6295:
5796:
6074:
6749:: a voter's happiness with a candidate goes up and then down as the candidate moves along some spectrum. For example, in a group of friends choosing a volume setting for music, each friend would likely have their own ideal volume; as the volume gets progressively too loud or too quiet, they would be increasingly dissatisfied. If the domain is restricted to profiles where every individual has a single-peaked preference with respect to the linear ordering, then social preferences are acyclic. In this situation, Condorcet methods satisfy a wide variety of highly-desirable properties, including being fully spoilerproof.
7027:) provide more information than rankings alone. Kaiser and Oswald conducted an empirical review of four decades of research including over 700,000 participants who provided self-reported ratings of utility, with the goal of identifying whether people "have a sense of an actual underlying scale for their innermost feelings". They found responses to these questions were consistent with all expectations of a well-specified quantitative measure. Furthermore, such ratings were highly predictive of important decisions (such as international migration and divorce) and had larger effect sizes than standard
924:
6642:
59:
899:
12013:
12003:
7271:
911:
10030:"Modern economic theory has insisted on the ordinal concept of utility; that is, only orderings can be observed, and therefore no measurement of utility independent of these orderings has any significance. In the field of consumer's demand theory the ordinalist position turned out to create no problems; cardinal utility had no explanatory power above and beyond ordinal. Leibniz' Principle of the
8156:"Modern economic theory has insisted on the ordinal concept of utility; that is, only orderings can be observed, and therefore no measurement of utility independent of these orderings has any significance. In the field of consumer's demand theory the ordinalist position turned out to create no problems; cardinal utility had no explanatory power above and beyond ordinal. Leibniz' Principle of the
5427:
6899:, leading him to focus his theorem on preference rankings; his goal in adding the independence axiom was, in part, to prevent from the social choice function from "sneaking in" cardinal information by attempting to infer it from the rankings. As a result, Arrow initially interpreted his theorem as a kind of mathematical proof for
6692:), because there can be a rock-paper-scissors cycle with three or more candidates defeating each other in a circle. Thus, Condorcet proved a weaker form of Arrow's impossibility theorem long before Arrow, under the stronger assumption that a voting system in the two-candidate case will agree with a simple majority vote.
10582:
Many value researchers have assumed that rankings of values are more valid than ratings of values because rankings force participants to differentiate more incisively between similarly regarded values ... Results indicated that ratings tended to evidence greater validity than rankings within moderate
5786:
For simplicity we have presented all rankings as if there are no ties. A complete proof taking possible ties into account is not essentially different from the one given here, except that one ought to say "not above" instead of "below" or "not below" instead of "above" in some cases. Full details are
6926:
rules to pass IIA. They argue the availability of a common language with verbal grades is sufficient for IIA by allowing voters to give consistent responses to questions about candidate quality. In other words, they argue most voters will not change their beliefs about whether a candidate is "good",
7548:
In the present stage of the discussion on the problem of social choice, it should be common knowledge that the
General Impossibility Theorem holds because only the ordinal preferences is or can be taken into account. If the intensity of preference or cardinal utility can be known or is reflected in
6780:
The
Campbell-Kelly theorem shows that Condorcet methods are the most spoiler-resistant class of ranked voting systems: whenever it is possible for some ranked voting system to avoid a spoiler effect, a Condorcet method will do so. In other words, replacing a ranked method with its Condorcet variant
8144:
IRV is subject to something called the "center squeeze." A popular moderate can receive relatively few first-place votes through no fault of her own but because of vote splitting from candidates to the right and left. Approval voting thus appears to solve the problem of vote splitting simply and
7031:
predictors like income and demographics. Ultimately, the authors concluded "this feelings-to-actions relationship takes a generic form, is consistently replicable, and is fairly close to linear in structure. Therefore, it seems that human beings can successfully operationalize an integer scale for
8025:
to the election if A beats B in a head-to-head majority vote. For example, although the 2000 U.S. Presidential
Election in Florida did not use ranked ballots, it is plausible (see Magee 2003) that Al Gore (A) would have won without Ralph Nader (B) in the election, and Gore would have beaten Nader
7821:
to the election if A beats B in a head-to-head majority vote. For example, although the 2000 U.S. Presidential
Election in Florida did not use ranked ballots, it is plausible (see Magee 2003) that Al Gore (A) would have won without Ralph Nader (B) in the election, and Gore would have beaten Nader
7251:
is not a condition of Arrow's theorem. This misconception is caused by a mistake by Arrow himself, who included the axiom in his original statement of the theorem but did not use it. Dropping the assumption does not allow for constructing a social welfare function that meets his other conditions.
10540:
The extremely high degree of correspondence found between ranking and rating averages ... does not leave any doubt about the preferability of the rating method for group description purposes. The obvious advantage of rating is that while its results are virtually identical to what is obtained by
8287:
Well, I’m a little inclined to think that score systems where you categorize in maybe three or four classes (in spite of what I said about manipulation) is probably the best. And some of these studies have been made. In France, Balinski has done some studies of this kind which seem to give some
10210:
Now there’s another possible way of thinking about it, which is not included in my theorem. But we have some idea how strongly people feel. In other words, you might do something like saying each voter does not just give a ranking. But says, this is good. And this is not good So this gives more
8200:
Now there’s another possible way of thinking about it, which is not included in my theorem. But we have some idea how strongly people feel. In other words, you might do something like saying each voter does not just give a ranking. But says, this is good. And this is not good So this gives more
7067:
that minimize these psychological effects, such as asking voters to give each candidate a verbal grade (e.g. "bad", "neutral", "good", "excellent") and issuing instructions to voters that refer to their ballots as judgments of individual candidates. Similar techniques are often discussed in the
5253:
7565:
9345:
Indeed, many different social welfare functions can meet Arrow's conditions under such restrictions of the domain. It has been proven, however, that under any such restriction, if there exists any social welfare function that adheres to Arrow's criteria, then
6707:
avoid the spoiler effect in non-cyclic elections, where candidates can be chosen by majority rule. Political scientists have found such cycles to be fairly rare, likely in the range of a few percent, suggesting they may be of limited practical concern.
5778:
whose ballot swings the societal outcome. We then prove that this voter is a partial dictator (in a specific technical sense, described below). Finally we conclude by showing that all of the partial dictators are the same person, hence this voter is a
1566:. However, this assumption is not needed or used in his proof, except to derive the weaker Pareto efficiency axiom, and as a result is not related to the paradox. While Arrow considered it an obvious requirement of any proposed social choice rule,
7051:), suggesting human behavior can cause IIA failures even if the voting method itself does not. However, past research has typically found such effects to be fairly small, and such psychological spoilers can appear regardless of electoral system.
6911:
first claimed interpersonal comparability is necessary for IIA, but later came to argue in favor of cardinal methods for assessing social choice, arguing it would only require "rather limited levels of partial comparability" to hold in practice.
6346:
In this part of the argument we refer back to the original ordering of voters, and compare the positions of the different pivotal voters (identified by applying parts one and two to the other pairs of candidates). First, the pivotal voter for
6615:
satisfy independence of irrelevant alternatives, but it says nothing about the frequency of spoilers. This led Arrow to remark that "Most systems are not going to work badly all of the time. All I proved is that all can work badly at times."
1752:
Morgenbesser, ordering dessert, is told by a waitress that he can choose between blueberry or apple pie. He orders apple. Soon the waitress comes back and explains cherry pie is also an option. Morgenbesser replies "In that case, I'll have
1165:
initially asserted the information provided by these systems was meaningless and therefore could not be used to prevent paradoxes, leading him to overlook them. However, he and other authors would later recognize this as a mistake, with
2191:
with having given an intuitive argument that presents the core of Arrow's theorem. However, Arrow's theorem is substantially more general; it applies to methods of making decisions other than one-man-one-vote elections, such as
5422:{\displaystyle {\begin{aligned}{\text{voters in }}G_{1}&:x\succ _{i}y\succ _{i}z\\{\text{voters in }}G_{2}&:z\succ _{i}x\succ _{i}y\\{\text{voters outside }}G&:y\succ _{i}z\succ _{i}x\end{aligned}}}
10192:
8301:
8269:
8182:
6516:
and the same argument for other pairs shows that all the pivotal voters (and hence all the dictators) occur at the same position in the list of voters. This voter is the dictator for the whole election.
7198:). These results provide some justification for the common requirement of a two-thirds majority for constitutional amendments, which is sufficient to prevent cyclic preferences in most situations.
3399:
3032:
5258:
2912:
10625:
the scale-of-values method can be used for approximately the same purposes as the order-of-merit method, but that the scale-of-values method is a better means of obtaining a record of judgments
6665:, and as a result uniquely minimize the possibility of a spoiler effect among ranked rules. Condorcet believed voting rules should satisfy both independence of irrelevant alternatives and the
6619:
Attempts at dealing with the effects of Arrow's theorem take one of two approaches: either accepting his rule and searching for the least spoiler-prone methods, or dropping his assumption of
2742:
10342:
7781:
Candidates C and D spoiled the election for B ... With them in the running, A won, whereas without them in the running, B would have won. ... Instant runoff voting ... does
3626:
3253:
8252:
It is shown that the utilitarian welfare function satisfies all of Arrow's social choice postulates — avoiding the celebrated impossibility theorem by making use of information which is
5774:
We will prove that any social choice system respecting unrestricted domain, unanimity, and independence of irrelevant alternatives (IIA) is a dictatorship. The key idea is to identify a
2648:
2588:
2552:
2493:
2437:
2381:
6934:
882:
2772:
4705:
4010:
3955:
6992:, and Hildreth pointed out that "any procedure that extends the partial ordering of must involve interpersonal comparisons of utility." These observations have led to the rise of
3738:
3686:
3325:
10556:
Maio, Gregory R.; Roese, Neal J.; Seligman, Clive; Katz, Albert (1 June 1996). "Rankings, Ratings, and the
Measurement of Values: Evidence for the Superior Validity of Ratings".
3141:
6799:
Holliday and Pacuit devised a voting system that provably minimizes the number of candidates who are capable of spoiling an election, albeit at the cost of occasionally failing
566:
7499:
Candidates C and D spoiled the election for B ... With them in the running, A won, whereas without them in the running, B would have won. ... Instant runoff voting ... does
6089:
causes the same switch to the societal outcome, by part one of the argument. Making any or all of the indicated switches to the other ballots has no effect on the outcome.
4758:
4323:
4266:
4117:
3900:
3878:
3802:
3780:
3558:
3536:
3487:
3465:
3443:
3421:
3185:
3163:
3095:
3073:
2712:
2690:
5211:
6835:. These systems ask voters to rate candidates on a numerical scale (e.g. from 0–10), and then elect the candidate with the highest average (for score voting) or median (
1413:
1387:
1361:
585:
5046:
2341:
10200:
8309:
8277:
8190:
7192:
5676:
5591:
5562:
5536:
5510:
4931:
4911:
4885:
4827:
4349:
4143:
1725:
1699:
1673:
1319:
4441:
2821:
9954:
5171:
5120:
4355:
Thenceforth assume that the social choice system satisfies unrestricted domain, Pareto efficiency, and IIA. Also assume that there are at least 3 distinct outcomes.
5735:
5703:
5650:
5618:
5461:
5246:
4985:
4859:
4550:
4415:
4213:
4083:
3856:
3829:
3514:
9256:
7629:
7145:
7117:
4659:
4495:
9480:"How an Ideologically Concentrated Minority Can Trump a Dispersed Majority: Nonmedian Voter Results for Plurality, Run-off, and Sequential Elimination Elections"
7715:"How an Ideologically Concentrated Minority Can Trump a Dispersed Majority: Nonmedian Voter Results for Plurality, Run-off, and Sequential Elimination Elections"
5484:
5148:
5086:
5066:
5008:
4953:
4798:
4778:
4725:
4633:
4613:
4593:
4573:
4518:
4469:
4383:
4290:
4233:
3758:
3281:
2955:
2935:
2841:
2792:
2668:
2608:
2513:
2457:
2401:
2315:
2291:
2260:
2230:
2182:
2162:
2142:
2122:
2104:, by a margin of two to one on each occasion. Thus, even though each individual voter has consistent preferences, the preferences of society are contradictory:
2102:
2082:
2062:
2042:
2022:
2002:
1982:
1962:
1942:
1922:
1839:
1819:
1799:
1076:
1048:
1028:
1008:
10709:
Huber, Joel; Payne, John W.; Puto, Christopher (1982). "Adding
Asymmetrically Dominated Alternatives: Violations of Regularity and the Similarity Hypothesis".
7091:
rules can avoid Arrow's theorem at the cost of being poorly-decisive (i.e. frequently failing to return a result). In this case, a threshold that requires a
11220:
Gives explicit examples of preference rankings and apparently anomalous results under different electoral system. States but does not prove Arrow's theorem.
1093:
However, Arrow's theorem is substantially broader, and can be applied to other methods of social decision-making besides voting. It therefore generalizes
11039:
952:
789:
7080:
In addition to the above practical resolutions, there exist unusual (less-than-practical) situations where Arrow's requirement of IIA can be satisfied.
10380:
6907:. However, he later reversed this opinion, admitting cardinal methods can provide useful information that allows them to evade his theorem. Similarly,
10040:
Racnchetti, Fabio (2002), "Choice without utility? Some reflections on the loose foundations of standard consumer theory", in
Bianchi, Marina (ed.),
8166:
Racnchetti, Fabio (2002), "Choice without utility? Some reflections on the loose foundations of standard consumer theory", in
Bianchi, Marina (ed.),
6781:(i.e. elect a Condorcet winner if they exist, and otherwise run the method) will sometimes prevent a spoiler effect, but can never create a new one.
6961:
each independently derived results showing such interpersonal comparisons of utility could be rigorously defined as individual preferences over the
10109:
9041:
9001:
8482:
7425:
7237:, which does not appear in his framework, though the theorem does have important implications for strategic voting (being used as a lemma to prove
9320:
8814:
6850:(i.e. have a single, clear, always-best strategy), so the informal dictum that "no voting system is perfect" still has some mathematical basis.
9927:
7608:
The abandonment of
Condition 3 makes it possible to formulate a procedure for arriving at a social choice. Such a procedure is described below
7011:, there is a near-universal scientific consensus for the usefulness and meaningfulness of self-reported ratings, which empirically show higher
6968:
Other scholars have noted that interpersonal comparisons of utility are not unique to cardinal voting, but are instead a necessity of any non-
1757:
Arrow's theorem shows that if a society wishes to make decisions while avoiding such self-contradictions, it cannot use methods that discard
10746:"Contrast Effects and Approval Voting: An Illustration of a Systematic Violation of the Independence of Irrelevant Alternatives Condition"
10395:
3044:: If there are at least three alternatives, then there is no social welfare function satisfying all three of the conditions listed below:
6946:
6942:
5741:
By Pareto, the entire set of voters is decisive. Thus by the group contraction lemma, there is a size-one decisive coalition—a dictator.
643:
10133:
8888:
8727:
8615:
7342:
11449:
9248:
7621:
13148:
11200:. The chapter "Defining Rationality: Personal and Group Decision Making" has a detailed discussion of the Arrow Theorem, with proof.
675:
537:
532:
11597:
6832:
3631:
1616:
1588:
986:
945:
638:
1735:
320:
1161:, where voters assign a separate grade to each candidate, are not affected by Arrow's theorem (allowing some to satisfy IIA).
12049:
11259:
11236:
11087:
10952:
10498:
10292:
9663:
9104:
9077:
8567:
8104:
1228:
that determines which of two outcomes or options is better, according to all members of a society. Such a procedure can be a
12948:
5930:
eventually moves to the top of the societal preference as the profile number increases, there must be some profile, number
844:
95:
9962:
9516:
As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates.
7751:
As with simple plurality elections, it is apparent the outcome will be highly sensitive to the distribution of candidates.
3330:
2963:
11340:
11307:
2858:
5765:
originated from
Salvador Barberá in 1980. The proof given here is a simplified version based on two proofs published in
5248:. Design the following voting pattern (notice that it is the cyclic voting pattern which causes the Condorcet paradox):
17:
13153:
12765:
12300:
12098:
11658:
10103:
9974:
Is there such a thing as a perfect voting system? The respondents were unanimous in their insistence that there is not.
9035:
8476:
7419:
938:
12584:
12403:
11627:
11464:
11389:
11213:
11193:
10405:
9937:
9910:
8129:
7774:
7492:
7289:
6876:
popular in psychology, some philosophers and economists rejected the idea of comparing internal human experiences of
839:
9864:"Characterization of Domains Admitting Nondictatorial Social Welfare Functions and Nonmanipulable Voting Procedures"
2717:
12205:
6753:
1333:. Individual preferences (or ballots) are required to satisfy intuitive properties of orderings, e.g. they must be
579:
550:
490:
9094:
6880:. Such philosophers claimed it was impossible to compare the strength of preferences across people who disagreed;
3563:
3190:
13143:
12674:
7314:
6752:
The rule does not fully generalize from the political spectrum to the political compass, a result related to the
2617:
2557:
2521:
2462:
2406:
2350:
1152:
561:
86:
10412:...the fictitious notion of 'original position' developed by Vickery (1945), Harsanyi (1955), and Rawls (1971).
10241:
Harsanyi, John C. (1955). "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility".
7785:
do away with the spoiler problem entirely, although it unquestionably makes it less likely to occur in practice.
1515:
In other words, it is possible for any candidate to defeat any other candidate, given some combination of votes.
12544:
12215:
6938:
2747:
624:
12383:
6214:
in the same position and imagine that any number (even all!) of the other voters change their ballots to move
688:
13158:
12725:
12143:
12118:
11876:
10583:
and low-differentiating participants. In addition, the validity of ratings was greater than rankings overall.
6772:
or can be accurately summarized by one or two dimensions, Condorcet cycles are rare (though not unheard of).
4664:
266:
251:
236:
6294:
5887:
to everything else by unanimity. Now arrange all the voters in some arbitrary but fixed order, and for each
3960:
3905:
13138:
13075:
12501:
12255:
12245:
12180:
11700:
10141:
9611:"Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences*"
8896:
8735:
8623:
7926:"Condorcet's paradox and the likelihood of its occurrence: different perspectives on balanced preferences*"
7350:
3691:
3639:
502:
425:
346:
10514:
Moore, Michael (1 July 1975). "Rating versus ranking in the Rokeach Value Survey: An Israeli comparison".
6073:
5795:
3286:
13133:
12295:
12275:
11530:
10783:
Huber, Joel; Payne, John W.; Puto, Christopher P. (2014). "Let's Be Honest About the Attraction Effect".
10471:
Procaccia, Ariel D.; Rosenschein, Jeffrey S. (2006). "The Distortion of Cardinal Preferences in Voting".
10090:
9022:
8950:
8463:
7406:
6993:
6836:
6828:
6175:
Then by the argument in part one (and the last observation in that part), the societal outcome must rank
3100:
1781:, given stronger conditions for fairness than Arrow's theorem assumes. Suppose we have three candidates (
867:
314:
296:
137:
1419:
that maps the individual orderings to a new ordering that represents the preferences of all of society.
13009:
12760:
12730:
12388:
12230:
12225:
11652:
11592:
10915:
Fishburn, Peter Clingerman (1970). "Arrow's impossibility theorem: concise proof and infinite voters".
10031:
9727:(1976). "Intransitivities in multidimensional voting models and some implications for agenda control".
8157:
6739:
6700:
6666:
6530:
Arrow's impossibility theorem still holds if Pareto efficiency is weakened to the following condition:
1120:
758:
741:
708:
472:
460:
430:
231:
189:
122:
11647:
11103:
10034:
demanded then the excision of cardinal utility from our thought patterns." Arrow (1967), as quoted on
9991:"How mathematical impossibility changed welfare economics: A history of Arrow's impossibility theorem"
9990:
8160:
demanded then the excision of cardinal utility from our thought patterns." Arrow (1967), as quoted on
13045:
12968:
12704:
12260:
12185:
12042:
11720:
11695:
11535:
9681:
9354:
9165:
8958:
8410:
8017:. "This is a kind of stability property of Condorcet winners: you cannot dislodge a Condorcet winner
7881:
7836:
5767:
1484:
614:
607:
91:
10481:
9059:
8972:
7299:
7194:(roughly 64%) of the vote to prevent cycles, so long as the distribution of voters is well-behaved (
6888:
was good or bad, because despite killing thousands of Romans, it had the positive effect of letting
6872:, i.e. statements about which outcomes are better or worse than others. Taking inspiration from the
13060:
12793:
12679:
12476:
12270:
12088:
11815:
9863:
7016:
6977:
6757:
4990:
By iterating the above two claims (note that decisiveness implies weak-decisiveness), we find that
1428:
668:
596:
448:
435:
418:
395:
373:
336:
326:
12863:
7813:
This is a kind of stability property of Condorcet winners: you cannot dislodge a Condorcet winner
4730:
4295:
4238:
4089:
3883:
3861:
3785:
3763:
3541:
3519:
3470:
3448:
3426:
3404:
3168:
3146:
3078:
3056:
2695:
2673:
877:
13065:
12664:
12634:
12290:
12078:
11943:
11903:
11780:
11577:
11495:
11399:
11394:
11333:
9572:"STAR Voting, equality of voice, and voter satisfaction: considerations for voting method reform"
7242:
7155:
6709:
5176:
1512:— the system does not ignore the voters entirely when choosing between some pairs of candidates.
1253:
1221:
1191:
794:
648:
331:
6796:
social welfare function. These correspond to preferences for which there is a Condorcet winner.
1392:
1366:
1340:
763:
13128:
13090:
13070:
13050:
12999:
12669:
12574:
12433:
12378:
12310:
12280:
12200:
12128:
11820:
11710:
10476:
8967:
7248:
6969:
6800:
6765:
5013:
4161:
3258:
2320:
2237:
1555:
1474:
1416:
1270:
1225:
1213:
1102:
823:
703:
633:
440:
11247:
10745:
7161:
5655:
5570:
5541:
5515:
5489:
4916:
4890:
4864:
4806:
4328:
4122:
1704:
1678:
1652:
1298:
13113:
and all other rules where a candidate's score can be determined from a ranking of candidates.
12549:
12534:
12108:
11978:
11963:
11938:
11933:
11861:
11805:
11785:
11690:
11525:
11419:
10374:
10174:
10035:
8929:
8768:
8656:
8161:
7383:
7222:
7012:
6804:
6696:
6661:. These rules limit spoilers to situations where majority rule is self-contradictory, called
4420:
2797:
1567:
731:
571:
455:
261:
240:
172:
150:
8554:, Studies in Choice and Welfare, Cham: Springer International Publishing, pp. 171–245,
5153:
5102:
12883:
12868:
12755:
12750:
12654:
12639:
12604:
12569:
12168:
12113:
12035:
11983:
11968:
11958:
11923:
11871:
11800:
11715:
11587:
11582:
11505:
11500:
11429:
10655:
7294:
7238:
7069:
7040:
6989:
6843:
6731:
6721:
5708:
5681:
5623:
5596:
5434:
5219:
4958:
4832:
4523:
4388:
4186:
4056:
3834:
3807:
3492:
1209:
1199:
1124:
1094:
969:
862:
849:
817:
81:
10059:
6738:, Arrow's conditions are all fully compatible, and all will be met by any rule satisfying
8:
13040:
12659:
12609:
12446:
12373:
12353:
12210:
12093:
11745:
11705:
11669:
11602:
11469:
11439:
11434:
11404:
11369:
11364:
10973:
8786:
8589:
7654:
7122:
7094:
6976:) choice procedure, with cardinal voting rules simply making these comparisons explicit.
6769:
6761:
4638:
4474:
2267:
1745:
1490:
1334:
1276:
768:
602:
255:
12699:
10659:
13019:
12878:
12709:
12689:
12539:
12418:
12323:
12250:
12195:
12016:
11973:
11953:
11918:
11893:
11866:
11664:
11617:
11607:
11565:
11560:
11520:
11515:
11424:
11384:
11326:
11167:
11134:
11126:
11020:
10897:
10808:
10726:
10686:
10643:
10453:
10323:
10266:
10258:
10166:
10158:
9783:
9706:
9698:
9507:
9379:
9371:
9190:
9182:
8993:
8985:
8921:
8913:
8760:
8752:
8705:
8648:
8640:
8435:
8427:
8390:
8074:
8007:
7906:
7898:
7861:
7853:
7802:
7742:
7593:
7519:
7375:
7367:
6885:
6735:
5972:
5469:
5133:
5071:
5051:
4993:
4938:
4783:
4763:
4710:
4618:
4598:
4578:
4558:
4503:
4454:
4368:
4275:
4218:
3743:
3266:
2940:
2920:
2826:
2777:
2653:
2593:
2498:
2442:
2386:
2300:
2276:
2263:
2245:
2215:
2193:
2167:
2147:
2127:
2107:
2087:
2067:
2047:
2027:
2007:
1987:
1967:
1947:
1927:
1907:
1824:
1804:
1784:
1229:
1217:
1061:
1033:
1013:
993:
928:
799:
410:
194:
10827:
9401:
9298:
8839:
8319:
Now, you mention that your theorem applies to preferential systems or ranking systems.
6013:
13004:
12973:
12928:
12823:
12694:
12649:
12624:
12554:
12428:
12358:
12348:
12240:
12190:
12138:
12006:
11988:
11928:
11908:
11898:
11825:
11810:
11730:
11725:
11555:
11550:
11510:
11379:
11302:
11255:
11232:
11209:
11189:
11171:
11083:
11012:
10948:
10928:
10889:
10847:
10843:
10812:
10800:
10765:
10730:
10691:
10673:
10616:
10573:
10531:
10494:
10445:
10401:
10362:
10287:
10270:
10099:
10010:
9933:
9906:
9882:
9844:
9775:
9740:
9710:
9659:
9630:
9591:
9549:
9499:
9460:
9421:
9417:
9383:
9229:
9225:
9194:
9145:
9141:
9100:
9073:
9031:
8859:
8855:
8697:
8563:
8525:
8521:
8472:
8439:
8382:
8237:
8135:
8125:
8100:
8066:
7984:
7945:
7910:
7865:
7770:
7734:
7695:
7585:
7539:
7488:
7463:
7459:
7415:
7309:
7206:
6980:
identified Arrow's original interpretation of the theorem as a mathematical proof of
6847:
6793:
6654:
6271:
3048:
1774:
1520:
1205:
1110:
923:
834:
804:
726:
663:
497:
224:
199:
182:
50:
10170:
9352:
Campbell, D. E.; Kelly, J. S. (2000). "A simple characterization of majority rule".
9128:
Barberá, Salvador (January 1980). "Pivotal voters: A new proof of arrow's theorem".
8997:
8925:
8764:
8652:
8026:
head-to-head. Thus, Gore should still have won with Nader included in the election."
7879:
Campbell, D. E.; Kelly, J. S. (2000). "A simple characterization of majority rule".
7834:
Campbell, D. E.; Kelly, J. S. (2000). "A simple characterization of majority rule".
7520:"The Possibility of a Paretian Liberal: Impossibility Theorems and Cardinal Utility"
7379:
7255:
Contrary to a common misconception, Arrow's theorem deals with the limited class of
7019:
than rankings in measuring human opinions. Research has consistently found cardinal
6034:
for simplicity. We will show that the pivotal voter dictates society's decision for
1570:
fails this condition. Arrow later corrected his statement of the theorem to include
13110:
13085:
13080:
13014:
12978:
12958:
12918:
12888:
12843:
12798:
12783:
12740:
12594:
12235:
12172:
12158:
12123:
11948:
11913:
11888:
11840:
11765:
11740:
11735:
11637:
11612:
11282:
11159:
11138:
11118:
11004:
10924:
10881:
10839:
10792:
10757:
10718:
10681:
10663:
10608:
10565:
10523:
10486:
10437:
10354:
10315:
10283:
10250:
10150:
10071:
10044:, Routledge Frontiers of Political Economy, vol. 20, Routledge, pp. 21–45
10002:
9878:
9834:
9767:
9736:
9724:
9690:
9622:
9583:
9541:
9491:
9452:
9413:
9363:
9294:
9221:
9174:
9137:
9065:
8977:
8905:
8851:
8744:
8689:
8632:
8555:
8517:
8419:
8374:
8229:
8170:, Routledge Frontiers of Political Economy, vol. 20, Routledge, pp. 21–45
8058:
7976:
7937:
7890:
7845:
7822:
head-to-head. Thus, Gore should still have won with Nader included in the election.
7726:
7685:
7577:
7531:
7455:
7359:
7284:
7276:
7245:
assumes all voter preferences are known and the only issue is in aggregating them.
7234:
6997:
6962:
6950:
6927:"bad", or "neutral" simply because another candidate joins or drops out of a race.
6896:
6877:
6859:
6815:
As shown above, the proof of Arrow's theorem relies crucially on the assumption of
6792:
gave a full characterization of domain restrictions admitting a nondictatorial and
6704:
5780:
4172:
1758:
1449:
1171:
1136:
1116:
1051:
915:
872:
751:
465:
341:
167:
161:
143:
132:
127:
115:
76:
38:
11143:
9679:
Campbell, D.E.; Kelly, J.S. (2000). "A simple characterization of majority rule".
8408:
Campbell, D.E.; Kelly, J.S. (2000). "A simple characterization of majority rule".
8218:"Bayesian decision theory, rule utilitarianism, and Arrow's impossibility theorem"
7674:"The doctrinal paradox: comparison of decision rules in a probabilistic framework"
12983:
12943:
12898:
12813:
12808:
12529:
12481:
12368:
12133:
12103:
12073:
11856:
11835:
11830:
11790:
11632:
11622:
11459:
11454:
11444:
11409:
11287:
11270:
11150:
Hansen, Paul (2002). "Another Graphical Proof of Arrow's Impossibility Theorem".
11077:
11073:
9802:
9110:
8336:
8332:
7764:
7482:
7214:
7210:
7052:
6958:
6915:
6865:
6662:
6636:
6070:. In part three of the proof we will see that these turn out to be the same too.
5983:. In part three of the proof we will show that these do turn out to be the same.
5803:
from the bottom to the top of voters' ballots. The voter whose change results in
2270:
2197:
1583:
1445:
1249:
1179:
1132:
1106:
981:
903:
736:
591:
556:
477:
388:
291:
214:
156:
34:
12848:
10569:
8559:
6355:
must appear earlier (or at the same position) in the line than the dictator for
12923:
12913:
12903:
12838:
12828:
12818:
12803:
12599:
12579:
12564:
12559:
12519:
12486:
12471:
12466:
12456:
12265:
11795:
11770:
11760:
11755:
11685:
11485:
11374:
11064:
Campbell, D. E. (2002). "Impossibility theorems in the Arrovian framework". In
9839:
9822:
9587:
9209:
8505:
7690:
7673:
7443:
7304:
7148:
6689:
6641:
2294:
1731:
1441:
1195:
1128:
1098:
1087:
1079:
773:
713:
698:
509:
378:
353:
204:
11163:
10358:
9626:
9545:
9178:
8981:
8547:
8217:
8122:
Gaming the vote : why elections aren't fair (and what we can do about it)
7980:
7941:
6712:
also suggest such paradoxes are likely to be infrequent or even non-existent.
5790:
13122:
12963:
12953:
12908:
12893:
12873:
12644:
12619:
12491:
12461:
12451:
12438:
12343:
12285:
12220:
12153:
11775:
11642:
11490:
11065:
11016:
10893:
10851:
10804:
10769:
10677:
10620:
10596:
10577:
10535:
10449:
10366:
10129:
10014:
10006:
9848:
9779:
9634:
9595:
9571:
9553:
9503:
9464:
9425:
9347:
9233:
9149:
8884:
8863:
8723:
8701:
8611:
8529:
8386:
8340:
8241:
8139:
8070:
7988:
7949:
7738:
7699:
7589:
7543:
7467:
7338:
7256:
7218:
7217:; however, Kirman and Sondermann demonstrated this requires disenfranchising
7088:
7064:
7060:
7044:
7028:
7008:
6954:
6930:
6869:
6820:
6816:
6620:
2844:
2201:
1778:
1571:
1463:
1233:
1167:
1162:
1140:
1083:
1055:
977:
973:
782:
482:
270:
108:
71:
46:
11314:
A proof by Terence Tao, assuming a much stronger version of non-dictatorship
10761:
10668:
10527:
10306:
Vickrey, William (1945). "Measuring Marginal Utility by Reactions to Risk".
9529:
9114:
8678:"Single Transferrable Vote: An Example of a Perverse Social Choice Function"
7964:
1466:
satisfies Arrow's axioms by "giving up" whenever there is a Condorcet cycle.
12938:
12933:
12788:
12363:
11572:
11545:
11540:
11313:
11179:
11095:
10695:
10597:"A Comparison of the Scale of Values Method with the Order-of-Merit Method"
9651:
8145:
elegantly. Range voting solves the problems of spoilers and vote splitting
8092:
7195:
7048:
7024:
7020:
7001:
6923:
6824:
6789:
6727:
6624:
1924:
is chosen as the winner, it can be argued any fair voting system would say
1237:
1175:
1158:
522:
286:
279:
209:
11122:
9694:
9610:
9367:
9069:
8423:
7925:
7894:
7849:
7225:
0), leading them to refer to such societies as "invisible dictatorships".
1459:
choice, and cannot simply "give up" when the voters have unusual opinions.
58:
13055:
12858:
12853:
12833:
12629:
12614:
12423:
12393:
12328:
12318:
12148:
12083:
12059:
11750:
11224:
11183:
11069:
10075:
9929:
Gaming the Vote: Why Elections Are not Fair (and What We Can Do About It)
9328:
Frisch Lecture Delivered to the World Congress of the Econometric Society
9282:
8822:
Frisch Lecture Delivered to the World Congress of the Econometric Society
7056:
6919:
6908:
6881:
6873:
6688:
Unfortunately, as Condorcet proved, this rule can be self-contradictory (
4168:
1280:
400:
358:
301:
246:
12027:
11130:
10796:
10490:
10089:
Arrow, Kenneth Joseph Arrow (1963). "III. The Social Welfare Function".
9702:
9375:
9186:
8989:
8431:
7902:
7857:
6768:. In most realistic situations, where voters' opinions follow a roughly-
6191:
from part one. Furthermore, by unanimity the societal outcome must rank
898:
12684:
12338:
11024:
10992:
10901:
10869:
10475:. Lecture Notes in Computer Science. Vol. 4149. pp. 317–331.
10457:
10425:
10327:
10262:
10162:
9787:
9511:
9479:
9456:
8917:
8756:
8709:
8677:
8644:
8394:
8362:
8233:
8078:
8046:
7746:
7714:
7371:
6785:
1148:
9755:
8787:"From social choice functions to dictatorial social welfare functions"
8590:"From social choice functions to dictatorial social welfare functions"
7597:
6054:, then that is the societal outcome. Note again that the dictator for
1248:
framework. Ideally, such a procedure should satisfy the properties of
1220:
to make optimal decisions. The goal of social choice is to identify a
1082:. In this context, Arrow's theorem can be restated as showing that no
12589:
12509:
12333:
10612:
10193:"Podcast 2012-10-06: Interview with Nobel Laureate Dr. Kenneth Arrow"
9440:
8302:"Podcast 2012-10-06: Interview with Nobel Laureate Dr. Kenneth Arrow"
8270:"Podcast 2012-10-06: Interview with Nobel Laureate Dr. Kenneth Arrow"
8183:"Podcast 2012-10-06: Interview with Nobel Laureate Dr. Kenneth Arrow"
6734:. The theorem proves that if voters and candidates are arranged on a
6250:, as in the previous case. In particular, the societal outcome ranks
5915:
at the top of the ballot for voter 1, but not for any of the others.
2188:
1554:
Arrow's original statement of the theorem included the assumption of
368:
363:
11318:
11008:
10885:
10828:"From social welfare ordering to acyclic aggregation of preferences"
10441:
10319:
10053:
10051:
9771:
9495:
8693:
8378:
7730:
6884:
gives as an example that it would be impossible to know whether the
6042:. That is, we show that no matter how the rest of society votes, if
4160:
contains only one voter, who controls the outcome—in other words, a
13024:
12524:
11271:"Computer-aided Proofs of Arrow's and Other Impossibility Theorems"
10722:
10254:
10154:
8909:
8748:
8636:
8062:
8012:
7807:
7581:
7535:
7363:
6981:
6900:
6375:
to the top of voters' ballots, the pivot point where society ranks
6014:
Part two: The pivotal voter for B over A is a dictator for B over C
1241:
619:
9058:
Sen, Amartya (2014-07-22). "Arrow and the Impossibility Theorem".
12745:
12735:
12413:
11350:
11082:. Vol. 1. Amsterdam, Netherlands: Elsevier. pp. 35–94.
10958:
for a concise discussion of social choice for infinite societies.
10048:
6630:
6278:
is positioned on the ballots, so pivotal voter is a dictator for
2917:
which aggregates voters' preferences into a single preference on
405:
11252:
Theory and Decision : Essays in Honor of Werner Leinfellner
7766:
Mathematics of Social Choice: Voting, Compensation, and Division
7484:
Mathematics of Social Choice: Voting, Compensation, and Division
6996:, which identifies ranked procedures with approximations of the
6864:
Arrow's framework assumed individual and social preferences are
1275:
In the context of Arrow's theorem, citizens are assumed to have
9478:
McGann, Anthony J.; Koetzle, William; Grofman, Bernard (2002).
7713:
McGann, Anthony J.; Koetzle, William; Grofman, Bernard (2002).
7270:
6985:
6973:
6904:
1245:
910:
10644:"The scientific value of numerical measures of human feelings"
9754:
Davis, Otto A.; DeGroot, Morris H.; Hinich, Melvin J. (1972).
6933:
noted Arrow's theorem could be considered a weaker version of
1744:
IIA is sometimes illustrated with a short joke by philosopher
1127:
are highly sensitive to spoilers, and can manufacture them in
1030:
should not depend on the quality of a third, unrelated option
12514:
11206:
Why flip a coin? : The art and science of good decisions
9163:
Yu, Ning Neil (2012). "A one-shot proof of Arrow's theorem".
6922:
disputed that any interpersonal comparisons are required for
6756:. However, a well-defined Condorcet winner does exist if the
2958:
1649:
In other words, the social preference should not change from
10042:
The Active Consumer: Novelty and Surprise in Consumer Choice
8168:
The Active Consumer: Novelty and Surprise in Consumer Choice
8113:
7566:"A Note on "Social Welfare Functions" and Cardinal Utility*"
11414:
6889:
6611:
Arrow's theorem establishes that no ranked voting rule can
1500:
choices as those depending on more than one person's input.
10397:
Arrow and the Foundations of the Theory of Economic Policy
7549:
social choice, the paradox of social choice can be solved.
6895:
Arrow originally agreed with these positions and rejected
6199:. Therefore, we know the outcome in this case completely.
1155:), spoiler effects can disappear entirely for such rules.
11040:"Remembering Kenneth Arrow and His Impossibility Theorem"
9099:(2nd ed.). Princeton University Press. Problem 9.5.
9096:
Lecture Notes in Microeconomic Theory: The Economic Agent
6853:
6810:
6606:
5923:
at the top for voters 1 and 2, but no others, and so on.
1634:
should only depend on the individual preferences between
1480:— the system does not depend on only one voter's ballot.
10541:
ranking, it supplies more information than ranking does.
9570:
Wolk, Sara; Quinn, Jameson; Ogren, Marcus (2023-09-01).
6842:
While Arrow's theorem does not apply to graded systems,
11096:#Alternatives based on functions of preference profiles
9804:
Multidimensional voting models: theory and applications
9321:"Individual and social welfare: a Bayesian perspective"
8815:"Individual and social welfare: a Bayesian perspective"
8349:
And as I said, that in effect implies more information.
6745:
More formally, Black's theorem assumes preferences are
6653:
The first set of methods studied by economists are the
3283:
whose preferences always prevail. That is, there is no
11104:"A pedagogical proof of Arrow's Impossibility Theorem"
10980:. Metaphysics Research Lab, Stanford University. 2019.
10968:
10966:
10964:
9402:"Independence of irrelevant alternatives before Arrow"
8840:"Independence of irrelevant alternatives before Arrow"
7661:. Metaphysics Research Lab, Stanford University. 2019.
7649:
7647:
6645:
An example of a Condorcet cycle, where some candidate
6289:
5883:
to everything else, then society would have to prefer
1944:
should win instead, since two voters (1 and 2) prefer
1730:
This is equivalent to the claim about independence of
1151:. Under some idealized models of voter behavior (e.g.
10744:
Ohtsubo, Yohsuke; Watanabe, Yoriko (September 2003).
10642:
Kaiser, Caspar; Oswald, Andrew J. (18 October 2022).
10595:
Conklin, E. S.; Sutherland, J. W. (1 February 1923).
10555:
8951:"Three Brief Proofs of Arrow's Impossibility Theorem"
8124:. Farrar, Straus and Giroux. pp. 168, 197, 234.
7209:
shows all of Arrow's conditions can be satisfied for
7164:
7125:
7097:
6363:: As we consider the argument of part one applied to
6242:. Furthermore, by IIA the societal outcome must rank
6113:. To begin, suppose that the ballots are as follows:
5711:
5684:
5658:
5626:
5599:
5573:
5544:
5518:
5492:
5472:
5437:
5256:
5222:
5179:
5156:
5136:
5122:, then it has a proper subset that is also decisive.
5105:
5074:
5054:
5016:
4996:
4961:
4941:
4919:
4893:
4867:
4835:
4809:
4786:
4766:
4733:
4713:
4667:
4641:
4621:
4601:
4581:
4561:
4526:
4506:
4477:
4457:
4423:
4391:
4371:
4331:
4298:
4278:
4241:
4221:
4189:
4152:
if and only if it is decisive over all ordered pairs.
4125:
4092:
4059:
3963:
3908:
3886:
3864:
3837:
3810:
3788:
3766:
3746:
3694:
3642:
3566:
3544:
3522:
3495:
3473:
3451:
3429:
3407:
3333:
3289:
3269:
3193:
3171:
3149:
3103:
3081:
3059:
2966:
2943:
2923:
2861:
2829:
2800:
2780:
2750:
2720:
2698:
2676:
2656:
2620:
2596:
2560:
2524:
2501:
2465:
2445:
2409:
2389:
2353:
2323:
2303:
2279:
2248:
2218:
2170:
2150:
2130:
2110:
2090:
2070:
2050:
2030:
2010:
1990:
1970:
1950:
1930:
1910:
1841:) and three voters whose preferences are as follows:
1827:
1807:
1787:
1777:
is already enough to see the impossibility of a fair
1707:
1681:
1655:
1395:
1369:
1343:
1301:
1064:
1036:
1016:
996:
10470:
9477:
8119:
7712:
7266:
7221:
members of a society (eligible voters form a set of
3394:{\displaystyle (R_{1},\ldots ,R_{N})\in \Pi (A)^{N}}
3027:{\displaystyle (R_{1},\ldots ,R_{N})\in \Pi (A)^{N}}
10961:
9903:
Majority judgment: measuring, ranking, and electing
9807:(Doctoral thesis). UCL (University College London).
9530:"On the empirical relevance of Condorcet's paradox"
9210:"Social choice theory without the Pareto Principle"
8506:"Social choice theory without the Pareto Principle"
7965:"On the empirical relevance of Condorcet's paradox"
7644:
7570:
Canadian Journal of Economics and Political Science
7444:"Social choice theory without the Pareto Principle"
6234:from part one and hence the societal outcome ranks
5986:Also note that by IIA the same argument applies if
5828:Say there are three choices for society, call them
4175:. The simplified proof uses an additional concept:
4167:The following proof is a simplification taken from
2907:{\displaystyle \mathrm {F} :\Pi (A)^{N}\to \Pi (A)}
11248:"What Does Arrow's Impossibility Theorem Tell Us?"
10993:"Manipulation of Voting Schemes: A General Result"
10296:. Princeton, NJ. Princeton University Press, 1953.
10082:
9753:
8363:"Manipulation of Voting Schemes: A General Result"
7186:
7139:
7111:
6407:must be at or later in line than the dictator for
5729:
5697:
5670:
5644:
5612:
5585:
5556:
5530:
5504:
5478:
5455:
5421:
5240:
5205:
5165:
5142:
5114:
5080:
5060:
5040:
5002:
4979:
4947:
4925:
4905:
4879:
4853:
4821:
4792:
4772:
4752:
4719:
4699:
4653:
4627:
4607:
4587:
4567:
4544:
4512:
4489:
4463:
4435:
4409:
4377:
4343:
4317:
4284:
4260:
4227:
4207:
4137:
4111:
4077:
4004:
3949:
3894:
3872:
3850:
3823:
3796:
3774:
3752:
3732:
3680:
3620:
3552:
3530:
3508:
3481:
3459:
3437:
3415:
3393:
3319:
3275:
3247:
3179:
3157:
3135:
3089:
3067:
3026:
2949:
2929:
2906:
2835:
2815:
2786:
2766:
2736:
2706:
2684:
2662:
2642:
2602:
2582:
2546:
2507:
2487:
2451:
2431:
2395:
2375:
2335:
2309:
2285:
2254:
2224:
2176:
2156:
2136:
2116:
2096:
2076:
2056:
2036:
2016:
1996:
1976:
1956:
1936:
1916:
1833:
1813:
1793:
1719:
1693:
1667:
1407:
1381:
1355:
1313:
1070:
1042:
1022:
1002:
10945:Social choice and the mathematics of manipulation
10594:
10343:"The impartial observer theorem of social ethics"
10227:Report of the NOAA panel on Contingent Valuation.
7156:spatial (n-dimensional ideology) models of voting
6775:
6383:must come at or before we reach the dictator for
6183:. This is because, except for a repositioning of
5791:Part one: There is a "pivotal" voter for B over A
13120:
9821:Holliday, Wesley H.; Pacuit, Eric (2023-09-01).
8457:
8455:
8453:
8451:
8449:
8002:Holliday, Wesley H.; Pacuit, Eric (2023-02-11),
7797:Holliday, Wesley H.; Pacuit, Eric (2023-02-11),
7563:
6326:of segment two. Likewise, the pivotal voter for
6274:IIA, this conclusion holds independently of how
5173:. Partition the coalition into nonempty subsets
1701:if voters change their preference about whether
1101:, and shows similar problems will exist for any
10776:
10743:
10648:Proceedings of the National Academy of Sciences
10134:"A Difficulty in the Concept of Social Welfare"
9756:"Social Preference Orderings and Majority Rule"
9016:
9014:
8889:"A Difficulty in the Concept of Social Welfare"
8728:"A Difficulty in the Concept of Social Welfare"
8616:"A Difficulty in the Concept of Social Welfare"
7400:
7398:
7396:
7343:"A Difficulty in the Concept of Social Welfare"
6018:In this part of the argument we refer to voter
5903:to the top of the ballots for voters 1 through
1295:are different candidates or alternatives, then
10908:
10867:
10782:
10708:
10637:
10635:
10633:
10379:: CS1 maint: DOI inactive as of August 2024 (
10211:information than simply what I have asked for.
9900:
9820:
9569:
8331:But the system that you're just referring to,
8201:information than simply what I have asked for.
8001:
7796:
6631:Minimizing IIA failures: Majority-rule methods
6422:denotes the position of the pivotal voter for
6258:, even though Pivotal Voter may have been the
5952:whose ballot change causes this to happen the
5860:. By unanimity, society must also prefer both
2737:{\displaystyle \mathbf {a} \succ \mathbf {b} }
1147:by restricting them to rare situations called
12043:
11334:
10426:"Alternative Conditions for Social Orderings"
9678:
9351:
9064:. Columbia University Press. pp. 29–42.
8446:
8407:
7878:
7833:
7790:
7756:
7564:Kemp, Murray; Asimakopulos, A. (1952-05-01).
6463:Now repeating the entire argument above with
5840:. Suppose first that everyone prefers option
2187:Because of this example, some authors credit
1736:standard construction of a placement function
1592:(IIA), which says that when deciding between
1518:This is typically replaced with the stronger
1493:) to allow rules that treat voters unequally.
946:
10641:
9011:
8675:
7995:
7672:Alabert, Aureli; Farré, Mercè (2022-05-01).
7671:
7393:
5035:
5017:
3621:{\displaystyle F(R_{1},R_{2},\ldots ,R_{N})}
3314:
3296:
3248:{\displaystyle F(R_{1},R_{2},\ldots ,R_{N})}
1562:the rank of an outcome should not make them
1455:In other words, the system must always make
10630:
9861:
8948:
8047:"On the Rationale of Group Decision-making"
6093:In the following, we call voters 1 through
2643:{\displaystyle (\mathbf {a} ,\mathbf {b} )}
2583:{\displaystyle (\mathbf {b} ,\mathbf {a} )}
2547:{\displaystyle (\mathbf {a} ,\mathbf {b} )}
2488:{\displaystyle (\mathbf {a} ,\mathbf {c} )}
2432:{\displaystyle (\mathbf {b} ,\mathbf {c} )}
2376:{\displaystyle (\mathbf {a} ,\mathbf {b} )}
1427:Arrow's theorem assumes as background that
1259:
27:Proof all ranked voting rules have spoilers
12050:
12036:
12002:
11341:
11327:
11250:. In Eberlein, G.; Berghel, H. A. (eds.).
10039:
9925:
9527:
9092:
8545:
8165:
7962:
7474:
6803:(though at a much lower rate than seen in
5998:by every voter, and the pivotal voter for
1622:— the social preference between candidate
1524:: if voters unanimously support candidate
1204:Arrow's theorem falls under the branch of
953:
939:
12057:
11286:
11101:
11063:
10685:
10667:
10480:
10098:. Yale University Press. pp. 31–33.
9838:
9276:
9274:
8971:
8011:
7806:
7689:
7503:do away with the spoiler problem entirely
7259:, rather than voting systems as a whole.
5879:On the other hand, if everyone preferred
5099:If a coalition is decisive, and has size
4086:if, when everyone in the coalition ranks
2767:{\displaystyle \mathbf {a} R\mathbf {b} }
11094:Surveys many of approaches discussed in
10947:. New York: Cambridge University Press.
10914:
10868:Caplin, Andrew; Nalebuff, Barry (1988).
10423:
10240:
9952:
9723:
9608:
9438:
8676:Doron, Gideon; Kronick, Richard (1977).
8215:
8211:
8209:
7923:
7228:
6726:Soon after Arrow published his theorem,
6640:
6293:
6072:
5948:in the societal rank. We call the voter
5794:
2670:is interpreted to mean that alternative
1145:minimize the number of spoiled elections
13109:in social choice, ranked rules include
11269:Tang, Pingzhong; Lin, Fangzhen (2009).
11268:
10990:
10978:The Stanford Encyclopedia of Philosophy
10551:
10549:
10305:
10124:
10122:
9896:
9894:
9892:
9314:
9312:
9310:
9308:
9280:
9127:
8944:
8942:
8784:
8587:
8499:
8497:
8495:
8360:
7956:
7917:
7762:
7659:The Stanford Encyclopedia of Philosophy
7559:
7557:
7480:
7201:
7035:
7004:), helping to make them more explicit.
6833:independence of irrelevant alternatives
6545:, there exists some preference profile
5737:. Now apply the field expansion lemma.
4700:{\displaystyle x\succ _{i}y\succ _{i}z}
3632:Independence of irrelevant alternatives
2774:. Denote the set of all preferences on
1617:Independence of irrelevant alternatives
1589:independence of irrelevant alternatives
1415:. The social choice function is then a
1109:. It can be generalized in turn by the
987:independence of irrelevant alternatives
984:. Specifically, any such rule violates
14:
13121:
11149:
11037:
10942:
10825:
10393:
10340:
10236:
10234:
10190:
10026:
10024:
9988:
9984:
9982:
9901:Balinski, M. L.; Laraki, Rida (2010).
9816:
9814:
9794:
9656:The theory of committees and elections
9646:
9644:
9565:
9563:
9399:
9395:
9393:
9341:
9339:
9337:
9271:
9246:
9207:
8837:
8833:
8831:
8808:
8806:
8804:
8671:
8669:
8541:
8539:
8503:
8299:
8267:
8180:
8097:The theory of committees and elections
7619:
7513:
7511:
7441:
7333:
7331:
7329:
7158:, this can be relaxed to require only
7083:
7047:involves violations of IIA (e.g. with
6854:Meaningfulness of cardinal information
6811:Eliminating IIA failures: Rated voting
6730:showed his own remarkable result, the
6715:
6607:Interpretation and practical solutions
6010:. We will use this observation below.
5068:is decisive over all ordered pairs in
5010:is decisive over all ordered pairs in
4829:. By coalition weak-decisiveness over
4005:{\displaystyle F(S_{1},\ldots ,S_{N})}
3950:{\displaystyle F(R_{1},\ldots ,R_{N})}
990:(IIA), the idea that a choice between
12031:
11348:
11322:
11245:
11203:
11079:Handbook of social choice and welfare
10863:
10861:
10516:European Journal of Social Psychology
10513:
10293:Theory of Games and Economic Behavior
10221:
10219:
10128:
10088:
9800:
9658:. Cambridge, Eng.: University Press.
9650:
9602:
9521:
9484:American Journal of Political Science
9350:will adhere to Arrow's criteria. See
9020:
8883:
8879:
8877:
8875:
8873:
8722:
8682:American Journal of Political Science
8610:
8461:
8206:
8099:. Cambridge, Eng.: University Press.
8091:
8044:
8040:
8038:
8036:
8034:
8032:
7872:
7719:American Journal of Political Science
7706:
7404:
7337:
7075:
6226:. Then aside from a repositioning of
6202:Now suppose that pivotal voter moves
6062:is not a priori the same as that for
3733:{\displaystyle (S_{1},\ldots ,S_{N})}
3681:{\displaystyle (R_{1},\ldots ,R_{N})}
1769:
1604:, one's opinion about a third option
1125:ranked-choice (instant-runoff) voting
11229:Collective choice and social welfare
11178:
10737:
10546:
10464:
10277:
10119:
9955:"What economists think about voting"
9889:
9672:
9305:
9240:
9021:Arrow, Kenneth Joseph Arrow (1963).
8939:
8604:
8492:
8462:Arrow, Kenneth Joseph Arrow (1963).
8401:
8150:
8085:
7613:
7554:
7435:
7405:Arrow, Kenneth Joseph Arrow (1963).
5975:, the same as the pivotal voter for
5048:. Then iterating that, we find that
3320:{\displaystyle i\in \{1,\ldots ,N\}}
1431:ranked social choice rules satisfy:
1422:
1254:avoid any kind of self-contradiction
1103:collective decision-making procedure
1050:. The result is most often cited in
11308:Stanford Encyclopedia of Philosophy
11303:"Arrow's impossibility theorem"
11223:
10558:Basic and Applied Social Psychology
10231:
10092:Social Choice and Individual Values
10057:
10021:
9979:
9862:Kalai, Ehud; Muller, Eitan (1977).
9811:
9641:
9609:Gehrlein, William V. (2002-03-01).
9560:
9471:
9439:Gehrlein, William V. (1983-06-01).
9390:
9334:
9057:
9024:Social Choice and Individual Values
8828:
8801:
8716:
8666:
8552:Social Choice and Democratic Values
8536:
8465:Social Choice and Individual Values
7924:Gehrlein, William V. (2002-03-01).
7508:
7408:Social Choice and Individual Values
7326:
6740:Condorcet's majority-rule principle
6695:Unlike pluralitarian rules such as
6391:. Likewise, reversing the roles of
6290:Part three: There exists a dictator
6222:, without changing the position of
4119:, society overall will always rank
3136:{\displaystyle R_{1},\ldots ,R_{N}}
3034:of voters' preferences is called a
2207:
1582:Among the most important axioms of
24:
12099:First-player and second-player win
11659:What the Tortoise Said to Achilles
11057:
10858:
10601:Journal of Experimental Psychology
10216:
10060:"The Possibility of Social Choice"
9926:Poundstone, William (2009-02-17).
9318:
9201:
9162:
8870:
8812:
8288:support to these scoring methods.
8029:
7517:
7233:Arrow's theorem is not related to
7119:majority for ordering 3 outcomes,
6846:still does: no voting game can be
6525:
6342:. That is, outside of Segment One.
5963:. Note that the pivotal voter for
4033:Arrow's proof used the concept of
3372:
3005:
2892:
2870:
2863:
2801:
2714:. This situation is often denoted
1610:should not affect their decision.
1440:— the social choice function is a
1182:) are not subject to his theorem.
1153:Duncan Black's left-right spectrum
57:
25:
13170:
11296:
11152:The Journal of Economic Education
10341:Mongin, Philippe (October 2001).
9528:Van Deemen, Adrian (2014-03-01).
7963:Van Deemen, Adrian (2014-03-01).
7763:Borgers, Christoph (2010-01-01).
7481:Borgers, Christoph (2010-01-01).
6155:Every voter in segment two ranks
6117:Every voter in segment one ranks
2024:. However, by the same argument
1574:and other perverse voting rules.
1137:majority-rule (Condorcet) methods
13149:Theorems in discrete mathematics
12206:Coalition-proof Nash equilibrium
12012:
12011:
12001:
10473:Cooperative Information Agents X
10115:from the original on 2022-10-09.
9827:Constitutional Political Economy
9576:Constitutional Political Economy
9208:Wilson, Robert (December 1972).
9047:from the original on 2022-10-09.
9007:from the original on 2022-10-09.
8504:Wilson, Robert (December 1972).
8488:from the original on 2022-10-09.
8216:Harsanyi, John C. (1979-09-01).
7442:Wilson, Robert (December 1972).
7431:from the original on 2022-10-09.
7269:
6754:McKelvey-Schofield Chaos Theorem
5787:given in the original articles.
5761:Proofs using the concept of the
4661:. So change the votes such that
4615:. By IIA, changing the votes on
4215:if and only if when every voter
3888:
3866:
3790:
3768:
3546:
3524:
3475:
3453:
3431:
3409:
3173:
3151:
3083:
3061:
2760:
2752:
2730:
2722:
2700:
2678:
2633:
2625:
2573:
2565:
2537:
2529:
2478:
2470:
2422:
2414:
2366:
2358:
1444:over the domain of all possible
922:
909:
897:
845:McKelvey–Schofield chaos theorem
491:Semi-proportional representation
123:First preference plurality (FPP)
11031:
10984:
10935:
10819:
10702:
10588:
10507:
10417:
10387:
10334:
10299:
10197:The Center for Election Science
10184:
9961:. Chicago Booth. Archived from
9946:
9919:
9855:
9747:
9717:
9432:
9281:McKenna, Phil (12 April 2008).
9156:
9121:
9086:
9061:The Arrow Impossibility Theorem
9051:
8778:
8581:
8354:
8306:The Center for Election Science
8293:
8274:The Center for Election Science
8261:
8187:The Center for Election Science
8174:
7827:
7665:
7315:Comparison of electoral systems
6939:utility representation theorems
4016:
2518:(Completeness) At least one of
1984:and only one voter (3) prefers
1212:, which deals with aggregating
1144:
13103:
12216:Evolutionarily stable strategy
11254:. Springer. pp. 273–286.
11188:. Cambridge University Press.
9905:. Cambridge, Mass: MIT Press.
8335:, falls within a class called
8256:in Arrow's original framework.
6776:Generalized stability theorems
6187:, this profile is the same as
5724:
5712:
5639:
5627:
4974:
4962:
4848:
4836:
4539:
4527:
4404:
4392:
4202:
4190:
4156:Our goal is to prove that the
4072:
4060:
4053:decisive over an ordered pair
3999:
3967:
3944:
3912:
3740:such that for all individuals
3727:
3695:
3675:
3643:
3615:
3570:
3382:
3375:
3366:
3334:
3242:
3197:
3015:
3008:
2999:
2967:
2901:
2895:
2889:
2880:
2873:
2810:
2804:
2637:
2621:
2577:
2561:
2541:
2525:
2482:
2466:
2426:
2410:
2370:
2354:
1577:
1264:
883:Harsanyi's utilitarian theorem
840:Moulin's impossibility theorem
805:Conflicting majorities paradox
13:
1:
12144:Simultaneous action selection
11102:Dardanoni, Valentino (2001).
11042:. Center for Election Science
10785:Journal of Marketing Research
9989:Lützen, Jesper (2019-02-01).
9953:Cockrell, Jeff (2016-03-08).
9299:10.1016/S0262-4079(08)60914-8
9247:Hamlin, Aaron (25 May 2015).
8120:Poundstone, William. (2013).
7620:Hamlin, Aaron (25 May 2015).
7320:
7290:Gibbard–Satterthwaite theorem
7241:). The Arrovian framework of
7147:for 4, etc. does not produce
3042:Arrow's impossibility theorem
1185:
966:Arrow's impossibility theorem
709:Frustrated majorities paradox
13076:List of games in game theory
12256:Quantal response equilibrium
12246:Perfect Bayesian equilibrium
12181:Bayes correlated equilibrium
11288:10.1016/j.artint.2009.02.005
11231:. Amsterdam: North-Holland.
11038:Hamlin, Aaron (March 2017).
10929:10.1016/0022-0531(70)90015-3
10844:10.1016/0165-4896(85)90002-2
10832:Mathematical Social Sciences
10826:Moulin, Hervé (1985-02-01).
10711:Journal of Consumer Research
10394:Feiwel, George, ed. (1987).
10243:Journal of Political Economy
10225:Arrow, Kenneth et al. 1993.
10191:Hamlin, Aaron (2012-10-06).
10142:Journal of Political Economy
9883:10.1016/0022-0531(77)90019-9
9741:10.1016/0022-0531(76)90040-5
9418:10.1016/0165-4896(95)00784-J
9406:Mathematical Social Sciences
9226:10.1016/0022-0531(72)90051-8
9142:10.1016/0165-1765(80)90050-6
8897:Journal of Political Economy
8856:10.1016/0165-4896(95)00784-J
8844:Mathematical Social Sciences
8736:Journal of Political Economy
8624:Journal of Political Economy
8522:10.1016/0022-0531(72)90051-8
8300:Hamlin, Aaron (2012-10-06).
8268:Hamlin, Aaron (2012-10-06).
8181:Hamlin, Aaron (2012-10-06).
8051:Journal of Political Economy
7524:Journal of Political Economy
7460:10.1016/0022-0531(72)90051-8
7351:Journal of Political Economy
7257:ranked-choice voting systems
6945:, which generally show that
6823:. As a result, systems like
6318:must appear among the first
5844:the least: everyone prefers
5799:Part one: Successively move
4753:{\displaystyle y\succ _{i}x}
4471:be an outcome distinct from
4318:{\displaystyle y\succ _{j}x}
4292:outside the coalition ranks
4261:{\displaystyle x\succ _{i}y}
4112:{\displaystyle x\succ _{i}y}
3895:{\displaystyle \mathbf {b} }
3873:{\displaystyle \mathbf {a} }
3797:{\displaystyle \mathbf {b} }
3775:{\displaystyle \mathbf {a} }
3636:For two preference profiles
3553:{\displaystyle \mathbf {b} }
3531:{\displaystyle \mathbf {a} }
3482:{\displaystyle \mathbf {b} }
3460:{\displaystyle \mathbf {a} }
3438:{\displaystyle \mathbf {b} }
3416:{\displaystyle \mathbf {a} }
3180:{\displaystyle \mathbf {b} }
3158:{\displaystyle \mathbf {a} }
3090:{\displaystyle \mathbf {b} }
3068:{\displaystyle \mathbf {a} }
2707:{\displaystyle \mathbf {b} }
2692:is preferred to alternative
2685:{\displaystyle \mathbf {a} }
878:Condorcet dominance theorems
818:Social and collective choice
7:
12545:Optional prisoner's dilemma
12276:Self-confirming equilibrium
11185:The Mathematics of Behavior
10570:10.1207/s15324834basp1802_4
10424:Hildreth, Clifford (1953).
9400:McLean, Iain (1995-10-01).
9253:Center for Election Science
9249:"CES Podcast with Dr Arrow"
8838:McLean, Iain (1995-10-01).
8560:10.1007/978-3-319-23261-4_4
7626:Center for Election Science
7622:"CES Podcast with Dr Arrow"
7518:Ng, Y. K. (November 1971).
7262:
6994:implicit utilitarian voting
6837:graduated majority judgment
6829:graduated majority judgment
6819:, and is not applicable to
6669:, i.e. if most voters rank
5512:. So at least one is true:
5206:{\displaystyle G_{1},G_{2}}
4026:Proof by decisive coalition
544:By mechanism of combination
315:Proportional representation
10:
13175:
13111:First-preference plurality
13010:Principal variation search
12726:Aumann's agreement theorem
12389:Strategy-stealing argument
12301:Trembling hand equilibrium
12231:Markov perfect equilibrium
12226:Mertens-stable equilibrium
10917:Journal of Economic Theory
10347:Economics & Philosophy
10032:identity of indiscernibles
9871:Journal of Economic Theory
9840:10.1007/s10602-022-09383-9
9729:Journal of Economic Theory
9588:10.1007/s10602-022-09389-3
9214:Journal of Economic Theory
9093:Rubinstein, Ariel (2012).
8949:Geanakoplos, John (2005).
8546:Lagerspetz, Eerik (2016),
8510:Journal of Economic Theory
8158:identity of indiscernibles
8021:by adding a new candidate
7817:by adding a new candidate
7691:10.1007/s00355-021-01372-5
7448:Journal of Economic Theory
6857:
6719:
6701:first-preference plurality
6697:ranked-choice runoff (RCV)
6634:
2843:be a positive integer. An
1764:
1568:ranked-choice runoff (RCV)
1408:{\displaystyle A\succeq C}
1382:{\displaystyle B\succeq C}
1356:{\displaystyle A\succeq B}
1268:
1189:
742:Multiple districts paradox
473:Fractional approval voting
461:Interactive representation
13154:Decision-making paradoxes
13046:Combinatorial game theory
13033:
12992:
12774:
12718:
12705:Princess and monster game
12500:
12402:
12309:
12261:Quasi-perfect equilibrium
12186:Bayesian Nash equilibrium
12167:
12066:
11997:
11849:
11678:
11478:
11357:
11204:Lewis, Harold W. (1997).
11164:10.1080/00220480209595188
11111:Social Choice and Welfare
10359:10.1017/S0266267101000219
9546:10.1007/s11127-013-0133-3
9179:10.1007/s00199-012-0693-3
9030:. Yale University Press.
8982:10.1007/s00199-004-0556-7
8785:Quesada, Antonio (2002).
8588:Quesada, Antonio (2002).
8471:. Yale University Press.
7981:10.1007/s11127-013-0133-3
7678:Social Choice and Welfare
7414:. Yale University Press.
7211:uncountably infinite sets
6537:For any two alternatives
6334:must appear among voters
5150:be a coalition with size
5041:{\displaystyle \{x,y,z\}}
2336:{\displaystyle A\times A}
1462:Without this assumption,
1170:admitting rules based on
689:Paradoxes and pathologies
538:Mixed-member proportional
533:Mixed-member majoritarian
528:By results of combination
419:Approval-based committees
13061:Evolutionary game theory
12794:Antoine Augustin Cournot
12680:Guess 2/3 of the average
12477:Strictly determined game
12271:Satisfaction equilibrium
12089:Escalation of commitment
11246:Skala, Heinz J. (2012).
10943:Taylor, Alan D. (2005).
10400:. Springer. p. 92.
10064:American Economic Review
10007:10.1016/j.hm.2018.11.001
9801:Dotti, V. (2016-09-28).
7187:{\displaystyle 1-e^{-1}}
6430:(for any two candidates
6399:, the pivotal voter for
6310:, the pivotal voter for
6298:Part three: Since voter
6022:, the pivotal voter for
5990:is any profile in which
5705:is weakly decisive over
5671:{\displaystyle z\succ y}
5620:is weakly decisive over
5586:{\displaystyle x\succ z}
5557:{\displaystyle z\succ y}
5531:{\displaystyle x\succ z}
5505:{\displaystyle x\succ y}
4926:{\displaystyle \square }
4906:{\displaystyle x\succ z}
4880:{\displaystyle x\succ y}
4822:{\displaystyle y\succ z}
4385:is weakly decisive over
4344:{\displaystyle x\succ y}
4138:{\displaystyle x\succ y}
4044:A subset of voters is a
2164:which is preferred over
2144:which is preferred over
1720:{\displaystyle A\succ C}
1694:{\displaystyle B\succ A}
1668:{\displaystyle A\succ B}
1496:This assumption defines
1314:{\displaystyle A\succ B}
1260:Axioms of voting systems
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:
13066:Glossary of game theory
12665:Stackelberg competition
12291:Strong Nash equilibrium
11578:Paradoxes of set theory
11275:Artificial Intelligence
10991:Gibbard, Allan (1973).
10762:10.1111/0162-895X.00340
10669:10.1073/pnas.2210412119
10528:10.1002/ejsp.2420050313
10361:(inactive 2024-08-02).
9627:10.1023/A:1015551010381
9283:"Vote of no confidence"
8361:Gibbard, Allan (1973).
7942:10.1023/A:1015551010381
6766:uniquely-defined median
6667:majority rule principle
6471:switched, we also have
6085:on the ballot of voter
5852:, and everyone prefers
5094:Group contraction lemma
4443:, then it is decisive.
4436:{\displaystyle x\neq y}
4235:in the coalition ranks
3902:have the same order in
3804:have the same order in
3263:There is no individual
2850:social welfare function
2816:{\displaystyle \Pi (A)}
1281:orderings of candidates
1192:Social welfare function
795:Tyranny of the majority
572:Fusion (majority bonus)
389:Quota-remainder methods
13144:Paradoxes in economics
13091:Tragedy of the commons
13071:List of game theorists
13051:Confrontation analysis
12761:Sprague–Grundy theorem
12281:Sequential equilibrium
12201:Correlated equilibrium
10870:"On 64%-Majority Rule"
8045:Black, Duncan (1948).
7188:
7141:
7113:
7059:discuss techniques of
7043:have shown individual
6762:rotationally symmetric
6650:
6649:cause a spoiler effect
6438:), then we have shown
6371:, successively moving
6343:
6090:
5872:. Call this situation
5825:
5754:Proof by pivotal voter
5731:
5699:
5672:
5646:
5614:
5587:
5558:
5532:
5506:
5480:
5457:
5423:
5242:
5207:
5167:
5166:{\displaystyle \geq 2}
5144:
5116:
5115:{\displaystyle \geq 2}
5082:
5062:
5042:
5004:
4981:
4949:
4927:
4907:
4881:
4855:
4823:
4794:
4774:
4754:
4721:
4701:
4655:
4629:
4609:
4589:
4569:
4546:
4514:
4491:
4465:
4437:
4411:
4379:
4345:
4319:
4286:
4262:
4229:
4209:
4139:
4113:
4079:
4006:
3951:
3896:
3874:
3852:
3825:
3798:
3776:
3754:
3734:
3682:
3622:
3554:
3532:
3510:
3483:
3461:
3439:
3417:
3395:
3321:
3277:
3249:
3181:
3159:
3137:
3091:
3069:
3028:
2951:
2931:
2908:
2837:
2817:
2788:
2768:
2738:
2708:
2686:
2664:
2644:
2604:
2584:
2548:
2509:
2489:
2453:
2433:
2397:
2377:
2337:
2311:
2287:
2256:
2226:
2178:
2158:
2138:
2118:
2098:
2078:
2058:
2038:
2018:
1998:
1978:
1958:
1938:
1918:
1835:
1815:
1795:
1721:
1695:
1669:
1542:should beat candidate
1409:
1383:
1357:
1315:
1271:Preference (economics)
1072:
1044:
1024:
1004:
929:Mathematics portal
835:Majority impossibility
824:Impossibility theorems
620:Negative vote transfer
441:Method of equal shares
62:
12864:Jean-François Mertens
11123:10.1007/s003550000062
10058:Sen, Amartya (1999).
9695:10.1007/s001990050318
9441:"Condorcet's paradox"
9368:10.1007/s001990050318
9255:. CES. Archived from
9070:10.7312/mask15328-003
8424:10.1007/s001990050318
7895:10.1007/s001990050318
7850:10.1007/s001990050318
7628:. CES. Archived from
7229:Common misconceptions
7189:
7142:
7114:
7041:Behavioral economists
6805:instant-runoff voting
6710:Spatial voting models
6644:
6623:to focus on studying
6297:
6076:
5798:
5732:
5730:{\displaystyle (z,y)}
5700:
5698:{\displaystyle G_{2}}
5673:
5647:
5645:{\displaystyle (x,z)}
5615:
5613:{\displaystyle G_{1}}
5588:
5559:
5533:
5507:
5486:is decisive, we have
5481:
5458:
5456:{\displaystyle x,y,z}
5424:
5243:
5241:{\displaystyle x,y,z}
5208:
5168:
5145:
5117:
5083:
5063:
5043:
5005:
4982:
4980:{\displaystyle (z,y)}
4950:
4928:
4908:
4882:
4856:
4854:{\displaystyle (x,y)}
4824:
4795:
4775:
4755:
4722:
4702:
4656:
4630:
4610:
4590:
4570:
4547:
4545:{\displaystyle (x,z)}
4515:
4492:
4466:
4438:
4412:
4410:{\displaystyle (x,y)}
4380:
4360:Field expansion lemma
4346:
4320:
4287:
4263:
4230:
4210:
4208:{\displaystyle (x,y)}
4140:
4114:
4080:
4078:{\displaystyle (x,y)}
4007:
3952:
3897:
3875:
3853:
3851:{\displaystyle S_{i}}
3826:
3824:{\displaystyle R_{i}}
3799:
3777:
3755:
3735:
3683:
3623:
3555:
3533:
3511:
3509:{\displaystyle R_{i}}
3484:
3462:
3440:
3418:
3396:
3322:
3278:
3250:
3182:
3160:
3138:
3092:
3070:
3029:
2952:
2932:
2909:
2838:
2818:
2789:
2769:
2739:
2709:
2687:
2665:
2645:
2605:
2585:
2549:
2510:
2490:
2454:
2434:
2398:
2378:
2338:
2312:
2297:), that is, a subset
2288:
2257:
2227:
2179:
2159:
2139:
2119:
2099:
2079:
2059:
2039:
2019:
1999:
1979:
1959:
1939:
1919:
1836:
1816:
1796:
1722:
1696:
1670:
1446:orderings of outcomes
1417:mathematical function
1410:
1384:
1358:
1316:
1269:Further information:
1226:mathematical function
1073:
1045:
1025:
1005:
732:Best-is-worst paradox
721:Pathological response
456:Direct representation
109:Single-winner methods
61:
13159:Social choice theory
12993:Search optimizations
12869:Jennifer Tour Chayes
12756:Revelation principle
12751:Purification theorem
12690:Nash bargaining game
12655:Bertrand competition
12640:El Farol Bar problem
12605:Electronic mail game
12570:Lewis signaling game
12114:Hierarchy of beliefs
11944:Kavka's toxin puzzle
11716:Income and fertility
10750:Political Psychology
10076:10.1257/aer.89.3.349
9995:Historia Mathematica
9725:McKelvey, Richard D.
7213:of voters given the
7202:Infinite populations
7162:
7123:
7095:
7070:contingent valuation
7036:Nonstandard spoilers
6949:requires consistent
6821:rated voting systems
6732:median voter theorem
6722:Median voter theorem
6302:is the dictator for
6230:this is the same as
6136:Pivotal voter ranks
6077:Part two: Switching
6006:will still be voter
5709:
5682:
5656:
5624:
5597:
5571:
5542:
5516:
5490:
5470:
5435:
5373:voters outside
5254:
5220:
5177:
5154:
5134:
5103:
5072:
5052:
5014:
4994:
4959:
4939:
4917:
4891:
4865:
4833:
4807:
4784:
4764:
4731:
4711:
4665:
4639:
4635:does not matter for
4619:
4599:
4579:
4559:
4524:
4504:
4475:
4455:
4421:
4389:
4369:
4329:
4296:
4276:
4239:
4219:
4187:
4123:
4090:
4057:
3961:
3906:
3884:
3862:
3835:
3808:
3786:
3764:
3744:
3692:
3640:
3564:
3542:
3520:
3493:
3471:
3449:
3427:
3405:
3331:
3287:
3267:
3191:
3169:
3147:
3101:
3079:
3057:
2964:
2941:
2921:
2859:
2827:
2798:
2778:
2748:
2718:
2696:
2674:
2654:
2618:
2594:
2558:
2522:
2499:
2463:
2443:
2407:
2387:
2351:
2321:
2301:
2293:(sometimes called a
2277:
2246:
2216:
2168:
2148:
2128:
2108:
2088:
2068:
2048:
2028:
2008:
1988:
1968:
1948:
1928:
1908:
1825:
1805:
1785:
1779:ranked voting system
1759:cardinal information
1705:
1679:
1653:
1393:
1367:
1341:
1299:
1210:social choice theory
1200:Social choice theory
1107:relative comparisons
1095:Nicolas de Condorcet
1062:
1034:
1014:
994:
916:Economics portal
863:Median voter theorem
82:Comparative politics
18:Arrow's Theorem
13139:Eponymous paradoxes
13041:Bounded rationality
12660:Cournot competition
12610:Rock paper scissors
12585:Battle of the sexes
12575:Volunteer's dilemma
12447:Perfect information
12374:Dominant strategies
12211:Epsilon-equilibrium
12094:Extensive-form game
11603:Temperature paradox
11526:Free choice paradox
11390:Fitch's knowability
10797:10.1509/jmr.14.0208
10660:2022PNAS..11910412K
10654:(42): e2210412119.
10491:10.1007/11839354_23
9615:Theory and Decision
9445:Theory and Decision
8222:Theory and Decision
7930:Theory and Decision
7300:Holmström's theorem
7140:{\displaystyle 3/4}
7112:{\displaystyle 2/3}
7084:Supermajority rules
6892:expand his palace.
6770:normal distribution
6764:or otherwise has a
6736:left-right spectrum
6716:Left-right spectrum
6492:Therefore, we have
5463:are not relevant.)
5097: —
4654:{\displaystyle x,z}
4490:{\displaystyle x,y}
4363: —
4035:decisive coalitions
1775:Condorcet's example
1746:Sidney Morgenbesser
1491:one vote, one value
1277:ordinal preferences
1131:where they are not
1121:first-past-the-post
968:is a key result in
904:Politics portal
615:Vote linkage system
586:Seat linkage system
173:Ranked-choice (RCV)
13134:Economics theorems
13020:Paranoid algorithm
13000:Alpha–beta pruning
12879:John Maynard Smith
12710:Rendezvous problem
12550:Traveler's dilemma
12540:Gift-exchange game
12535:Prisoner's dilemma
12452:Large Poisson game
12419:Bargaining problem
12324:Backward induction
12296:Subgame perfection
12251:Proper equilibrium
11979:Prisoner's dilemma
11665:Heat death paradox
11653:Unexpected hanging
11618:Chicken or the egg
11225:Sen, Amartya Kumar
10288:Morgenstern, Oskar
9457:10.1007/BF00143070
9259:on 27 October 2018
8791:Economics Bulletin
8594:Economics Bulletin
8234:10.1007/BF00126382
7632:on 27 October 2018
7184:
7137:
7109:
7076:Esoteric solutions
6990:circular reasoning
6951:cardinal utilities
6886:Great Fire of Rome
6874:strict behaviorism
6655:majority-rule, or
6651:
6344:
6091:
5954:pivotal voter for
5826:
5807:being ranked over
5727:
5695:
5668:
5642:
5610:
5583:
5554:
5528:
5502:
5476:
5453:
5431:(Items other than
5419:
5417:
5238:
5203:
5163:
5140:
5128:
5112:
5095:
5078:
5058:
5038:
5000:
4977:
4945:
4923:
4903:
4877:
4851:
4819:
4790:
4770:
4750:
4717:
4697:
4651:
4625:
4605:
4585:
4565:
4542:
4510:
4487:
4461:
4449:
4433:
4407:
4375:
4361:
4341:
4315:
4282:
4258:
4225:
4205:
4158:decisive coalition
4135:
4109:
4075:
4002:
3947:
3892:
3870:
3848:
3821:
3794:
3772:
3750:
3730:
3678:
3618:
3550:
3528:
3506:
3479:
3457:
3435:
3413:
3391:
3327:such that for all
3317:
3273:
3245:
3177:
3155:
3133:
3097:for all orderings
3087:
3065:
3036:preference profile
3024:
2947:
2927:
2904:
2833:
2813:
2784:
2764:
2734:
2704:
2682:
2660:
2640:
2600:
2580:
2544:
2505:
2485:
2449:
2429:
2393:
2373:
2347:(Transitivity) If
2333:
2307:
2283:
2252:
2222:
2174:
2154:
2134:
2124:is preferred over
2114:
2094:
2074:
2054:
2034:
2014:
1994:
1974:
1954:
1934:
1914:
1831:
1811:
1791:
1770:Intuitive argument
1732:spoiler candidates
1717:
1691:
1665:
1405:
1379:
1353:
1311:
1222:social choice rule
1172:cardinal utilities
1159:Rated voting rules
1086:can eliminate the
1084:ranked voting rule
1068:
1040:
1020:
1000:
978:ranked voting rule
976:, showing that no
800:Discursive dilemma
759:Lesser evil voting
634:Supermixed systems
337:Largest remainders
195:Round-robin voting
63:
13099:
13098:
13005:Aspiration window
12974:Suzanne Scotchmer
12929:Oskar Morgenstern
12824:Donald B. Gillies
12766:Zermelo's theorem
12695:Induction puzzles
12650:Fair cake-cutting
12625:Public goods game
12555:Coordination game
12429:Intransitive game
12359:Forward induction
12241:Pareto efficiency
12221:Gibbs equilibrium
12191:Berge equilibrium
12139:Simultaneous game
12025:
12024:
11696:Arrow information
11281:(11): 1041–1053.
11261:978-94-009-3895-3
11238:978-0-444-85127-7
11089:978-0-444-82914-6
11066:Arrow, Kenneth J.
10974:"Arrow's Theorem"
10954:978-0-521-00883-9
10941:See Chapter 6 of
10500:978-3-540-38569-1
10284:Neumann, John von
10130:Arrow, Kenneth J.
9665:978-0-89838-189-4
9130:Economics Letters
9106:978-1-4008-4246-9
9079:978-0-231-52686-9
8885:Arrow, Kenneth J.
8724:Arrow, Kenneth J.
8612:Arrow, Kenneth J.
8569:978-3-319-23261-4
8548:"Arrow's Theorem"
8106:978-0-89838-189-4
7655:"Arrow's Theorem"
7339:Arrow, Kenneth J.
7310:Condorcet paradox
7295:Gibbard's theorem
7239:Gibbard's theorem
6947:rational behavior
6844:Gibbard's theorem
6705:Condorcet methods
6685:in the election.
6522:
6521:
6322:voters. That is,
5813:pivotal voter for
5746:
5745:
5479:{\displaystyle G}
5374:
5319:
5264:
5143:{\displaystyle G}
5126:
5093:
5081:{\displaystyle X}
5061:{\displaystyle G}
5003:{\displaystyle G}
4955:is decisive over
4948:{\displaystyle G}
4793:{\displaystyle G}
4773:{\displaystyle z}
4720:{\displaystyle G}
4628:{\displaystyle y}
4608:{\displaystyle z}
4588:{\displaystyle x}
4568:{\displaystyle G}
4520:is decisive over
4513:{\displaystyle G}
4464:{\displaystyle z}
4447:
4378:{\displaystyle G}
4359:
4285:{\displaystyle j}
4228:{\displaystyle i}
3753:{\displaystyle i}
3276:{\displaystyle i}
3049:Pareto efficiency
2950:{\displaystyle N}
2930:{\displaystyle A}
2836:{\displaystyle N}
2787:{\displaystyle A}
2663:{\displaystyle R}
2603:{\displaystyle R}
2508:{\displaystyle R}
2452:{\displaystyle R}
2396:{\displaystyle R}
2310:{\displaystyle R}
2286:{\displaystyle A}
2255:{\displaystyle A}
2225:{\displaystyle A}
2177:{\displaystyle A}
2157:{\displaystyle C}
2137:{\displaystyle B}
2117:{\displaystyle A}
2097:{\displaystyle A}
2077:{\displaystyle C}
2057:{\displaystyle B}
2037:{\displaystyle A}
2017:{\displaystyle B}
1997:{\displaystyle C}
1977:{\displaystyle C}
1957:{\displaystyle B}
1937:{\displaystyle B}
1917:{\displaystyle C}
1902:
1901:
1856:Third preference
1853:Second preference
1834:{\displaystyle C}
1814:{\displaystyle B}
1794:{\displaystyle A}
1536:, then candidate
1521:Pareto efficiency
1423:Basic assumptions
1206:welfare economics
1111:doctrinal paradox
1080:spoiler candidate
1071:{\displaystyle C}
1043:{\displaystyle C}
1023:{\displaystyle B}
1003:{\displaystyle A}
982:behave rationally
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
13166:
13114:
13107:
13086:Topological game
13081:No-win situation
12979:Thomas Schelling
12959:Robert B. Wilson
12919:Merrill M. Flood
12889:John von Neumann
12799:Ariel Rubinstein
12784:Albert W. Tucker
12635:War of attrition
12595:Matching pennies
12236:Nash equilibrium
12159:Mechanism design
12124:Normal-form game
12079:Cooperative game
12052:
12045:
12038:
12029:
12028:
12015:
12014:
12005:
12004:
11816:Service recovery
11670:Olbers's paradox
11370:Buridan's bridge
11343:
11336:
11329:
11320:
11319:
11292:
11290:
11265:
11242:
11219:
11199:
11175:
11142:
11108:
11093:
11074:Suzumura, Kōtarō
11052:
11051:
11049:
11047:
11035:
11029:
11028:
10988:
10982:
10981:
10970:
10959:
10957:
10939:
10933:
10932:
10912:
10906:
10905:
10865:
10856:
10855:
10823:
10817:
10816:
10780:
10774:
10773:
10741:
10735:
10734:
10706:
10700:
10699:
10689:
10671:
10639:
10628:
10627:
10613:10.1037/h0074763
10592:
10586:
10585:
10553:
10544:
10543:
10511:
10505:
10504:
10484:
10468:
10462:
10461:
10421:
10415:
10414:
10391:
10385:
10384:
10378:
10370:
10338:
10332:
10331:
10303:
10297:
10281:
10275:
10274:
10238:
10229:
10223:
10214:
10204:
10199:. Archived from
10188:
10182:
10181:
10179:
10173:. Archived from
10138:
10126:
10117:
10116:
10114:
10097:
10086:
10080:
10079:
10055:
10046:
10045:
10028:
10019:
10018:
9986:
9977:
9976:
9971:
9970:
9950:
9944:
9943:
9923:
9917:
9916:
9898:
9887:
9886:
9868:
9859:
9853:
9852:
9842:
9818:
9809:
9808:
9798:
9792:
9791:
9751:
9745:
9744:
9721:
9715:
9714:
9676:
9670:
9669:
9648:
9639:
9638:
9606:
9600:
9599:
9567:
9558:
9557:
9525:
9519:
9518:
9475:
9469:
9468:
9436:
9430:
9429:
9397:
9388:
9387:
9348:Condorcet method
9343:
9332:
9331:
9325:
9316:
9303:
9302:
9278:
9269:
9268:
9266:
9264:
9244:
9238:
9237:
9205:
9199:
9198:
9160:
9154:
9153:
9125:
9119:
9118:
9090:
9084:
9083:
9055:
9049:
9048:
9046:
9029:
9018:
9009:
9008:
9006:
8975:
8955:
8946:
8937:
8936:
8934:
8928:. Archived from
8893:
8881:
8868:
8867:
8835:
8826:
8825:
8819:
8810:
8799:
8798:
8782:
8776:
8775:
8773:
8767:. Archived from
8732:
8720:
8714:
8713:
8673:
8664:
8663:
8661:
8655:. Archived from
8620:
8608:
8602:
8601:
8585:
8579:
8578:
8577:
8576:
8543:
8534:
8533:
8501:
8490:
8489:
8487:
8470:
8459:
8444:
8443:
8405:
8399:
8398:
8358:
8352:
8339:. So not within
8337:cardinal systems
8313:
8308:. Archived from
8297:
8291:
8281:
8276:. Archived from
8265:
8259:
8258:
8249:
8248:
8213:
8204:
8194:
8189:. Archived from
8178:
8172:
8171:
8154:
8148:
8147:
8117:
8111:
8110:
8089:
8083:
8082:
8042:
8027:
8016:
8015:
7999:
7993:
7992:
7960:
7954:
7953:
7921:
7915:
7914:
7876:
7870:
7869:
7831:
7825:
7824:
7810:
7794:
7788:
7787:
7760:
7754:
7753:
7710:
7704:
7703:
7693:
7669:
7663:
7662:
7651:
7642:
7641:
7639:
7637:
7617:
7611:
7610:
7605:
7604:
7561:
7552:
7551:
7530:(6): 1397–1402.
7515:
7506:
7505:
7478:
7472:
7471:
7439:
7433:
7432:
7430:
7413:
7402:
7391:
7390:
7388:
7382:. Archived from
7347:
7335:
7279:
7277:Economics portal
7274:
7273:
7235:strategic voting
7193:
7191:
7190:
7185:
7183:
7182:
7149:voting paradoxes
7146:
7144:
7143:
7138:
7133:
7118:
7116:
7115:
7110:
7105:
6998:utilitarian rule
6963:lottery of birth
6897:cardinal utility
6860:Cardinal utility
6663:Condorcet cycles
6601:
6574:
6569:is preferred to
6568:
6562:
5994:is ranked above
5750:
5749:
5736:
5734:
5733:
5728:
5704:
5702:
5701:
5696:
5694:
5693:
5677:
5675:
5674:
5669:
5651:
5649:
5648:
5643:
5619:
5617:
5616:
5611:
5609:
5608:
5592:
5590:
5589:
5584:
5563:
5561:
5560:
5555:
5537:
5535:
5534:
5529:
5511:
5509:
5508:
5503:
5485:
5483:
5482:
5477:
5462:
5460:
5459:
5454:
5428:
5426:
5425:
5420:
5418:
5411:
5410:
5398:
5397:
5375:
5372:
5363:
5362:
5350:
5349:
5330:
5329:
5320:
5317:
5308:
5307:
5295:
5294:
5275:
5274:
5265:
5262:
5247:
5245:
5244:
5239:
5212:
5210:
5209:
5204:
5202:
5201:
5189:
5188:
5172:
5170:
5169:
5164:
5149:
5147:
5146:
5141:
5121:
5119:
5118:
5113:
5098:
5087:
5085:
5084:
5079:
5067:
5065:
5064:
5059:
5047:
5045:
5044:
5039:
5009:
5007:
5006:
5001:
4986:
4984:
4983:
4978:
4954:
4952:
4951:
4946:
4932:
4930:
4929:
4924:
4912:
4910:
4909:
4904:
4886:
4884:
4883:
4878:
4860:
4858:
4857:
4852:
4828:
4826:
4825:
4820:
4799:
4797:
4796:
4791:
4779:
4777:
4776:
4771:
4759:
4757:
4756:
4751:
4746:
4745:
4726:
4724:
4723:
4718:
4706:
4704:
4703:
4698:
4693:
4692:
4680:
4679:
4660:
4658:
4657:
4652:
4634:
4632:
4631:
4626:
4614:
4612:
4611:
4606:
4594:
4592:
4591:
4586:
4574:
4572:
4571:
4566:
4555:Let everyone in
4551:
4549:
4548:
4543:
4519:
4517:
4516:
4511:
4496:
4494:
4493:
4488:
4470:
4468:
4467:
4462:
4442:
4440:
4439:
4434:
4416:
4414:
4413:
4408:
4384:
4382:
4381:
4376:
4364:
4350:
4348:
4347:
4342:
4324:
4322:
4321:
4316:
4311:
4310:
4291:
4289:
4288:
4283:
4267:
4265:
4264:
4259:
4254:
4253:
4234:
4232:
4231:
4226:
4214:
4212:
4211:
4206:
4173:Ariel Rubinstein
4144:
4142:
4141:
4136:
4118:
4116:
4115:
4110:
4105:
4104:
4084:
4082:
4081:
4076:
4022:
4021:
4011:
4009:
4008:
4003:
3998:
3997:
3979:
3978:
3956:
3954:
3953:
3948:
3943:
3942:
3924:
3923:
3901:
3899:
3898:
3893:
3891:
3879:
3877:
3876:
3871:
3869:
3857:
3855:
3854:
3849:
3847:
3846:
3830:
3828:
3827:
3822:
3820:
3819:
3803:
3801:
3800:
3795:
3793:
3781:
3779:
3778:
3773:
3771:
3759:
3757:
3756:
3751:
3739:
3737:
3736:
3731:
3726:
3725:
3707:
3706:
3687:
3685:
3684:
3679:
3674:
3673:
3655:
3654:
3627:
3625:
3624:
3619:
3614:
3613:
3595:
3594:
3582:
3581:
3559:
3557:
3556:
3551:
3549:
3538:is preferred to
3537:
3535:
3534:
3529:
3527:
3515:
3513:
3512:
3507:
3505:
3504:
3488:
3486:
3485:
3480:
3478:
3467:is preferred to
3466:
3464:
3463:
3458:
3456:
3444:
3442:
3441:
3436:
3434:
3422:
3420:
3419:
3414:
3412:
3400:
3398:
3397:
3392:
3390:
3389:
3365:
3364:
3346:
3345:
3326:
3324:
3323:
3318:
3282:
3280:
3279:
3274:
3259:Non-dictatorship
3254:
3252:
3251:
3246:
3241:
3240:
3222:
3221:
3209:
3208:
3186:
3184:
3183:
3178:
3176:
3165:is preferred to
3164:
3162:
3161:
3156:
3154:
3142:
3140:
3139:
3134:
3132:
3131:
3113:
3112:
3096:
3094:
3093:
3088:
3086:
3075:is preferred to
3074:
3072:
3071:
3066:
3064:
3033:
3031:
3030:
3025:
3023:
3022:
2998:
2997:
2979:
2978:
2956:
2954:
2953:
2948:
2936:
2934:
2933:
2928:
2913:
2911:
2910:
2905:
2888:
2887:
2866:
2846:ordinal (ranked)
2842:
2840:
2839:
2834:
2822:
2820:
2819:
2814:
2793:
2791:
2790:
2785:
2773:
2771:
2770:
2765:
2763:
2755:
2743:
2741:
2740:
2735:
2733:
2725:
2713:
2711:
2710:
2705:
2703:
2691:
2689:
2688:
2683:
2681:
2669:
2667:
2666:
2661:
2649:
2647:
2646:
2641:
2636:
2628:
2609:
2607:
2606:
2601:
2589:
2587:
2586:
2581:
2576:
2568:
2553:
2551:
2550:
2545:
2540:
2532:
2514:
2512:
2511:
2506:
2494:
2492:
2491:
2486:
2481:
2473:
2458:
2456:
2455:
2450:
2438:
2436:
2435:
2430:
2425:
2417:
2402:
2400:
2399:
2394:
2382:
2380:
2379:
2374:
2369:
2361:
2342:
2340:
2339:
2334:
2316:
2314:
2313:
2308:
2292:
2290:
2289:
2284:
2261:
2259:
2258:
2253:
2231:
2229:
2228:
2223:
2208:Formal statement
2183:
2181:
2180:
2175:
2163:
2161:
2160:
2155:
2143:
2141:
2140:
2135:
2123:
2121:
2120:
2115:
2103:
2101:
2100:
2095:
2084:is preferred to
2083:
2081:
2080:
2075:
2063:
2061:
2060:
2055:
2044:is preferred to
2043:
2041:
2040:
2035:
2023:
2021:
2020:
2015:
2003:
2001:
2000:
1995:
1983:
1981:
1980:
1975:
1963:
1961:
1960:
1955:
1943:
1941:
1940:
1935:
1923:
1921:
1920:
1915:
1850:First preference
1844:
1843:
1840:
1838:
1837:
1832:
1820:
1818:
1817:
1812:
1800:
1798:
1797:
1792:
1726:
1724:
1723:
1718:
1700:
1698:
1697:
1692:
1674:
1672:
1671:
1666:
1645:
1639:
1633:
1627:
1609:
1603:
1597:
1547:
1541:
1535:
1529:
1476:Non-dictatorship
1450:partial function
1437:Universal domain
1414:
1412:
1411:
1406:
1388:
1386:
1385:
1380:
1362:
1360:
1359:
1354:
1332:
1327:is preferred to
1326:
1320:
1318:
1317:
1312:
1294:
1288:
1077:
1075:
1074:
1069:
1052:election science
1049:
1047:
1046:
1041:
1029:
1027:
1026:
1021:
1009:
1007:
1006:
1001:
972:, discovered by
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:
29:
21:
13174:
13173:
13169:
13168:
13167:
13165:
13164:
13163:
13119:
13118:
13117:
13108:
13104:
13100:
13095:
13029:
13015:max^n algorithm
12988:
12984:William Vickrey
12944:Reinhard Selten
12899:Kenneth Binmore
12814:David K. Levine
12809:Daniel Kahneman
12776:
12770:
12746:Negamax theorem
12736:Minimax theorem
12714:
12675:Diner's dilemma
12530:All-pay auction
12496:
12482:Stochastic game
12434:Mean-field game
12405:
12398:
12369:Markov strategy
12305:
12171:
12163:
12134:Sequential game
12119:Information set
12104:Game complexity
12074:Congestion game
12062:
12056:
12026:
12021:
11993:
11904:Decision-making
11850:Decision theory
11845:
11674:
11598:Hilbert's Hotel
11531:Grelling–Nelson
11474:
11353:
11347:
11299:
11262:
11239:
11216:
11196:
11106:
11090:
11070:Sen, Amartya K.
11060:
11058:Further reading
11055:
11045:
11043:
11036:
11032:
11009:10.2307/1914083
10989:
10985:
10972:
10971:
10962:
10955:
10940:
10936:
10913:
10909:
10886:10.2307/1912699
10866:
10859:
10824:
10820:
10781:
10777:
10742:
10738:
10707:
10703:
10640:
10631:
10593:
10589:
10554:
10547:
10512:
10508:
10501:
10482:10.1.1.113.2486
10469:
10465:
10442:10.2307/1906944
10422:
10418:
10408:
10392:
10388:
10372:
10371:
10339:
10335:
10320:10.2307/1906925
10304:
10300:
10282:
10278:
10239:
10232:
10224:
10217:
10213:
10212:
10189:
10185:
10177:
10136:
10127:
10120:
10112:
10106:
10095:
10087:
10083:
10056:
10049:
10029:
10022:
9987:
9980:
9968:
9966:
9951:
9947:
9940:
9924:
9920:
9913:
9899:
9890:
9866:
9860:
9856:
9823:"Stable Voting"
9819:
9812:
9799:
9795:
9772:10.2307/1909727
9752:
9748:
9722:
9718:
9682:Economic Theory
9677:
9673:
9666:
9649:
9642:
9607:
9603:
9568:
9561:
9526:
9522:
9496:10.2307/3088418
9476:
9472:
9437:
9433:
9398:
9391:
9355:Economic Theory
9344:
9335:
9323:
9319:Pearce, David.
9317:
9306:
9293:(2651): 30–33.
9279:
9272:
9262:
9260:
9245:
9241:
9206:
9202:
9166:Economic Theory
9161:
9157:
9126:
9122:
9107:
9091:
9087:
9080:
9056:
9052:
9044:
9038:
9027:
9019:
9012:
9004:
8973:10.1.1.193.6817
8959:Economic Theory
8953:
8947:
8940:
8932:
8891:
8882:
8871:
8836:
8829:
8817:
8813:Pearce, David.
8811:
8802:
8783:
8779:
8771:
8730:
8721:
8717:
8694:10.2307/2110496
8674:
8667:
8659:
8618:
8609:
8605:
8586:
8582:
8574:
8572:
8570:
8544:
8537:
8502:
8493:
8485:
8479:
8468:
8460:
8447:
8411:Economic Theory
8406:
8402:
8379:10.2307/1914083
8359:
8355:
8351:
8350:
8344:
8341:ranking systems
8333:approval voting
8326:
8320:
8298:
8294:
8290:
8266:
8262:
8246:
8244:
8214:
8207:
8203:
8202:
8179:
8175:
8155:
8151:
8132:
8118:
8114:
8107:
8090:
8086:
8043:
8030:
8000:
7996:
7961:
7957:
7922:
7918:
7882:Economic Theory
7877:
7873:
7837:Economic Theory
7832:
7828:
7795:
7791:
7777:
7761:
7757:
7731:10.2307/3088418
7711:
7707:
7670:
7666:
7653:
7652:
7645:
7635:
7633:
7618:
7614:
7602:
7600:
7562:
7555:
7516:
7509:
7495:
7479:
7475:
7440:
7436:
7428:
7422:
7411:
7403:
7394:
7386:
7345:
7336:
7327:
7323:
7275:
7268:
7265:
7231:
7215:axiom of choice
7204:
7175:
7171:
7163:
7160:
7159:
7129:
7124:
7121:
7120:
7101:
7096:
7093:
7092:
7086:
7078:
7038:
6988:with a kind of
6935:his own theorem
6862:
6856:
6848:straightforward
6813:
6801:vote positivity
6778:
6724:
6718:
6639:
6637:Condorcet cycle
6633:
6609:
6599:
6590:
6583:
6576:
6570:
6564:
6561:
6552:
6546:
6528:
6526:Generalizations
6523:
6512:
6505:
6501:
6487:
6480:
6458:
6451:
6447:
6421:
6415:. In short, if
6292:
6016:
5895:be the same as
5793:
5768:Economic Theory
5755:
5747:
5739:
5710:
5707:
5706:
5689:
5685:
5683:
5680:
5679:
5657:
5654:
5653:
5625:
5622:
5621:
5604:
5600:
5598:
5595:
5594:
5572:
5569:
5568:
5543:
5540:
5539:
5517:
5514:
5513:
5491:
5488:
5487:
5471:
5468:
5467:
5436:
5433:
5432:
5416:
5415:
5406:
5402:
5393:
5389:
5379:
5371:
5368:
5367:
5358:
5354:
5345:
5341:
5331:
5325:
5321:
5318:voters in
5316:
5313:
5312:
5303:
5299:
5290:
5286:
5276:
5270:
5266:
5263:voters in
5261:
5257:
5255:
5252:
5251:
5221:
5218:
5217:
5197:
5193:
5184:
5180:
5178:
5175:
5174:
5155:
5152:
5151:
5135:
5132:
5131:
5124:
5104:
5101:
5100:
5096:
5090:
5073:
5070:
5069:
5053:
5050:
5049:
5015:
5012:
5011:
4995:
4992:
4991:
4960:
4957:
4956:
4940:
4937:
4936:
4918:
4915:
4914:
4892:
4889:
4888:
4866:
4863:
4862:
4834:
4831:
4830:
4808:
4805:
4804:
4785:
4782:
4781:
4765:
4762:
4761:
4741:
4737:
4732:
4729:
4728:
4712:
4709:
4708:
4688:
4684:
4675:
4671:
4666:
4663:
4662:
4640:
4637:
4636:
4620:
4617:
4616:
4600:
4597:
4596:
4580:
4577:
4576:
4560:
4557:
4556:
4525:
4522:
4521:
4505:
4502:
4501:
4476:
4473:
4472:
4456:
4453:
4452:
4445:
4422:
4419:
4418:
4390:
4387:
4386:
4370:
4367:
4366:
4365:if a coalition
4362:
4330:
4327:
4326:
4306:
4302:
4297:
4294:
4293:
4277:
4274:
4273:
4249:
4245:
4240:
4237:
4236:
4220:
4217:
4216:
4188:
4185:
4184:
4181:weakly decisive
4179:A coalition is
4148:A coalition is
4124:
4121:
4120:
4100:
4096:
4091:
4088:
4087:
4058:
4055:
4054:
4051:A coalition is
4027:
4019:
3993:
3989:
3974:
3970:
3962:
3959:
3958:
3938:
3934:
3919:
3915:
3907:
3904:
3903:
3887:
3885:
3882:
3881:
3865:
3863:
3860:
3859:
3858:, alternatives
3842:
3838:
3836:
3833:
3832:
3815:
3811:
3809:
3806:
3805:
3789:
3787:
3784:
3783:
3767:
3765:
3762:
3761:
3760:, alternatives
3745:
3742:
3741:
3721:
3717:
3702:
3698:
3693:
3690:
3689:
3669:
3665:
3650:
3646:
3641:
3638:
3637:
3609:
3605:
3590:
3586:
3577:
3573:
3565:
3562:
3561:
3545:
3543:
3540:
3539:
3523:
3521:
3518:
3517:
3500:
3496:
3494:
3491:
3490:
3474:
3472:
3469:
3468:
3452:
3450:
3447:
3446:
3430:
3428:
3425:
3424:
3408:
3406:
3403:
3402:
3385:
3381:
3360:
3356:
3341:
3337:
3332:
3329:
3328:
3288:
3285:
3284:
3268:
3265:
3264:
3236:
3232:
3217:
3213:
3204:
3200:
3192:
3189:
3188:
3172:
3170:
3167:
3166:
3150:
3148:
3145:
3144:
3127:
3123:
3108:
3104:
3102:
3099:
3098:
3082:
3080:
3077:
3076:
3060:
3058:
3055:
3054:
3053:If alternative
3018:
3014:
2993:
2989:
2974:
2970:
2965:
2962:
2961:
2942:
2939:
2938:
2922:
2919:
2918:
2883:
2879:
2862:
2860:
2857:
2856:
2828:
2825:
2824:
2799:
2796:
2795:
2779:
2776:
2775:
2759:
2751:
2749:
2746:
2745:
2729:
2721:
2719:
2716:
2715:
2699:
2697:
2694:
2693:
2677:
2675:
2672:
2671:
2655:
2652:
2651:
2632:
2624:
2619:
2616:
2615:
2595:
2592:
2591:
2572:
2564:
2559:
2556:
2555:
2536:
2528:
2523:
2520:
2519:
2500:
2497:
2496:
2477:
2469:
2464:
2461:
2460:
2444:
2441:
2440:
2421:
2413:
2408:
2405:
2404:
2388:
2385:
2384:
2365:
2357:
2352:
2349:
2348:
2322:
2319:
2318:
2302:
2299:
2298:
2278:
2275:
2274:
2271:binary relation
2247:
2244:
2243:
2217:
2214:
2213:
2210:
2198:weighted voting
2169:
2166:
2165:
2149:
2146:
2145:
2129:
2126:
2125:
2109:
2106:
2105:
2089:
2086:
2085:
2069:
2066:
2065:
2049:
2046:
2045:
2029:
2026:
2025:
2009:
2006:
2005:
1989:
1986:
1985:
1969:
1966:
1965:
1949:
1946:
1945:
1929:
1926:
1925:
1909:
1906:
1905:
1826:
1823:
1822:
1806:
1803:
1802:
1786:
1783:
1782:
1772:
1767:
1734:when using the
1706:
1703:
1702:
1680:
1677:
1676:
1654:
1651:
1650:
1641:
1635:
1629:
1623:
1605:
1599:
1593:
1584:rational choice
1580:
1543:
1537:
1531:
1530:over candidate
1525:
1425:
1394:
1391:
1390:
1368:
1365:
1364:
1342:
1339:
1338:
1328:
1322:
1300:
1297:
1296:
1290:
1284:
1273:
1267:
1262:
1250:rational choice
1202:
1190:Main articles:
1188:
1180:approval voting
1135:. By contrast,
1063:
1060:
1059:
1035:
1032:
1031:
1015:
1012:
1011:
995:
992:
991:
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:
13172:
13162:
13161:
13156:
13151:
13146:
13141:
13136:
13131:
13116:
13115:
13101:
13097:
13096:
13094:
13093:
13088:
13083:
13078:
13073:
13068:
13063:
13058:
13053:
13048:
13043:
13037:
13035:
13031:
13030:
13028:
13027:
13022:
13017:
13012:
13007:
13002:
12996:
12994:
12990:
12989:
12987:
12986:
12981:
12976:
12971:
12966:
12961:
12956:
12951:
12949:Robert Axelrod
12946:
12941:
12936:
12931:
12926:
12924:Olga Bondareva
12921:
12916:
12914:Melvin Dresher
12911:
12906:
12904:Leonid Hurwicz
12901:
12896:
12891:
12886:
12881:
12876:
12871:
12866:
12861:
12856:
12851:
12846:
12841:
12839:Harold W. Kuhn
12836:
12831:
12829:Drew Fudenberg
12826:
12821:
12819:David M. Kreps
12816:
12811:
12806:
12804:Claude Shannon
12801:
12796:
12791:
12786:
12780:
12778:
12772:
12771:
12769:
12768:
12763:
12758:
12753:
12748:
12743:
12741:Nash's theorem
12738:
12733:
12728:
12722:
12720:
12716:
12715:
12713:
12712:
12707:
12702:
12697:
12692:
12687:
12682:
12677:
12672:
12667:
12662:
12657:
12652:
12647:
12642:
12637:
12632:
12627:
12622:
12617:
12612:
12607:
12602:
12600:Ultimatum game
12597:
12592:
12587:
12582:
12580:Dollar auction
12577:
12572:
12567:
12565:Centipede game
12562:
12557:
12552:
12547:
12542:
12537:
12532:
12527:
12522:
12520:Infinite chess
12517:
12512:
12506:
12504:
12498:
12497:
12495:
12494:
12489:
12487:Symmetric game
12484:
12479:
12474:
12472:Signaling game
12469:
12467:Screening game
12464:
12459:
12457:Potential game
12454:
12449:
12444:
12436:
12431:
12426:
12421:
12416:
12410:
12408:
12400:
12399:
12397:
12396:
12391:
12386:
12384:Mixed strategy
12381:
12376:
12371:
12366:
12361:
12356:
12351:
12346:
12341:
12336:
12331:
12326:
12321:
12315:
12313:
12307:
12306:
12304:
12303:
12298:
12293:
12288:
12283:
12278:
12273:
12268:
12266:Risk dominance
12263:
12258:
12253:
12248:
12243:
12238:
12233:
12228:
12223:
12218:
12213:
12208:
12203:
12198:
12193:
12188:
12183:
12177:
12175:
12165:
12164:
12162:
12161:
12156:
12151:
12146:
12141:
12136:
12131:
12126:
12121:
12116:
12111:
12109:Graphical game
12106:
12101:
12096:
12091:
12086:
12081:
12076:
12070:
12068:
12064:
12063:
12055:
12054:
12047:
12040:
12032:
12023:
12022:
12020:
12019:
12009:
11998:
11995:
11994:
11992:
11991:
11986:
11981:
11976:
11971:
11966:
11961:
11956:
11951:
11946:
11941:
11936:
11931:
11926:
11921:
11916:
11911:
11906:
11901:
11896:
11891:
11886:
11881:
11880:
11879:
11874:
11869:
11859:
11853:
11851:
11847:
11846:
11844:
11843:
11838:
11833:
11828:
11823:
11821:St. Petersburg
11818:
11813:
11808:
11803:
11798:
11793:
11788:
11783:
11778:
11773:
11768:
11763:
11758:
11753:
11748:
11743:
11738:
11733:
11728:
11723:
11718:
11713:
11708:
11703:
11698:
11693:
11688:
11682:
11680:
11676:
11675:
11673:
11672:
11667:
11662:
11655:
11650:
11645:
11640:
11635:
11630:
11625:
11620:
11615:
11610:
11605:
11600:
11595:
11590:
11585:
11580:
11575:
11570:
11569:
11568:
11563:
11558:
11553:
11548:
11538:
11533:
11528:
11523:
11518:
11513:
11508:
11503:
11498:
11493:
11488:
11482:
11480:
11476:
11475:
11473:
11472:
11467:
11462:
11457:
11452:
11450:Rule-following
11447:
11442:
11437:
11432:
11427:
11422:
11417:
11412:
11407:
11402:
11397:
11392:
11387:
11382:
11377:
11375:Dream argument
11372:
11367:
11361:
11359:
11355:
11354:
11346:
11345:
11338:
11331:
11323:
11317:
11316:
11311:
11305:entry in the
11298:
11297:External links
11295:
11294:
11293:
11266:
11260:
11243:
11237:
11221:
11214:
11208:. John Wiley.
11201:
11194:
11176:
11158:(3): 217–235.
11147:
11117:(1): 107–112.
11099:
11088:
11059:
11056:
11054:
11053:
11030:
11003:(4): 587–601.
10983:
10960:
10953:
10934:
10923:(1): 103–106.
10907:
10880:(4): 787–814.
10857:
10818:
10791:(4): 520–525.
10775:
10756:(3): 549–559.
10736:
10723:10.1086/208899
10701:
10629:
10587:
10564:(2): 171–181.
10545:
10522:(3): 405–408.
10506:
10499:
10463:
10416:
10406:
10386:
10353:(2): 147–179.
10333:
10314:(4): 319–333.
10298:
10276:
10255:10.1086/257678
10249:(4): 309–321.
10230:
10215:
10206:
10205:
10203:on 2023-06-05.
10183:
10180:on 2011-07-20.
10155:10.1086/256963
10149:(4): 328–346.
10118:
10105:978-0300013641
10104:
10081:
10070:(3): 349–378.
10047:
10020:
9978:
9945:
9938:
9918:
9911:
9888:
9877:(2): 457–469.
9854:
9833:(3): 421–433.
9810:
9793:
9766:(1): 147–157.
9746:
9735:(3): 472–482.
9716:
9689:(3): 689–700.
9671:
9664:
9640:
9621:(2): 171–199.
9601:
9582:(3): 310–334.
9559:
9540:(3): 311–330.
9520:
9490:(1): 134–147.
9470:
9451:(2): 161–197.
9431:
9412:(2): 107–126.
9389:
9362:(3): 689–700.
9333:
9304:
9270:
9239:
9220:(3): 478–486.
9200:
9173:(2): 523–525.
9155:
9120:
9105:
9085:
9078:
9050:
9037:978-0300013641
9036:
9010:
8966:(1): 211–215.
8938:
8935:on 2011-07-20.
8910:10.1086/256963
8904:(4): 328–346.
8869:
8850:(2): 107–126.
8827:
8800:
8777:
8774:on 2011-07-20.
8749:10.1086/256963
8743:(4): 328–346.
8715:
8688:(2): 303–311.
8665:
8662:on 2011-07-20.
8637:10.1086/256963
8631:(4): 328–346.
8603:
8580:
8568:
8535:
8516:(3): 478–486.
8491:
8478:978-0300013641
8477:
8445:
8418:(3): 689–700.
8400:
8373:(4): 587–601.
8353:
8345:
8327:
8321:
8315:
8314:
8312:on 2023-06-05.
8292:
8282:
8280:on 2023-06-05.
8260:
8228:(3): 289–317.
8205:
8196:
8195:
8193:on 2023-06-05.
8173:
8149:
8130:
8112:
8105:
8084:
8063:10.1086/256633
8028:
7994:
7975:(3): 311–330.
7955:
7936:(2): 171–199.
7916:
7889:(3): 689–700.
7871:
7844:(3): 689–700.
7826:
7789:
7775:
7755:
7725:(1): 134–147.
7705:
7684:(4): 863–895.
7664:
7643:
7612:
7582:10.2307/138144
7576:(2): 195–200.
7553:
7536:10.1086/259845
7507:
7493:
7473:
7454:(3): 478–486.
7434:
7421:978-0300013641
7420:
7392:
7389:on 2011-07-20.
7364:10.1086/256963
7358:(4): 328–346.
7324:
7322:
7319:
7318:
7317:
7312:
7307:
7305:Market failure
7302:
7297:
7292:
7287:
7281:
7280:
7264:
7261:
7249:Non-perversity
7243:social welfare
7230:
7227:
7203:
7200:
7181:
7178:
7174:
7170:
7167:
7136:
7132:
7128:
7108:
7104:
7100:
7085:
7082:
7077:
7074:
7037:
7034:
6858:Main article:
6855:
6852:
6812:
6809:
6777:
6774:
6720:Main article:
6717:
6714:
6681:should defeat
6635:Main article:
6632:
6629:
6608:
6605:
6604:
6603:
6595:
6588:
6581:
6557:
6550:
6535:
6534:Non-imposition
6527:
6524:
6520:
6519:
6514:
6513:
6510:
6503:
6499:
6490:
6489:
6485:
6478:
6461:
6460:
6456:
6449:
6445:
6419:
6291:
6288:
6262:voter to rank
6173:
6172:
6153:
6134:
6015:
6012:
5792:
5789:
5757:
5756:
5753:
5748:
5744:
5743:
5726:
5723:
5720:
5717:
5714:
5692:
5688:
5667:
5664:
5661:
5641:
5638:
5635:
5632:
5629:
5607:
5603:
5582:
5579:
5576:
5553:
5550:
5547:
5527:
5524:
5521:
5501:
5498:
5495:
5475:
5452:
5449:
5446:
5443:
5440:
5414:
5409:
5405:
5401:
5396:
5392:
5388:
5385:
5382:
5380:
5378:
5370:
5369:
5366:
5361:
5357:
5353:
5348:
5344:
5340:
5337:
5334:
5332:
5328:
5324:
5315:
5314:
5311:
5306:
5302:
5298:
5293:
5289:
5285:
5282:
5279:
5277:
5273:
5269:
5260:
5259:
5237:
5234:
5231:
5228:
5225:
5200:
5196:
5192:
5187:
5183:
5162:
5159:
5139:
5125:
5111:
5108:
5091:
5077:
5057:
5037:
5034:
5031:
5028:
5025:
5022:
5019:
4999:
4976:
4973:
4970:
4967:
4964:
4944:
4922:
4902:
4899:
4896:
4876:
4873:
4870:
4850:
4847:
4844:
4841:
4838:
4818:
4815:
4812:
4789:
4769:
4749:
4744:
4740:
4736:
4716:
4696:
4691:
4687:
4683:
4678:
4674:
4670:
4650:
4647:
4644:
4624:
4604:
4584:
4564:
4541:
4538:
4535:
4532:
4529:
4509:
4486:
4483:
4480:
4460:
4446:
4432:
4429:
4426:
4406:
4403:
4400:
4397:
4394:
4374:
4357:
4353:
4352:
4340:
4337:
4334:
4314:
4309:
4305:
4301:
4281:
4257:
4252:
4248:
4244:
4224:
4204:
4201:
4198:
4195:
4192:
4154:
4153:
4146:
4134:
4131:
4128:
4108:
4103:
4099:
4095:
4074:
4071:
4068:
4065:
4062:
4049:
4029:
4028:
4025:
4020:
4018:
4015:
4014:
4013:
4001:
3996:
3992:
3988:
3985:
3982:
3977:
3973:
3969:
3966:
3946:
3941:
3937:
3933:
3930:
3927:
3922:
3918:
3914:
3911:
3890:
3868:
3845:
3841:
3818:
3814:
3792:
3770:
3749:
3729:
3724:
3720:
3716:
3713:
3710:
3705:
3701:
3697:
3677:
3672:
3668:
3664:
3661:
3658:
3653:
3649:
3645:
3634:
3629:
3617:
3612:
3608:
3604:
3601:
3598:
3593:
3589:
3585:
3580:
3576:
3572:
3569:
3548:
3526:
3503:
3499:
3477:
3455:
3433:
3411:
3388:
3384:
3380:
3377:
3374:
3371:
3368:
3363:
3359:
3355:
3352:
3349:
3344:
3340:
3336:
3316:
3313:
3310:
3307:
3304:
3301:
3298:
3295:
3292:
3272:
3261:
3256:
3244:
3239:
3235:
3231:
3228:
3225:
3220:
3216:
3212:
3207:
3203:
3199:
3196:
3175:
3153:
3130:
3126:
3122:
3119:
3116:
3111:
3107:
3085:
3063:
3051:
3021:
3017:
3013:
3010:
3007:
3004:
3001:
2996:
2992:
2988:
2985:
2982:
2977:
2973:
2969:
2946:
2926:
2915:
2914:
2903:
2900:
2897:
2894:
2891:
2886:
2882:
2878:
2875:
2872:
2869:
2865:
2852:is a function
2832:
2812:
2809:
2806:
2803:
2783:
2762:
2758:
2754:
2732:
2728:
2724:
2702:
2680:
2659:
2639:
2635:
2631:
2627:
2623:
2612:
2611:
2599:
2579:
2575:
2571:
2567:
2563:
2543:
2539:
2535:
2531:
2527:
2516:
2504:
2484:
2480:
2476:
2472:
2468:
2448:
2428:
2424:
2420:
2416:
2412:
2392:
2372:
2368:
2364:
2360:
2356:
2332:
2329:
2326:
2306:
2295:total preorder
2282:
2251:
2221:
2209:
2206:
2202:ranked ballots
2173:
2153:
2133:
2113:
2093:
2073:
2053:
2033:
2013:
1993:
1973:
1953:
1933:
1913:
1900:
1899:
1896:
1893:
1890:
1886:
1885:
1882:
1879:
1876:
1872:
1871:
1868:
1865:
1862:
1858:
1857:
1854:
1851:
1848:
1830:
1810:
1790:
1771:
1768:
1766:
1763:
1755:
1754:
1742:
1741:
1740:
1739:
1728:
1716:
1713:
1710:
1690:
1687:
1684:
1664:
1661:
1658:
1628:and candidate
1579:
1576:
1552:
1551:
1550:
1549:
1516:
1509:Non-imposition
1504:
1503:
1502:
1501:
1494:
1470:
1469:
1468:
1467:
1460:
1442:total function
1429:non-degenerate
1424:
1421:
1404:
1401:
1398:
1378:
1375:
1372:
1352:
1349:
1346:
1310:
1307:
1304:
1266:
1263:
1261:
1258:
1196:Voting systems
1187:
1184:
1117:Plurality-rule
1099:voting paradox
1088:spoiler effect
1067:
1039:
1019:
999:
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:
9:
6:
4:
3:
2:
13171:
13160:
13157:
13155:
13152:
13150:
13147:
13145:
13142:
13140:
13137:
13135:
13132:
13130:
13129:Voting theory
13127:
13126:
13124:
13112:
13106:
13102:
13092:
13089:
13087:
13084:
13082:
13079:
13077:
13074:
13072:
13069:
13067:
13064:
13062:
13059:
13057:
13054:
13052:
13049:
13047:
13044:
13042:
13039:
13038:
13036:
13034:Miscellaneous
13032:
13026:
13023:
13021:
13018:
13016:
13013:
13011:
13008:
13006:
13003:
13001:
12998:
12997:
12995:
12991:
12985:
12982:
12980:
12977:
12975:
12972:
12970:
12969:Samuel Bowles
12967:
12965:
12964:Roger Myerson
12962:
12960:
12957:
12955:
12954:Robert Aumann
12952:
12950:
12947:
12945:
12942:
12940:
12937:
12935:
12932:
12930:
12927:
12925:
12922:
12920:
12917:
12915:
12912:
12910:
12909:Lloyd Shapley
12907:
12905:
12902:
12900:
12897:
12895:
12894:Kenneth Arrow
12892:
12890:
12887:
12885:
12882:
12880:
12877:
12875:
12874:John Harsanyi
12872:
12870:
12867:
12865:
12862:
12860:
12857:
12855:
12852:
12850:
12847:
12845:
12844:Herbert Simon
12842:
12840:
12837:
12835:
12832:
12830:
12827:
12825:
12822:
12820:
12817:
12815:
12812:
12810:
12807:
12805:
12802:
12800:
12797:
12795:
12792:
12790:
12787:
12785:
12782:
12781:
12779:
12773:
12767:
12764:
12762:
12759:
12757:
12754:
12752:
12749:
12747:
12744:
12742:
12739:
12737:
12734:
12732:
12729:
12727:
12724:
12723:
12721:
12717:
12711:
12708:
12706:
12703:
12701:
12698:
12696:
12693:
12691:
12688:
12686:
12683:
12681:
12678:
12676:
12673:
12671:
12668:
12666:
12663:
12661:
12658:
12656:
12653:
12651:
12648:
12646:
12645:Fair division
12643:
12641:
12638:
12636:
12633:
12631:
12628:
12626:
12623:
12621:
12620:Dictator game
12618:
12616:
12613:
12611:
12608:
12606:
12603:
12601:
12598:
12596:
12593:
12591:
12588:
12586:
12583:
12581:
12578:
12576:
12573:
12571:
12568:
12566:
12563:
12561:
12558:
12556:
12553:
12551:
12548:
12546:
12543:
12541:
12538:
12536:
12533:
12531:
12528:
12526:
12523:
12521:
12518:
12516:
12513:
12511:
12508:
12507:
12505:
12503:
12499:
12493:
12492:Zero-sum game
12490:
12488:
12485:
12483:
12480:
12478:
12475:
12473:
12470:
12468:
12465:
12463:
12462:Repeated game
12460:
12458:
12455:
12453:
12450:
12448:
12445:
12443:
12441:
12437:
12435:
12432:
12430:
12427:
12425:
12422:
12420:
12417:
12415:
12412:
12411:
12409:
12407:
12401:
12395:
12392:
12390:
12387:
12385:
12382:
12380:
12379:Pure strategy
12377:
12375:
12372:
12370:
12367:
12365:
12362:
12360:
12357:
12355:
12352:
12350:
12347:
12345:
12344:De-escalation
12342:
12340:
12337:
12335:
12332:
12330:
12327:
12325:
12322:
12320:
12317:
12316:
12314:
12312:
12308:
12302:
12299:
12297:
12294:
12292:
12289:
12287:
12286:Shapley value
12284:
12282:
12279:
12277:
12274:
12272:
12269:
12267:
12264:
12262:
12259:
12257:
12254:
12252:
12249:
12247:
12244:
12242:
12239:
12237:
12234:
12232:
12229:
12227:
12224:
12222:
12219:
12217:
12214:
12212:
12209:
12207:
12204:
12202:
12199:
12197:
12194:
12192:
12189:
12187:
12184:
12182:
12179:
12178:
12176:
12174:
12170:
12166:
12160:
12157:
12155:
12154:Succinct game
12152:
12150:
12147:
12145:
12142:
12140:
12137:
12135:
12132:
12130:
12127:
12125:
12122:
12120:
12117:
12115:
12112:
12110:
12107:
12105:
12102:
12100:
12097:
12095:
12092:
12090:
12087:
12085:
12082:
12080:
12077:
12075:
12072:
12071:
12069:
12065:
12061:
12053:
12048:
12046:
12041:
12039:
12034:
12033:
12030:
12018:
12010:
12008:
12000:
11999:
11996:
11990:
11987:
11985:
11982:
11980:
11977:
11975:
11972:
11970:
11967:
11965:
11962:
11960:
11957:
11955:
11952:
11950:
11949:Morton's fork
11947:
11945:
11942:
11940:
11937:
11935:
11932:
11930:
11927:
11925:
11922:
11920:
11917:
11915:
11912:
11910:
11907:
11905:
11902:
11900:
11897:
11895:
11892:
11890:
11889:Buridan's ass
11887:
11885:
11882:
11878:
11875:
11873:
11870:
11868:
11865:
11864:
11863:
11862:Apportionment
11860:
11858:
11855:
11854:
11852:
11848:
11842:
11839:
11837:
11834:
11832:
11829:
11827:
11824:
11822:
11819:
11817:
11814:
11812:
11809:
11807:
11804:
11802:
11799:
11797:
11794:
11792:
11789:
11787:
11784:
11782:
11779:
11777:
11774:
11772:
11769:
11767:
11764:
11762:
11759:
11757:
11754:
11752:
11749:
11747:
11744:
11742:
11739:
11737:
11734:
11732:
11729:
11727:
11724:
11722:
11721:Downs–Thomson
11719:
11717:
11714:
11712:
11709:
11707:
11704:
11702:
11699:
11697:
11694:
11692:
11689:
11687:
11684:
11683:
11681:
11677:
11671:
11668:
11666:
11663:
11660:
11656:
11654:
11651:
11649:
11646:
11644:
11641:
11639:
11638:Plato's beard
11636:
11634:
11631:
11629:
11626:
11624:
11621:
11619:
11616:
11614:
11611:
11609:
11606:
11604:
11601:
11599:
11596:
11594:
11591:
11589:
11586:
11584:
11581:
11579:
11576:
11574:
11571:
11567:
11564:
11562:
11559:
11557:
11554:
11552:
11549:
11547:
11544:
11543:
11542:
11539:
11537:
11536:Kleene–Rosser
11534:
11532:
11529:
11527:
11524:
11522:
11519:
11517:
11514:
11512:
11509:
11507:
11504:
11502:
11499:
11497:
11494:
11492:
11489:
11487:
11484:
11483:
11481:
11477:
11471:
11468:
11466:
11463:
11461:
11460:Theseus' ship
11458:
11456:
11453:
11451:
11448:
11446:
11443:
11441:
11438:
11436:
11433:
11431:
11428:
11426:
11423:
11421:
11420:Mere addition
11418:
11416:
11413:
11411:
11408:
11406:
11403:
11401:
11398:
11396:
11393:
11391:
11388:
11386:
11383:
11381:
11378:
11376:
11373:
11371:
11368:
11366:
11363:
11362:
11360:
11358:Philosophical
11356:
11352:
11344:
11339:
11337:
11332:
11330:
11325:
11324:
11321:
11315:
11312:
11310:
11309:
11304:
11301:
11300:
11289:
11284:
11280:
11276:
11272:
11267:
11263:
11257:
11253:
11249:
11244:
11240:
11234:
11230:
11226:
11222:
11217:
11215:0-471-29645-7
11211:
11207:
11202:
11197:
11195:9780521850124
11191:
11187:
11186:
11181:
11177:
11173:
11169:
11165:
11161:
11157:
11153:
11148:
11145:
11140:
11136:
11132:
11128:
11124:
11120:
11116:
11112:
11105:
11100:
11097:
11091:
11085:
11081:
11080:
11075:
11071:
11067:
11062:
11061:
11041:
11034:
11026:
11022:
11018:
11014:
11010:
11006:
11002:
10998:
10994:
10987:
10979:
10975:
10969:
10967:
10965:
10956:
10950:
10946:
10938:
10930:
10926:
10922:
10918:
10911:
10903:
10899:
10895:
10891:
10887:
10883:
10879:
10875:
10871:
10864:
10862:
10853:
10849:
10845:
10841:
10837:
10833:
10829:
10822:
10814:
10810:
10806:
10802:
10798:
10794:
10790:
10786:
10779:
10771:
10767:
10763:
10759:
10755:
10751:
10747:
10740:
10732:
10728:
10724:
10720:
10716:
10712:
10705:
10697:
10693:
10688:
10683:
10679:
10675:
10670:
10665:
10661:
10657:
10653:
10649:
10645:
10638:
10636:
10634:
10626:
10622:
10618:
10614:
10610:
10606:
10602:
10598:
10591:
10584:
10579:
10575:
10571:
10567:
10563:
10559:
10552:
10550:
10542:
10537:
10533:
10529:
10525:
10521:
10517:
10510:
10502:
10496:
10492:
10488:
10483:
10478:
10474:
10467:
10459:
10455:
10451:
10447:
10443:
10439:
10435:
10431:
10427:
10420:
10413:
10409:
10407:9781349073573
10403:
10399:
10398:
10390:
10382:
10376:
10368:
10364:
10360:
10356:
10352:
10348:
10344:
10337:
10329:
10325:
10321:
10317:
10313:
10309:
10302:
10295:
10294:
10289:
10285:
10280:
10272:
10268:
10264:
10260:
10256:
10252:
10248:
10244:
10237:
10235:
10228:
10222:
10220:
10209:
10202:
10198:
10194:
10187:
10176:
10172:
10168:
10164:
10160:
10156:
10152:
10148:
10144:
10143:
10135:
10131:
10125:
10123:
10111:
10107:
10101:
10094:
10093:
10085:
10077:
10073:
10069:
10065:
10061:
10054:
10052:
10043:
10037:
10033:
10027:
10025:
10016:
10012:
10008:
10004:
10000:
9996:
9992:
9985:
9983:
9975:
9965:on 2016-03-26
9964:
9960:
9959:Capital Ideas
9956:
9949:
9941:
9939:9780809048922
9935:
9932:. Macmillan.
9931:
9930:
9922:
9914:
9912:9780262545716
9908:
9904:
9897:
9895:
9893:
9884:
9880:
9876:
9872:
9865:
9858:
9850:
9846:
9841:
9836:
9832:
9828:
9824:
9817:
9815:
9806:
9805:
9797:
9789:
9785:
9781:
9777:
9773:
9769:
9765:
9761:
9757:
9750:
9742:
9738:
9734:
9730:
9726:
9720:
9712:
9708:
9704:
9700:
9696:
9692:
9688:
9684:
9683:
9675:
9667:
9661:
9657:
9653:
9652:Black, Duncan
9647:
9645:
9636:
9632:
9628:
9624:
9620:
9616:
9612:
9605:
9597:
9593:
9589:
9585:
9581:
9577:
9573:
9566:
9564:
9555:
9551:
9547:
9543:
9539:
9535:
9534:Public Choice
9531:
9524:
9517:
9513:
9509:
9505:
9501:
9497:
9493:
9489:
9485:
9481:
9474:
9466:
9462:
9458:
9454:
9450:
9446:
9442:
9435:
9427:
9423:
9419:
9415:
9411:
9407:
9403:
9396:
9394:
9385:
9381:
9377:
9373:
9369:
9365:
9361:
9357:
9356:
9349:
9342:
9340:
9338:
9329:
9322:
9315:
9313:
9311:
9309:
9300:
9296:
9292:
9288:
9287:New Scientist
9284:
9277:
9275:
9258:
9254:
9250:
9243:
9235:
9231:
9227:
9223:
9219:
9215:
9211:
9204:
9196:
9192:
9188:
9184:
9180:
9176:
9172:
9168:
9167:
9159:
9151:
9147:
9143:
9139:
9135:
9131:
9124:
9116:
9112:
9108:
9102:
9098:
9097:
9089:
9081:
9075:
9071:
9067:
9063:
9062:
9054:
9043:
9039:
9033:
9026:
9025:
9017:
9015:
9003:
8999:
8995:
8991:
8987:
8983:
8979:
8974:
8969:
8965:
8961:
8960:
8952:
8945:
8943:
8931:
8927:
8923:
8919:
8915:
8911:
8907:
8903:
8899:
8898:
8890:
8886:
8880:
8878:
8876:
8874:
8865:
8861:
8857:
8853:
8849:
8845:
8841:
8834:
8832:
8823:
8816:
8809:
8807:
8805:
8796:
8792:
8788:
8781:
8770:
8766:
8762:
8758:
8754:
8750:
8746:
8742:
8738:
8737:
8729:
8725:
8719:
8711:
8707:
8703:
8699:
8695:
8691:
8687:
8683:
8679:
8672:
8670:
8658:
8654:
8650:
8646:
8642:
8638:
8634:
8630:
8626:
8625:
8617:
8613:
8607:
8599:
8595:
8591:
8584:
8571:
8565:
8561:
8557:
8553:
8549:
8542:
8540:
8531:
8527:
8523:
8519:
8515:
8511:
8507:
8500:
8498:
8496:
8484:
8480:
8474:
8467:
8466:
8458:
8456:
8454:
8452:
8450:
8441:
8437:
8433:
8429:
8425:
8421:
8417:
8413:
8412:
8404:
8396:
8392:
8388:
8384:
8380:
8376:
8372:
8368:
8364:
8357:
8348:
8342:
8338:
8334:
8330:
8324:
8318:
8311:
8307:
8303:
8296:
8289:
8286:
8279:
8275:
8271:
8264:
8257:
8255:
8243:
8239:
8235:
8231:
8227:
8223:
8219:
8212:
8210:
8199:
8192:
8188:
8184:
8177:
8169:
8163:
8159:
8153:
8146:
8141:
8137:
8133:
8131:9781429957649
8127:
8123:
8116:
8108:
8102:
8098:
8094:
8093:Black, Duncan
8088:
8080:
8076:
8072:
8068:
8064:
8060:
8056:
8052:
8048:
8041:
8039:
8037:
8035:
8033:
8024:
8020:
8014:
8009:
8005:
8004:Stable Voting
7998:
7990:
7986:
7982:
7978:
7974:
7970:
7969:Public Choice
7966:
7959:
7951:
7947:
7943:
7939:
7935:
7931:
7927:
7920:
7912:
7908:
7904:
7900:
7896:
7892:
7888:
7884:
7883:
7875:
7867:
7863:
7859:
7855:
7851:
7847:
7843:
7839:
7838:
7830:
7823:
7820:
7816:
7809:
7804:
7800:
7799:Stable Voting
7793:
7786:
7784:
7778:
7776:9780898716955
7772:
7768:
7767:
7759:
7752:
7748:
7744:
7740:
7736:
7732:
7728:
7724:
7720:
7716:
7709:
7701:
7697:
7692:
7687:
7683:
7679:
7675:
7668:
7660:
7656:
7650:
7648:
7631:
7627:
7623:
7616:
7609:
7599:
7595:
7591:
7587:
7583:
7579:
7575:
7571:
7567:
7560:
7558:
7550:
7545:
7541:
7537:
7533:
7529:
7525:
7521:
7514:
7512:
7504:
7502:
7496:
7494:9780898716955
7490:
7486:
7485:
7477:
7469:
7465:
7461:
7457:
7453:
7449:
7445:
7438:
7427:
7423:
7417:
7410:
7409:
7401:
7399:
7397:
7385:
7381:
7377:
7373:
7369:
7365:
7361:
7357:
7353:
7352:
7344:
7340:
7334:
7332:
7330:
7325:
7316:
7313:
7311:
7308:
7306:
7303:
7301:
7298:
7296:
7293:
7291:
7288:
7286:
7285:May's theorem
7283:
7282:
7278:
7272:
7267:
7260:
7258:
7253:
7250:
7246:
7244:
7240:
7236:
7226:
7224:
7220:
7216:
7212:
7208:
7199:
7197:
7179:
7176:
7172:
7168:
7165:
7157:
7152:
7150:
7134:
7130:
7126:
7106:
7102:
7098:
7090:
7089:Supermajority
7081:
7073:
7071:
7066:
7065:psychometrics
7063:derived from
7062:
7061:ballot design
7058:
7054:
7050:
7049:decoy effects
7046:
7045:irrationality
7042:
7033:
7030:
7029:socioeconomic
7026:
7025:Likert scales
7022:
7021:rating scales
7018:
7014:
7010:
7009:psychometrics
7005:
7003:
6999:
6995:
6991:
6987:
6983:
6979:
6975:
6971:
6966:
6964:
6960:
6956:
6952:
6948:
6944:
6940:
6936:
6932:
6931:John Harsanyi
6928:
6925:
6921:
6917:
6913:
6910:
6906:
6902:
6898:
6893:
6891:
6887:
6883:
6879:
6875:
6871:
6867:
6861:
6851:
6849:
6845:
6840:
6838:
6834:
6830:
6826:
6822:
6818:
6817:ranked voting
6808:
6806:
6802:
6797:
6795:
6794:strategyproof
6791:
6787:
6782:
6773:
6771:
6767:
6763:
6760:of voters is
6759:
6755:
6750:
6748:
6747:single-peaked
6743:
6741:
6737:
6733:
6729:
6723:
6713:
6711:
6706:
6702:
6698:
6693:
6691:
6686:
6684:
6680:
6676:
6672:
6668:
6664:
6660:
6658:
6648:
6643:
6638:
6628:
6626:
6622:
6621:ranked voting
6617:
6614:
6598:
6594:
6587:
6580:
6573:
6567:
6560:
6556:
6549:
6544:
6540:
6536:
6533:
6532:
6531:
6518:
6509:
6498:
6495:
6494:
6493:
6484:
6477:
6474:
6473:
6472:
6470:
6466:
6455:
6444:
6441:
6440:
6439:
6437:
6433:
6429:
6425:
6418:
6414:
6410:
6406:
6402:
6398:
6394:
6390:
6386:
6382:
6378:
6374:
6370:
6366:
6362:
6358:
6354:
6350:
6341:
6337:
6333:
6329:
6325:
6321:
6317:
6313:
6309:
6305:
6301:
6296:
6287:
6285:
6281:
6277:
6273:
6269:
6265:
6261:
6257:
6253:
6249:
6245:
6241:
6237:
6233:
6229:
6225:
6221:
6217:
6213:
6209:
6205:
6200:
6198:
6194:
6190:
6189:profile k − 1
6186:
6182:
6178:
6170:
6166:
6162:
6158:
6154:
6151:
6147:
6143:
6139:
6135:
6132:
6128:
6124:
6120:
6116:
6115:
6114:
6112:
6108:
6104:
6101:, and voters
6100:
6096:
6088:
6084:
6080:
6075:
6071:
6069:
6065:
6061:
6057:
6053:
6049:
6045:
6044:pivotal voter
6041:
6037:
6033:
6032:pivotal voter
6029:
6025:
6021:
6011:
6009:
6005:
6001:
5997:
5993:
5989:
5984:
5982:
5978:
5974:
5970:
5966:
5962:
5961:
5957:
5951:
5947:
5944:
5940:
5937:
5933:
5929:
5924:
5922:
5918:
5914:
5910:
5906:
5902:
5898:
5894:
5890:
5886:
5882:
5877:
5875:
5871:
5867:
5863:
5859:
5855:
5851:
5847:
5843:
5839:
5835:
5831:
5823:
5820:
5817:
5814:
5810:
5806:
5802:
5797:
5788:
5784:
5782:
5777:
5776:pivotal voter
5772:
5770:
5769:
5764:
5763:pivotal voter
5759:
5758:
5752:
5751:
5742:
5738:
5721:
5718:
5715:
5690:
5686:
5665:
5662:
5659:
5636:
5633:
5630:
5605:
5601:
5580:
5577:
5574:
5565:
5551:
5548:
5545:
5525:
5522:
5519:
5499:
5496:
5493:
5473:
5464:
5450:
5447:
5444:
5441:
5438:
5429:
5412:
5407:
5403:
5399:
5394:
5390:
5386:
5383:
5381:
5376:
5364:
5359:
5355:
5351:
5346:
5342:
5338:
5335:
5333:
5326:
5322:
5309:
5304:
5300:
5296:
5291:
5287:
5283:
5280:
5278:
5271:
5267:
5249:
5235:
5232:
5229:
5226:
5223:
5216:Fix distinct
5214:
5198:
5194:
5190:
5185:
5181:
5160:
5157:
5137:
5123:
5109:
5106:
5089:
5075:
5055:
5032:
5029:
5026:
5023:
5020:
4997:
4988:
4971:
4968:
4965:
4942:
4933:
4920:
4900:
4897:
4894:
4874:
4871:
4868:
4845:
4842:
4839:
4816:
4813:
4810:
4801:
4787:
4767:
4747:
4742:
4738:
4734:
4714:
4694:
4689:
4685:
4681:
4676:
4672:
4668:
4648:
4645:
4642:
4622:
4602:
4582:
4562:
4553:
4536:
4533:
4530:
4507:
4498:
4484:
4481:
4478:
4458:
4444:
4430:
4427:
4424:
4401:
4398:
4395:
4372:
4356:
4338:
4335:
4332:
4312:
4307:
4303:
4299:
4279:
4271:
4255:
4250:
4246:
4242:
4222:
4199:
4196:
4193:
4182:
4178:
4177:
4176:
4174:
4170:
4165:
4163:
4159:
4151:
4147:
4132:
4129:
4126:
4106:
4101:
4097:
4093:
4085:
4069:
4066:
4063:
4050:
4047:
4043:
4042:
4041:
4038:
4036:
4031:
4030:
4024:
4023:
3994:
3990:
3986:
3983:
3980:
3975:
3971:
3964:
3939:
3935:
3931:
3928:
3925:
3920:
3916:
3909:
3843:
3839:
3816:
3812:
3747:
3722:
3718:
3714:
3711:
3708:
3703:
3699:
3670:
3666:
3662:
3659:
3656:
3651:
3647:
3635:
3633:
3630:
3610:
3606:
3602:
3599:
3596:
3591:
3587:
3583:
3578:
3574:
3567:
3501:
3497:
3386:
3378:
3369:
3361:
3357:
3353:
3350:
3347:
3342:
3338:
3311:
3308:
3305:
3302:
3299:
3293:
3290:
3270:
3262:
3260:
3257:
3237:
3233:
3229:
3226:
3223:
3218:
3214:
3210:
3205:
3201:
3194:
3128:
3124:
3120:
3117:
3114:
3109:
3105:
3052:
3050:
3047:
3046:
3045:
3043:
3039:
3037:
3019:
3011:
3002:
2994:
2990:
2986:
2983:
2980:
2975:
2971:
2960:
2944:
2924:
2898:
2884:
2876:
2867:
2855:
2854:
2853:
2851:
2848:
2847:
2830:
2807:
2781:
2756:
2726:
2657:
2629:
2597:
2569:
2533:
2517:
2502:
2474:
2446:
2418:
2390:
2362:
2346:
2345:
2344:
2330:
2327:
2324:
2304:
2296:
2280:
2272:
2269:
2265:
2249:
2241:
2240:
2235:
2219:
2205:
2203:
2199:
2195:
2190:
2185:
2171:
2151:
2131:
2111:
2091:
2071:
2051:
2031:
2011:
1991:
1971:
1951:
1931:
1911:
1897:
1894:
1891:
1888:
1887:
1883:
1880:
1877:
1874:
1873:
1869:
1866:
1863:
1860:
1859:
1855:
1852:
1849:
1846:
1845:
1842:
1828:
1808:
1788:
1780:
1776:
1762:
1760:
1751:
1750:
1749:
1747:
1737:
1733:
1729:
1714:
1711:
1708:
1688:
1685:
1682:
1662:
1659:
1656:
1648:
1647:
1644:
1638:
1632:
1626:
1621:
1620:
1618:
1613:
1612:
1611:
1608:
1602:
1596:
1591:
1590:
1585:
1575:
1573:
1569:
1565:
1561:
1557:
1556:nonperversity
1546:
1540:
1534:
1528:
1523:
1522:
1517:
1514:
1513:
1511:
1510:
1506:
1505:
1499:
1495:
1492:
1488:
1487:
1483:This weakens
1482:
1481:
1479:
1478:
1477:
1472:
1471:
1465:
1464:majority rule
1461:
1458:
1454:
1453:
1451:
1448:, not just a
1447:
1443:
1439:
1438:
1434:
1433:
1432:
1430:
1420:
1418:
1402:
1399:
1396:
1376:
1373:
1370:
1350:
1347:
1344:
1336:
1331:
1325:
1308:
1305:
1302:
1293:
1287:
1282:
1278:
1272:
1257:
1255:
1251:
1247:
1243:
1239:
1235:
1234:voting system
1231:
1227:
1223:
1219:
1215:
1211:
1207:
1201:
1197:
1193:
1183:
1181:
1177:
1173:
1169:
1164:
1160:
1156:
1154:
1150:
1146:
1142:
1141:ranked voting
1138:
1134:
1130:
1126:
1122:
1119:methods like
1118:
1114:
1112:
1108:
1104:
1100:
1096:
1091:
1089:
1085:
1081:
1065:
1057:
1056:voting theory
1053:
1037:
1017:
997:
989:
988:
983:
979:
975:
974:Kenneth Arrow
971:
970:social choice
967:
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
45:
44:
40:
36:
32:
31:
19:
13105:
12939:Peyton Young
12934:Paul Milgrom
12849:Hervé Moulin
12789:Amos Tversky
12731:Folk theorem
12442:-player game
12439:
12364:Grim trigger
11969:Preparedness
11883:
11801:Productivity
11781:Mandeville's
11573:Opposite Day
11501:Burali-Forti
11496:Bhartrhari's
11306:
11278:
11274:
11251:
11228:
11205:
11184:
11155:
11151:
11114:
11110:
11078:
11044:. Retrieved
11033:
11000:
10997:Econometrica
10996:
10986:
10977:
10944:
10937:
10920:
10916:
10910:
10877:
10874:Econometrica
10873:
10835:
10831:
10821:
10788:
10784:
10778:
10753:
10749:
10739:
10717:(1): 90–98.
10714:
10710:
10704:
10651:
10647:
10624:
10607:(1): 44–57.
10604:
10600:
10590:
10581:
10561:
10557:
10539:
10519:
10515:
10509:
10472:
10466:
10436:(1): 81–94.
10433:
10430:Econometrica
10429:
10419:
10411:
10396:
10389:
10375:cite journal
10350:
10346:
10336:
10311:
10308:Econometrica
10307:
10301:
10291:
10279:
10246:
10242:
10226:
10207:
10201:the original
10196:
10186:
10175:the original
10146:
10140:
10091:
10084:
10067:
10063:
10041:
9998:
9994:
9973:
9967:. Retrieved
9963:the original
9958:
9948:
9928:
9921:
9902:
9874:
9870:
9857:
9830:
9826:
9803:
9796:
9763:
9760:Econometrica
9759:
9749:
9732:
9728:
9719:
9686:
9680:
9674:
9655:
9618:
9614:
9604:
9579:
9575:
9537:
9533:
9523:
9515:
9487:
9483:
9473:
9448:
9444:
9434:
9409:
9405:
9359:
9353:
9327:
9290:
9286:
9261:. Retrieved
9257:the original
9252:
9242:
9217:
9213:
9203:
9170:
9164:
9158:
9136:(1): 13–16.
9133:
9129:
9123:
9095:
9088:
9060:
9053:
9023:
8963:
8957:
8930:the original
8901:
8895:
8847:
8843:
8821:
8794:
8790:
8780:
8769:the original
8740:
8734:
8718:
8685:
8681:
8657:the original
8628:
8622:
8606:
8597:
8593:
8583:
8573:, retrieved
8551:
8513:
8509:
8464:
8415:
8409:
8403:
8370:
8367:Econometrica
8366:
8356:
8346:
8328:
8322:
8316:
8310:the original
8305:
8295:
8284:
8283:
8278:the original
8273:
8263:
8253:
8251:
8245:. Retrieved
8225:
8221:
8197:
8191:the original
8186:
8176:
8167:
8152:
8143:
8121:
8115:
8096:
8087:
8057:(1): 23–34.
8054:
8050:
8022:
8018:
8003:
7997:
7972:
7968:
7958:
7933:
7929:
7919:
7886:
7880:
7874:
7841:
7835:
7829:
7818:
7814:
7812:
7798:
7792:
7782:
7780:
7765:
7758:
7750:
7722:
7718:
7708:
7681:
7677:
7667:
7658:
7634:. Retrieved
7630:the original
7625:
7615:
7607:
7601:. Retrieved
7573:
7569:
7547:
7527:
7523:
7500:
7498:
7483:
7476:
7451:
7447:
7437:
7407:
7384:the original
7355:
7349:
7254:
7247:
7232:
7205:
7196:quasiconcave
7153:
7087:
7079:
7039:
7006:
7002:score voting
6978:David Pearce
6967:
6929:
6924:rated voting
6914:
6894:
6863:
6841:
6825:score voting
6814:
6798:
6790:Eitan Muller
6783:
6779:
6758:distribution
6751:
6746:
6744:
6728:Duncan Black
6725:
6694:
6690:intransitive
6687:
6682:
6678:
6674:
6670:
6656:
6652:
6646:
6625:rated voting
6618:
6612:
6610:
6596:
6592:
6585:
6578:
6571:
6565:
6558:
6554:
6547:
6542:
6538:
6529:
6515:
6507:
6496:
6491:
6482:
6475:
6468:
6464:
6462:
6453:
6442:
6435:
6431:
6427:
6423:
6416:
6412:
6408:
6404:
6400:
6396:
6392:
6388:
6384:
6380:
6376:
6372:
6368:
6364:
6360:
6356:
6352:
6348:
6345:
6339:
6335:
6331:
6327:
6323:
6319:
6315:
6311:
6307:
6303:
6299:
6283:
6279:
6275:
6267:
6263:
6259:
6255:
6251:
6247:
6243:
6239:
6235:
6231:
6227:
6223:
6219:
6215:
6211:
6210:, but keeps
6207:
6203:
6201:
6196:
6192:
6188:
6184:
6180:
6176:
6174:
6168:
6164:
6160:
6156:
6149:
6145:
6141:
6137:
6130:
6126:
6122:
6118:
6110:
6106:
6102:
6098:
6094:
6092:
6086:
6082:
6078:
6067:
6063:
6059:
6055:
6051:
6047:
6043:
6039:
6035:
6031:
6027:
6023:
6019:
6017:
6007:
6003:
5999:
5995:
5991:
5987:
5985:
5980:
5976:
5968:
5964:
5959:
5955:
5953:
5949:
5945:
5942:
5938:
5935:
5934:, for which
5931:
5927:
5925:
5920:
5916:
5912:
5908:
5904:
5900:
5896:
5892:
5888:
5884:
5880:
5878:
5873:
5869:
5865:
5861:
5857:
5853:
5849:
5845:
5841:
5837:
5833:
5829:
5827:
5821:
5818:
5815:
5812:
5808:
5804:
5800:
5785:
5775:
5773:
5766:
5762:
5760:
5740:
5566:
5465:
5430:
5250:
5215:
5129:
5092:
4989:
4934:
4802:
4554:
4499:
4450:
4358:
4354:
4272:every voter
4269:
4180:
4166:
4157:
4155:
4149:
4052:
4045:
4040:Definition:
4039:
4034:
4032:
4017:Formal proof
3041:
3040:
3035:
2916:
2849:
2845:
2614:The element
2613:
2343:satisfying:
2238:
2234:alternatives
2233:
2232:be a set of
2211:
2186:
1903:
1773:
1756:
1743:
1642:
1636:
1630:
1624:
1615:
1614:
1606:
1600:
1594:
1587:
1581:
1563:
1559:
1553:
1544:
1538:
1532:
1526:
1519:
1508:
1507:
1497:
1485:
1475:
1473:
1456:
1436:
1435:
1426:
1329:
1323:
1291:
1285:
1274:
1240:, or even a
1238:constitution
1203:
1157:
1115:
1092:
1078:is called a
985:
965:
964:
856:
855:
829:
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
181:
180:
113:
13056:Coopetition
12859:Jean Tirole
12854:John Conway
12834:Eric Maskin
12630:Blotto game
12615:Pirate game
12424:Global game
12394:Tit for tat
12329:Bid shading
12319:Appeasement
12169:Equilibrium
12149:Solved game
12084:Determinacy
12067:Definitions
12060:game theory
11899:Condorcet's
11751:Giffen good
11711:Competition
11465:White horse
11440:Omnipotence
10838:(1): 1–17.
8254:unavailable
7068:context of
7032:feelings".
7017:reliability
6970:dictatorial
6943:VNM theorem
6909:Amartya Sen
6111:segment two
6099:segment one
5899:, but move
4935:Similarly,
4803:By Pareto,
4780:outside of
4169:Amartya Sen
2590:must be in
2200:, based on
1753:blueberry."
1578:Rationality
1265:Preferences
1214:preferences
1149:cyclic ties
664:Single vote
567:Conditional
562:Coexistence
411:Quota Borda
401:Schulze STV
359:Closed list
302:STAR voting
247:Borda count
13123:Categories
12700:Trust game
12685:Kuhn poker
12354:Escalation
12349:Deterrence
12339:Cheap talk
12311:Strategies
12129:Preference
12058:Topics of
11974:Prevention
11964:Parrondo's
11954:Navigation
11939:Inventor's
11934:Hedgehog's
11894:Chainstore
11877:Population
11872:New states
11806:Prosperity
11786:Mayfield's
11628:Entailment
11608:Barbershop
11521:Epimenides
11180:Hunt, Earl
10208:Dr. Arrow:
10036:p. 33
9969:2016-09-05
8797:(16): 1–7.
8600:(16): 1–7.
8575:2024-07-20
8347:Dr. Arrow:
8323:Dr. Arrow:
8285:Dr. Arrow:
8247:2020-03-20
8198:Dr. Arrow:
8162:p. 33
8013:2108.00542
7808:2108.00542
7603:2020-03-20
7321:References
7219:almost all
6937:and other
6878:well-being
6786:Ehud Kalai
6563:such that
2268:transitive
2239:preference
1560:increasing
1335:transitive
1186:Background
1129:situations
769:Truncation
498:Cumulative
321:Party-list
96:By country
87:Comparison
12884:John Nash
12590:Stag hunt
12334:Collusion
11989:Willpower
11984:Tolerance
11959:Newcomb's
11924:Fredkin's
11811:Scitovsky
11731:Edgeworth
11726:Easterlin
11691:Antitrust
11588:Russell's
11583:Richard's
11556:Pinocchio
11511:Crocodile
11430:Newcomb's
11400:Goodman's
11395:Free will
11380:Epicurean
11351:paradoxes
11172:145127710
11017:0012-9682
10894:0012-9682
10852:0165-4896
10813:143974563
10805:0022-2437
10770:0162-895X
10731:120998684
10678:0027-8424
10621:0022-1015
10578:0197-3533
10536:1099-0992
10477:CiteSeerX
10450:0012-9682
10367:1474-0028
10271:222434288
10015:0315-0860
10001:: 56–87.
9849:1572-9966
9780:0012-9682
9711:122290254
9635:1573-7187
9596:1572-9966
9554:1573-7101
9504:0092-5853
9465:1573-7187
9426:0165-4896
9384:122290254
9234:0022-0531
9195:121998270
9150:0165-1765
9115:29649010M
8968:CiteSeerX
8864:0165-4896
8702:0092-5853
8530:0022-0531
8440:122290254
8387:0012-9682
8242:1573-7187
8140:872601019
8071:0022-3808
7989:1573-7101
7950:1573-7187
7911:122290254
7866:122290254
7739:0092-5853
7700:1432-217X
7590:0315-4890
7544:0022-3808
7468:0022-0531
7177:−
7169:−
6941:like the
6866:orderings
6784:In 1977,
6673:ahead of
6659:, methods
6657:Condorcet
6232:profile k
6030:, as the
5988:profile 0
5917:Profile 2
5909:profile 1
5897:profile 0
5893:profile i
5874:profile 0
5663:≻
5578:≻
5549:≻
5523:≻
5497:≻
5404:≻
5391:≻
5356:≻
5343:≻
5301:≻
5288:≻
5158:≥
5107:≥
4921:◻
4898:≻
4872:≻
4814:≻
4739:≻
4686:≻
4673:≻
4428:≠
4417:for some
4336:≻
4304:≻
4247:≻
4130:≻
4098:≻
4046:coalition
3984:…
3929:…
3712:…
3660:…
3600:…
3373:Π
3370:∈
3351:…
3306:…
3294:∈
3227:…
3118:…
3006:Π
3003:∈
2984:…
2893:Π
2890:→
2871:Π
2802:Π
2727:≻
2650:being in
2328:×
2189:Condorcet
1712:≻
1686:≻
1660:≻
1486:anonymity
1400:⪰
1374:⪰
1348:⪰
1306:≻
1174:(such as
1143:uniquely
1105:based on
676:Dual-vote
369:Panachage
364:Open list
354:List type
232:Plurality
128:Two-round
116:plurality
39:Economics
13025:Lazy SMP
12719:Theorems
12670:Deadlock
12525:Checkers
12406:of games
12173:concepts
12017:Category
11914:Ellsberg
11766:Leontief
11746:Gibson's
11741:European
11736:Ellsberg
11706:Braess's
11701:Bertrand
11679:Economic
11613:Catch-22
11593:Socratic
11435:Nihilism
11405:Hedonism
11365:Analysis
11349:Notable
11227:(1979).
11182:(2007).
11144:preprint
11131:41106398
11076:(eds.).
10696:36191179
10171:13923619
10132:(1950).
10110:Archived
9703:25055296
9654:(1968).
9376:25055296
9187:41486021
9042:Archived
9002:Archived
8998:17101545
8990:25055941
8926:13923619
8887:(1950).
8765:13923619
8726:(1950).
8653:13923619
8614:(1950).
8483:Archived
8432:25055296
8095:(1968).
7903:25055296
7858:25055296
7769:. SIAM.
7487:. SIAM.
7426:Archived
7380:13923619
7341:(1950).
7263:See also
7207:Fishburn
7053:Balinski
7013:validity
6982:nihilism
6972:(or non-
6955:Harsanyi
6916:Balinski
6901:nihilism
6870:rankings
6338:through
6105:through
5973:a priori
5971:is not,
5781:dictator
4162:dictator
4150:decisive
3401:and all
2264:complete
1889:Voter 3
1875:Voter 2
1861:Voter 1
1058:, where
396:Hare STV
35:Politics
33:A joint
12777:figures
12560:Chicken
12414:Auction
12404:Classes
11919:Fenno's
11884:Arrow's
11867:Alabama
11857:Abilene
11836:Tullock
11791:Metzler
11633:Lottery
11623:Drinker
11566:Yablo's
11561:Quine's
11516:Curry's
11479:Logical
11455:Sorites
11445:Preface
11425:Moore's
11410:Liberal
11385:Fiction
11139:7589377
11025:1914083
10902:1912699
10687:9586273
10656:Bibcode
10458:1906944
10328:1906925
10263:1827128
10163:1828886
9788:1909727
9512:3088418
9263:9 March
8918:1828886
8757:1828886
8710:2110496
8645:1828886
8395:1914083
8079:1825026
7747:3088418
7636:9 March
7372:1828886
7223:measure
6959:Vickrey
6627:rules.
6324:outside
5811:is the
5678:, then
5593:, then
4887:. Thus
4500:Claim:
4325:, then
3445:, when
3143:, then
2459:, then
2194:markets
1765:Theorem
1572:runoffs
1558:, i.e.
1389:, then
1279:, i.e.
1246:ethical
1218:beliefs
1208:called
406:CPO-STV
256:Baldwin
205:Schulze
200:Minimax
118:methods
11826:Thrift
11796:Plenty
11771:Lerner
11761:Jevons
11756:Icarus
11686:Allais
11648:Ross's
11486:Barber
11470:Zeno's
11415:Meno's
11258:
11235:
11212:
11192:
11170:
11137:
11129:
11086:
11023:
11015:
10951:
10900:
10892:
10850:
10811:
10803:
10768:
10729:
10694:
10684:
10676:
10619:
10576:
10534:
10497:
10479:
10456:
10448:
10404:
10365:
10326:
10269:
10261:
10169:
10161:
10102:
10013:
9936:
9909:
9847:
9786:
9778:
9709:
9701:
9662:
9633:
9594:
9552:
9510:
9502:
9463:
9424:
9382:
9374:
9232:
9193:
9185:
9148:
9113:
9103:
9076:
9034:
8996:
8988:
8970:
8924:
8916:
8862:
8763:
8755:
8708:
8700:
8651:
8643:
8566:
8528:
8475:
8438:
8430:
8393:
8385:
8240:
8138:
8128:
8103:
8077:
8069:
7987:
7948:
7909:
7901:
7864:
7856:
7773:
7745:
7737:
7698:
7598:138144
7596:
7588:
7542:
7491:
7466:
7418:
7378:
7370:
7057:Laraki
7023:(e.g.
7000:(i.e.
6986:egoism
6974:egoist
6920:Laraki
6905:egoism
6613:always
6379:above
6266:above
6254:above
6246:above
6238:above
6218:below
6206:above
6195:above
6179:above
6167:above
6159:above
6148:above
6140:above
6129:above
6121:above
6046:ranks
5941:moves
5926:Since
5836:, and
5466:Since
3957:as in
3831:as in
2823:. Let
2495:is in
2439:is in
2383:is in
2064:, and
1821:, and
1498:social
1321:means
1230:market
1198:, and
1133:forced
271:Coombs
41:series
12515:Chess
12502:Games
11929:Green
11909:Downs
11841:Value
11776:Lucas
11643:Raven
11551:No-no
11506:Court
11491:Berry
11168:S2CID
11135:S2CID
11127:JSTOR
11107:(PDF)
11046:5 May
11021:JSTOR
10898:JSTOR
10809:S2CID
10727:S2CID
10454:JSTOR
10324:JSTOR
10267:S2CID
10259:JSTOR
10178:(PDF)
10167:S2CID
10159:JSTOR
10137:(PDF)
10113:(PDF)
10096:(PDF)
9867:(PDF)
9784:JSTOR
9707:S2CID
9699:JSTOR
9508:JSTOR
9380:S2CID
9372:JSTOR
9324:(PDF)
9191:S2CID
9183:JSTOR
9045:(PDF)
9028:(PDF)
9005:(PDF)
8994:S2CID
8986:JSTOR
8954:(PDF)
8933:(PDF)
8922:S2CID
8914:JSTOR
8892:(PDF)
8818:(PDF)
8772:(PDF)
8761:S2CID
8753:JSTOR
8731:(PDF)
8706:JSTOR
8660:(PDF)
8649:S2CID
8641:JSTOR
8619:(PDF)
8486:(PDF)
8469:(PDF)
8436:S2CID
8428:JSTOR
8391:JSTOR
8075:JSTOR
8008:arXiv
7907:S2CID
7899:JSTOR
7862:S2CID
7854:JSTOR
7803:arXiv
7743:JSTOR
7594:JSTOR
7429:(PDF)
7412:(PDF)
7387:(PDF)
7376:S2CID
7368:JSTOR
7346:(PDF)
6831:pass
6679:Alice
6671:Alice
6591:, …,
6553:, …,
6426:over
6411:over
6403:over
6387:over
6359:over
6351:over
6330:over
6314:over
6306:over
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