
4322:
4319:
4316:
4313:
4310:
4307:
4304:
4301:
4298:
4296:
4293:
4292:
4288:
4285:
4282:
4279:
4276:
4273:
4270:
4267:
4264:
4261:
4258:
4255:
4252:
4249:
4246:
4244:
4241:
4240:
4236:
4233:
4230:
4227:
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:
4138:
4137:Random ballot
4135:
4134:
4130:
4127:
4124:
4121:
4118:
4115:
4112:
4109:
4106:
4103:
4100:
4097:
4094:
4091:
4088:
4086:
4083:
4082:
4078:
4075:
4072:
4069:
4066:
4063:
4060:
4057:
4054:
4051:
4048:
4045:
4042:
4039:
4036:
4034:
4031:
4030:
4026:
4023:
4020:
4016:
4013:
4010:
4007:
4004:
4001:
3998:
3995:
3991:
3988:
3985:
3982:
3980:
3977:
3976:
3972:
3969:
3966:
3963:
3960:
3957:
3954:
3951:
3948:
3945:
3942:
3939:
3936:
3933:
3930:
3928:
3925:
3924:
3920:
3917:
3914:
3911:
3908:
3905:
3902:
3899:
3896:
3893:
3890:
3887:
3884:
3881:
3878:
3876:
3873:
3872:
3868:
3865:
3862:
3859:
3855:
3852:
3849:
3845:
3842:
3839:
3836:
3833:
3829:
3825:
3822:
3820:
3817:
3816:
3812:
3809:
3806:
3803:
3800:
3797:
3794:
3791:
3788:
3785:
3782:
3779:
3776:
3773:
3770:
3768:
3765:
3764:
3760:
3757:
3754:
3751:
3748:
3745:
3742:
3739:
3736:
3733:
3730:
3727:
3724:
3721:
3718:
3716:
3713:
3712:
3708:
3705:
3702:
3699:
3696:
3693:
3690:
3687:
3684:
3681:
3678:
3675:
3672:
3669:
3666:
3664:
3661:
3660:
3656:
3653:
3650:
3647:
3644:
3641:
3638:
3635:
3632:
3629:
3626:
3623:
3620:
3617:
3614:
3612:
3609:
3608:
3604:
3601:
3598:
3595:
3592:
3589:
3586:
3583:
3580:
3577:
3574:
3571:
3568:
3565:
3562:
3560:
3557:
3556:
3552:
3549:
3546:
3543:
3540:
3537:
3534:
3531:
3528:
3525:
3522:
3519:
3516:
3513:
3510:
3508:
3505:
3504:
3500:
3497:
3494:
3491:
3488:
3485:
3482:
3479:
3476:
3473:
3470:
3467:
3464:
3461:
3458:
3456:
3453:
3452:
3448:
3445:
3442:
3439:
3436:
3433:
3430:
3426:
3423:
3420:
3417:
3414:
3411:
3408:
3405:
3403:
3400:
3399:
3395:
3392:
3389:
3386:
3383:
3380:
3377:
3374:
3371:
3368:
3365:
3362:
3359:
3356:
3353:
3351:
3348:
3347:
3341:
3338:
3335:
3332:
3331:Later-no-help
3329:
3326:
3325:Later-no-harm
3323:
3321:
3320:Participation
3318:
3316:
3313:
3311:
3308:
3305:
3301:
3298:
3295:
3292:
3289:
3286:
3284:
3281:
3278:
3275:
3273:
3270:
3268:
3265:
3263:
3260:
3250:
3249:
3241:
3235:
3233:
3230:
3226:
3224:
3220:
3216:
3211:
3207:
3203:
3198:
3196:
3188:
3186:
3184:
3163:
3159:
3155:
3149:
3129:
3121:
3117:
3113:
3108:
3105:
3100:
3098:
3090:
3083:
3081:
3078:
3077:
3076:
3075:
3069:
3067:
3064:
3063:
3062:
3061:
3055:
3053:
3050:
3049:
3048:
3047:
3041:
3039:
3036:
3035:
3034:
3033:
3032:
3030:
3022:
3015:
3013:
3010:
3009:
3008:
3007:
3001:
2999:
2996:
2995:
2994:
2993:
2987:
2985:
2984:Later-no-harm
2982:
2981:
2980:
2979:
2973:
2971:
2970:Participation
2968:
2967:
2966:
2965:
2959:
2957:
2954:
2953:
2952:
2951:
2945:
2943:
2940:
2939:
2938:
2937:
2931:
2929:
2926:
2925:
2924:
2923:
2922:
2920:
2912:
2905:
2903:
2900:
2899:
2898:
2897:
2891:
2889:Reinforcement
2888:
2887:
2886:
2885:
2879:
2875:
2873:
2870:
2869:
2868:
2867:
2861:
2857:
2855:
2852:
2851:
2850:
2849:
2843:
2841:
2838:
2837:
2836:
2835:
2829:
2827:
2824:
2823:
2822:
2821:
2815:
2813:
2810:
2809:
2808:
2807:
2806:
2800:
2793:
2791:
2788:
2787:
2786:
2785:
2779:
2777:
2774:
2773:
2772:
2771:
2765:
2763:
2760:
2759:
2758:
2757:
2751:
2749:
2746:
2745:
2744:
2743:
2742:
2736:
2734:
2732:
2727:
2721:
2719:
2710:
2707:
2704:
2701:
2698:
2694:
2693:
2690:
2687:
2684:
2681:
2678:
2675:
2671:
2670:
2667:
2664:
2662:
2659:
2656:
2653:
2650:
2646:
2645:
2642:
2639:
2637:
2634:
2632:
2629:
2626:
2623:
2619:
2618:
2614:
2610:
2607:
2603:
2600:
2596:
2593:
2589:
2587:
2586:
2583:
2580:
2578:
2567:
2564:
2563:
2559:
2556:
2555:
2551:
2548:
2547:
2543:
2540:
2539:
2535:
2530:
2529:
2526:
2517:
2514:
2511:
2508:
2505:
2504:
2500:
2497:
2494:
2491:
2488:
2487:
2483:
2480:
2477:
2474:
2471:
2470:
2466:
2463:
2460:
2457:
2454:
2453:
2449:
2446:
2443:
2440:
2437:
2436:
2432:
2429:
2426:
2423:
2420:
2419:
2415:
2412:
2409:
2406:
2403:
2402:
2398:
2395:
2392:
2389:
2386:
2385:
2381:
2378:
2375:
2372:
2369:
2368:
2364:
2361:
2358:
2355:
2352:
2351:
2347:
2344:
2341:
2338:
2335:
2334:
2330:
2327:
2324:
2321:
2318:
2317:
2313:
2310:
2307:
2304:
2301:
2300:
2296:
2293:
2290:
2287:
2284:
2283:
2279:
2276:
2273:
2270:
2267:
2266:
2262:
2259:
2256:
2253:
2250:
2249:
2245:
2242:
2239:
2236:
2233:
2232:
2228:
2225:
2222:
2219:
2216:
2215:
2211:
2208:
2205:
2202:
2199:
2198:
2194:
2191:
2188:
2185:
2182:
2181:
2177:
2174:
2171:
2168:
2165:
2164:
2160:
2157:
2154:
2151:
2148:
2147:
2143:
2140:
2137:
2134:
2131:
2130:
2126:
2123:
2120:
2117:
2114:
2113:
2107:
2102:
2097:
2092:
2087:
2086:
2083:
2076:
2073:
2070:
2067:
2064:
2061:
2060:
2059:
2037:
2023:X = Nashville
2021:
2007:X = Nashville
2005:
1989:
1973:
1957:
1953:
1950:
1947:
1946:
1936:
1933:
1924:
1921:
1918:
1915:
1912:
1907:
1906:
1902:
1899:
1896:
1893:
1890:
1885:
1884:
1880:
1877:
1874:
1871:
1868:
1863:
1862:
1858:
1855:
1852:
1849:
1846:
1841:
1840:
1837:
1832:
1830:
1825:
1823:
1818:
1816:
1811:
1809:
1808:
1805:
1803:
1790:
1787:
1784:
1782:
1779:
1778:
1777:
1772:
1769:
1766:
1764:
1761:
1760:
1759:
1754:
1751:
1748:
1746:
1743:
1742:
1741:
1736:
1733:
1730:
1728:
1725:
1724:
1723:
1722:
1715:17% of voters
1708:15% of voters
1701:26% of voters
1694:42% of voters
1692:
1689:
1683:
1680:
1677:
1674:
1671:
1668:
1665:
1662:
1661:
1660:
1658:
1654:
1650:
1647:Suppose that
1645:
1643:
1634:
1629:
1627:
1622:
1620:
1615:
1614:
1611:
1606:
1599:
1597:
1594:
1593:
1587:
1585:
1582:
1581:
1577:
1575:
1572:
1571:
1567:
1565:Kemeny–Young
1564:
1563:
1559:
1556:
1555:
1552:
1548:
1539:
1536:
1533:
1530:
1527:
1523:
1522:
1519:
1516:
1513:
1510:
1507:
1504:
1500:
1499:
1496:
1493:
1491:
1488:
1485:
1482:
1479:
1475:
1474:
1471:
1468:
1466:
1463:
1461:
1458:
1455:
1452:
1448:
1447:
1444:
1440:
1438:
1434:
1432:
1428:
1426:
1422:
1420:
1419:
1416:
1409:
1407:
1404:
1398:
1395:
1392:
1389:
1388:
1387:
1381:
1379:
1373:
1370:
1367:
1364:
1361:
1358:
1357:
1356:
1349:
1346:
1343:
1340:
1339:
1338:
1334:
1313:
1297:
1281:
1265:
1249:
1237:Y = Meredith
1233:
1229:
1226:
1223:
1222:
1212:
1209:
1188:
1172:
1156:
1140:
1124:
1112:Y = Meredith
1108:
1104:
1101:
1098:
1097:
1087:
1084:
1073:
1070:
1069:
1065:
1062:
1061:
1057:
1054:
1053:
1049:
1044:
1043:
1040:
1036:
1034:
1030:
1025:
1021:
1019:
1014:
1011:
1003:
1001:
999:
995:
993:
988:
984:
979:
975:
973:
969:
965:
961:
957:
945:
940:
938:
933:
931:
926:
925:
923:
922:
919:
914:
906:
901:
896:
894:
889:
884:
883:
881:
880:
873:
870:
868:
865:
863:
862:May's theorem
860:
858:
855:
853:
850:
849:
848:
847:
840:
837:
835:
832:
830:
827:
825:
822:
820:
817:
816:
815:
814:
808:
803:
802:
795:
792:
790:
787:
785:
782:
780:
777:
776:
775:
774:
773:
772:majority rule
770:Paradoxes of
764:
761:
759:
756:
754:
751:
749:
746:
745:
744:
743:
742:
732:
729:
728:
727:
724:
722:
719:
717:
714:
713:
712:
711:
704:
701:
699:
696:
694:
691:
689:
686:
685:
684:
679:
674:
673:
666:
663:
659:
656:
655:
654:
651:
650:
649:
648:
639:
636:
634:
631:
629:
626:
625:
624:
621:
615:
612:
610:
607:
606:
605:
602:
598:
593:
589:
587:
582:
578:
577:
576:
573:
572:
571:
570:
566:
562:
559:
557:
554:
552:
549:
547:
544:
543:
542:
541:
536:
535:
534:
528:
525:
523:
520:
519:
518:
513:
512:Mixed systems
508:
507:
500:
497:
493:
490:
489:
488:
485:
484:
483:
482:
481:
473:
472:Random ballot
470:
468:
465:
463:
460:
456:
453:
451:
448:
447:
446:
443:
442:
441:
440:
439:
431:
428:
426:
423:
421:
418:
416:
413:
412:
411:
410:
409:
401:
398:
396:
393:
391:
388:
386:
383:
382:
381:
380:
379:
369:
366:
364:
361:
359:
356:
354:
351:
349:
346:
345:
344:
341:
337:
334:
332:
329:
327:
324:
322:
319:
318:
317:
316:Apportionment
314:
313:
312:
311:
305:
300:
299:
292:
289:
287:
284:
282:
279:
277:
274:
273:
272:
271:
270:
261:
257:
252:
251:Antiplurality
249:
246:
242:
237:
234:
231:
227:
222:
219:
218:
217:
216:
215:
205:
202:
200:
197:
195:
192:
190:
187:
186:
185:
182:
180:
179:Condorcet-IRV
177:
176:
175:
174:
173:
163:
158:
154:
152:
147:
143:
142:
141:
138:
134:
131:
130:
128:
123:
118:
115:
113:
110:
109:
108:
106:
99:
94:
93:
86:
82:
79:
77:
74:
72:
69:
67:
64:
62:
61:Social choice
59:
58:
56:
55:
49:
45:
44:
41:
37:
36:Social choice
33:
29:
25:
21:
20:
5836:
5830:
5446:Mixed-member
5431:Proportional
5406:Score voting
5347:Ranked pairs
5331:
5266:Part of the
5265:
5170:VoteFair.org
5144:
5136:
5131:
5123:
5120:
5115:
5107:
5102:
5094:
5091:
5086:
5061:
5057:
5044:
5032:
4990:
4986:
4977:
4961:
4955:
4946:
4871:
4867:
4857:
4822:
4813:
4804:
4796:
4775:
4767:
4764:
4742:
4739:
4709:
4696:
4681:
4672:
4636:
4627:
4557:Table Notes
4289:Single mark
4190:Ranked pairs
4184:Single mark
4131:Single mark
3927:Kemeny–Young
3396:Single mark
3239:
3231:
3227:
3202:Peyton Young
3199:
3192:
3109:
3101:
3094:
3028:
3026:
2918:
2916:
2840:Monotonicity
2804:
2740:
2728:
2725:
2716:
2696:
2688:
2673:
2665:
2660:
2648:
2640:
2635:
2630:
2621:
2612:
2605:
2598:
2591:
2581:
2573:
2552:Chattanooga
2523:
2080:
2055:
1930:
1910:
1888:
1866:
1844:
1835:
1828:
1821:
1814:
1798:
1785:Chattanooga
1780:
1762:
1749:Chattanooga
1744:
1734:Chattanooga
1726:
1687:
1646:
1639:
1610:
1549:
1545:
1525:
1517:
1502:
1494:
1489:
1477:
1469:
1464:
1459:
1450:
1442:
1436:
1430:
1424:
1413:
1405:
1402:
1385:
1377:
1353:
1335:
1331:
1299:X = Meredith
1283:X = Meredith
1206:
1174:X = Meredith
1158:X = Meredith
1081:
1037:
1026:
1022:
1015:
1007:
997:
990:
986:
982:
980:
976:
955:
953:
845:
844:
811:
769:
768:
753:Exaggeration
739:
738:
709:
708:
682:
646:
645:
614:Mixed ballot
569:Compensatory
567:
540:compensatory
537:
532:
516:
478:
477:
436:
435:
406:
405:
376:
375:
363:List-free PR
308:
276:Score voting
267:
266:
212:
211:
199:Ranked pairs
170:
169:
102:
5789:Spoilt vote
5552:Droop quota
5491:Schulze STV
5466:Rural–urban
5411:STAR voting
5307:Borda count
4874:: 130–157.
4793:M. A. Trick
4586:consistency
3206:consistency
3195:John Kemeny
2998:Consistency
2649:Chattanooga
2599:Chattanooga
2509:Chattanooga
2492:Chattanooga
2478:Chattanooga
2464:Chattanooga
2444:Chattanooga
2430:Chattanooga
2404:Chattanooga
2387:Chattanooga
2370:Chattanooga
2353:Chattanooga
2336:Chattanooga
2319:Chattanooga
2308:Chattanooga
2294:Chattanooga
2271:Chattanooga
2254:Chattanooga
2243:Chattanooga
2223:Chattanooga
2206:Chattanooga
2192:Chattanooga
2169:Chattanooga
2152:Chattanooga
2141:Chattanooga
2121:Chattanooga
1991:X = Memphis
1975:X = Memphis
1959:X = Memphis
1889:Chattanooga
1829:Chattanooga
1763:Chattanooga
1711:Center-East
1676:Chattanooga
1317:Y = Roland
1301:Y = Roland
1285:Y = Elliot
1269:Y = Roland
1253:Y = Elliot
1192:Y = Roland
1176:Y = Roland
1160:Y = Elliot
1144:Y = Roland
1128:Y = Elliot
1033:bubble sort
1004:Description
983:Kemeny rule
653:Single vote
556:Conditional
551:Coexistence
400:Quota Borda
390:Schulze STV
348:Closed list
291:STAR voting
236:Borda count
5852:Categories
5808:Comparison
5562:Hare quota
5512:Allocation
5498:Spare vote
5486:Hare-Clark
5456:Party-list
4952:Lawler, E.
4881:1704.06304
4215:LIIA Only
3952:LIIA Only
2560:Knoxville
2544:Nashville
2531:Preference
1788:Nashville
1770:Nashville
1767:Knoxville
1752:Knoxville
1737:Knoxville
1731:Nashville
1315:X = Elliot
1267:X = Selden
1251:X = Selden
1235:X = Selden
1190:X = Elliot
1142:X = Selden
1126:X = Selden
1110:X = Selden
1045:Preference
996:, and the
962:that uses
758:Truncation
487:Cumulative
310:Party-list
85:By country
76:Comparison
5799:Unseating
5794:Sortition
5396:Plurality
5272:Economics
5220:QuickVote
5078:0165-4896
5025:253742611
5008:1956/4556
4925:" (2006).
4898:0022-0000
4604:criteria.
4401:Sortition
4085:Plurality
3294:Smith-IIA
3252:Criterion
3223:Condorcet
3210:epistemic
3200:In 1978,
3197:in 1959.
2878:Smith set
2860:Smith set
2674:Knoxville
2622:Nashville
2611:... over
2606:Knoxville
2604:... over
2597:... over
2592:Nashville
2590:... over
2512:Nashville
2506:Knoxville
2498:Nashville
2489:Knoxville
2475:Nashville
2472:Knoxville
2458:Nashville
2455:Knoxville
2447:Nashville
2438:Knoxville
2427:Nashville
2421:Knoxville
2410:Nashville
2407:Knoxville
2396:Nashville
2390:Knoxville
2376:Knoxville
2373:Nashville
2362:Knoxville
2356:Nashville
2345:Nashville
2342:Knoxville
2328:Knoxville
2325:Nashville
2305:Knoxville
2302:Nashville
2288:Knoxville
2285:Nashville
2274:Knoxville
2268:Nashville
2260:Knoxville
2251:Nashville
2240:Knoxville
2234:Nashville
2226:Knoxville
2217:Nashville
2209:Nashville
2203:Knoxville
2189:Nashville
2186:Knoxville
2175:Nashville
2172:Knoxville
2158:Knoxville
2155:Nashville
2138:Knoxville
2135:Nashville
2124:Knoxville
2118:Nashville
1911:Knoxville
1867:Nashville
1836:Knoxville
1822:Nashville
1781:Knoxville
1745:Nashville
1682:Knoxville
1670:Nashville
1649:Tennessee
1596:Plurality
1574:Condorcet
1441:... over
1435:... over
1429:... over
1423:... over
665:Dual-vote
358:Panachage
353:Open list
343:List type
221:Plurality
117:Two-round
105:plurality
28:Economics
5666:Criteria
5619:Scorporo
5268:politics
4849:11189107
4740:Daedalus
4718:Archived
3715:Copeland
3402:Approval
3262:Majority
3066:Schwartz
2568:Memphis
1833:... over
1826:... over
1819:... over
1812:... over
1804:counts:
1791:Memphis
1773:Memphis
1755:Memphis
1718:Far-East
1697:Far-West
1526:Meredith
1443:Meredith
1399:Meredith
1347:Meredith
1195:+1 vote
1185:+1 vote
1169:+1 vote
1153:+1 vote
1137:+1 vote
1118:+1 vote
1018:rankings
385:Hare STV
24:Politics
22:A joint
5838:Project
5529:D'Hondt
5481:CPO-STV
5439:Systems
5188:library
5017:2885638
4906:2357131
4500:Scores
4395:Scores
4295:Schulze
3979:Minimax
3869:Scores
3767:Dodgson
3611:Bucklin
3455:Baldwin
3342:Ballot
3189:History
3097:NP-hard
2697:Memphis
2695:Prefer
2672:Prefer
2647:Prefer
2620:Prefer
2613:Memphis
2565:Fourth
2549:Second
2536:Choice
2515:Memphis
2495:Memphis
2481:Memphis
2461:Memphis
2441:Memphis
2424:Memphis
2413:Memphis
2393:Memphis
2379:Memphis
2359:Memphis
2339:Memphis
2322:Memphis
2311:Memphis
2291:Memphis
2277:Memphis
2257:Memphis
2237:Memphis
2220:Memphis
2200:Memphis
2183:Memphis
2166:Memphis
2149:Memphis
2132:Memphis
2115:Memphis
2108:Ranking
1845:Memphis
1815:Memphis
1727:Memphis
1664:Memphis
1653:capital
1607:Example
1600:Selden
1578:Roland
1568:Roland
1557:Method
1524:Prefer
1501:Prefer
1476:Prefer
1449:Prefer
1066:Roland
1063:Second
1058:Elliot
1050:Choice
395:CPO-STV
245:Baldwin
194:Schulze
189:Minimax
107:methods
5832:Portal
5769:Ballot
5545:Quotas
5274:series
5152:
5076:
5023:
5015:
4904:
4896:
4847:
4837:
4600:, and
4243:Runoff
4033:Nanson
3663:Coombs
3257:Method
2557:Third
2541:First
2533:order
2110:score
2105:choice
2103:Fourth
2100:choice
2095:choice
2093:Second
2090:choice
1908:Prefer
1886:Prefer
1864:Prefer
1842:Prefer
1704:Center
1503:Selden
1478:Elliot
1451:Roland
1437:Selden
1431:Elliot
1425:Roland
1396:Selden
1393:Elliot
1390:Roland
1350:Selden
1344:Roland
1341:Elliot
1071:Third
1055:First
1047:order
994:method
989:, the
958:is an
260:Coombs
30:series
5762:Other
5581:Mixed
5054:(PDF)
5021:S2CID
4902:S2CID
4876:arXiv
4845:S2CID
4701:Notes
4448:None
4348:Score
3559:Borda
3507:Black
3344:type
3288:Smith
3029:fails
2919:fails
2098:Third
2088:First
597:'MMP'
586:'AMS'
5270:and
5150:ISBN
5074:ISSN
4894:ISSN
4835:ISBN
4534:Yes
4528:Yes
4525:Yes
4522:Yes
4519:Yes
4516:Yes
4513:Yes
4510:Yes
4485:Yes
4470:Yes
4461:Yes
4454:STAR
4445:Yes
4442:Yes
4439:Yes
4436:Yes
4433:Yes
4427:Yes
4392:Yes
4389:Yes
4383:Yes
4380:Yes
4377:Yes
4326:Yes
4323:Yes
4317:Yes
4314:Yes
4311:Yes
4308:Yes
4305:Yes
4302:Yes
4299:Yes
4283:Yes
4280:Yes
4259:Yes
4250:Yes
4247:Yes
4221:Yes
4218:Yes
4212:Yes
4209:Yes
4206:Yes
4203:Yes
4200:Yes
4197:Yes
4194:Yes
4181:Yes
4178:Yes
4175:Yes
4172:Yes
4169:Yes
4166:Yes
4163:Yes
4125:Yes
4122:Yes
4119:Yes
4116:Yes
4089:Yes
4052:Yes
4049:Yes
4046:Yes
4043:Yes
4040:Yes
4037:Yes
4011:Yes
3983:Yes
3958:Yes
3949:Yes
3946:Yes
3943:Yes
3940:Yes
3937:Yes
3934:Yes
3931:Yes
3915:Yes
3912:Yes
3903:Yes
3891:Yes
3885:Yes
3882:Yes
3879:Yes
3866:Yes
3863:Yes
3853:Yes
3850:Yes
3823:Yes
3780:Yes
3771:Yes
3746:Yes
3737:Yes
3734:Yes
3731:Yes
3728:Yes
3725:Yes
3722:Yes
3719:Yes
3706:Yes
3679:Yes
3673:Yes
3670:Yes
3667:Yes
3651:Yes
3642:Yes
3621:Yes
3618:Yes
3615:Yes
3599:Yes
3593:Yes
3590:Yes
3575:Yes
3566:Yes
3538:Yes
3523:Yes
3520:Yes
3514:Yes
3511:Yes
3474:Yes
3471:Yes
3468:Yes
3465:Yes
3462:Yes
3459:Yes
3446:Yes
3443:Yes
3437:Yes
3434:Yes
3431:Yes
3406:Yes
3393:Yes
3384:Yes
3381:Yes
3357:Yes
3304:LIIA
2708:42%
2705:42%
2702:42%
2699:...
2682:17%
2679:32%
2676:...
2654:32%
2651:...
2624:...
2615:...
2608:...
2601:...
2594:...
2518:255
2501:239
2484:291
2467:275
2450:223
2433:259
2416:321
2399:305
2382:357
2365:341
2348:289
2331:325
2314:327
2297:311
2280:393
2263:377
2246:295
2229:361
2212:207
2195:243
2178:273
2161:309
2144:279
2127:345
2050:17%
2044:83%
2034:32%
2028:68%
2018:32%
2012:68%
2002:58%
1996:42%
1986:58%
1980:42%
1970:58%
1964:42%
1903:83%
1881:68%
1859:42%
1528:...
1505:...
1480:...
1453:...
966:and
954:The
538:Non-
492:SNTV
81:List
38:and
26:and
5594:MMP
5185:PHP
5066:doi
5003:hdl
4995:doi
4966:doi
4886:doi
4872:105
4827:doi
4763:",
4549:No
4546:No
4543:No
4540:No
4537:No
4531:No
4497:No
4494:No
4491:No
4488:No
4482:No
4479:No
4476:No
4473:No
4467:No
4464:No
4458:No
4430:No
4424:No
4421:No
4418:No
4415:No
4412:No
4409:No
4406:No
4386:No
4373:Yes
4370:No
4367:No
4364:No
4361:No
4358:No
4355:No
4352:No
4339:No
4336:No
4333:No
4320:No
4286:No
4277:No
4274:No
4271:No
4268:No
4265:No
4262:No
4256:No
4253:No
4234:No
4231:No
4228:No
4160:No
4157:No
4154:No
4151:No
4148:No
4145:No
4142:No
4128:No
4113:No
4110:No
4107:No
4104:No
4101:No
4098:No
4095:No
4092:No
4076:No
4073:No
4070:No
4067:No
4064:No
4061:No
4058:No
4055:No
4024:No
4021:No
4014:No
4008:No
4005:No
4002:No
3999:No
3996:No
3992:Yes
3989:No
3986:No
3970:No
3967:No
3964:No
3961:No
3955:No
3918:No
3909:No
3906:No
3900:No
3897:No
3894:No
3888:No
3860:No
3846:Yes
3843:No
3840:No
3837:No
3834:No
3826:Yes
3810:No
3807:No
3804:No
3801:No
3798:No
3795:No
3792:No
3789:No
3786:No
3783:No
3777:No
3774:No
3758:No
3755:No
3752:No
3749:No
3743:No
3740:No
3703:No
3700:No
3697:No
3694:No
3691:No
3688:No
3685:No
3682:No
3676:No
3654:No
3648:No
3645:No
3639:No
3636:No
3633:No
3630:No
3627:No
3624:No
3602:No
3596:No
3587:No
3584:No
3581:No
3578:No
3572:No
3569:No
3563:No
3550:No
3547:No
3544:No
3541:No
3535:No
3532:No
3529:No
3526:No
3517:No
3498:No
3495:No
3492:No
3489:No
3486:No
3483:No
3480:No
3477:No
3440:No
3427:Yes
3424:No
3421:No
3418:No
3415:No
3412:No
3409:No
3390:No
3387:No
3378:No
3375:No
3372:No
3369:No
3366:No
3363:No
3360:No
3354:No
3300:IIA
3114:in
2689:58%
2666:58%
2661:83%
2641:58%
2636:68%
2631:68%
2579:.)
1922:17%
1919:32%
1916:58%
1913:...
1897:32%
1894:58%
1891:...
1878:68%
1872:58%
1869:...
1856:42%
1853:42%
1847:...
1537:40
1534:40
1531:30
1511:40
1508:40
1483:30
1326:70
1320:30
1310:70
1304:30
1294:60
1288:40
1278:60
1272:40
1262:60
1256:40
1246:40
1243:10
1240:50
256:el.
241:el.
230:IRV
226:el.
5854::
5835:—
5095:82
5072:.
5062:65
5060:.
5056:.
5019:,
5013:MR
5011:,
5001:,
4991:50
4989:,
4962:11
4960:,
4930:^
4914:^
4900:.
4892:.
4884:.
4870:.
4866:.
4843:.
4833:.
4784:^
4768:35
4750:^
4743:88
4729:^
4660:^
4645:^
4609:^
4596:,
4592:,
4588:,
4564:^
4329:No
4224:No
4017:No
3856:No
3830:No
2711:-
2685:-
2657:-
2627:-
2047:0
2031:0
2015:0
1999:0
1983:0
1967:0
1925:-
1540:-
1518:50
1514:-
1495:60
1490:60
1486:-
1470:70
1465:60
1460:70
1456:-
1323:0
1307:0
1291:0
1275:0
1259:0
1201:0
1198:0
1182:0
1179:0
1166:0
1163:0
1150:0
1147:0
1134:0
1131:0
1121:0
1115:0
1000:.
985:,
592:NZ
581:UK
157:US
146:UK
129:)
122:US
5249:e
5242:t
5235:v
5200:.
5124:9
5080:.
5068::
5005::
4997::
4968::
4908:.
4888::
4878::
4851:.
4829::
4724:.
3302:/
3169:)
3164:n
3160:2
3156:n
3153:(
3150:O
3130:n
1900:-
1875:-
1850:-
1632:e
1625:t
1618:v
1031:(
943:e
936:t
929:v
594::
583::
262:)
253:(
247:)
238:(
232:)
223:(
159::
148::
124::
119:(
87:)
83:(
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