The Probability of a Cyclical Majority

DeMeyer, Frank; Plott, Charles R.

doi:10.2307/1913015

Cited by 113 publications

(48 citation statements)

References 7 publications

(10 reference statements)

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“…Dual cultures have been criticized for being too unrealistic (Regenwetter et al, 2006). Nevertheless, they are relevant for their susceptibility to analytical methods that helped to improve the understanding of voting phenomena (see, e.g., (DeMeyer and Plott, 1970)). If we add anonymity by having indistinguishable voters, the set of profiles is partitioned into equivalence classes.…”

Section: Stochastic Modelsmentioning

confidence: 99%

On the Discriminative Power of Tournament Solutions

Brandt

Seedig

2016

Operations Research Proceedings

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Tournament solutions constitute an important class of social choice functions that only depend on the pairwise majority comparisons between alternatives. Recent analytical results have shown that several concepts with appealing axiomatic properties such as the Banks set or the minimal covering set tend to not discriminate at all when the tournaments are chosen from the uniform distribution. This is in sharp contrast to empirical studies which have found that real-world preference profiles often exhibit Condorcet winners, i.e., alternatives that all tournament solutions select as the unique winner. In this work, we aim to fill the gap between these extremes by examining the distribution of the number of alternatives returned by common tournament solutions for empirical data as well as data generated according to stochastic preference models such as impartial culture, impartial anonymous culture, Mallows mixtures, spatial models, and Pólya-Eggenberger urn models.

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Section: Stochastic Modelsmentioning

confidence: 99%

On the Discriminative Power of Tournament Solutions

Brandt

Seedig

2016

Operations Research Proceedings

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“…He was not able to give further calculations but he conjectured that the probability of the paradox "increases rapidly with an increase in the number of motions" (Black 1958: 51). Since Black, several researchers have calculated the probabilities of the Condorcet paradox by means of computer simulations (Campbell and Tullock, 1965;Klahr, 1966) as well as by means of analytical expressions (DeMeyer and Plott, 1970;May, 1971;Niemi and Weisberg, 1968;Garman and Kamien, 1968;Gehrlein and Fishburn, 1976;Gehrlein, 1983). The general conclusion to be drawn from the calculations is that, indeed, the probabilities rapidly increase with an increasing number of voters but this increase is less than in the case of a growing number of alternatives.…”

Section: The Relevance Of the Condorcet Paradoxmentioning

confidence: 99%

Empirical evidence of paradoxes of voting in Dutch elections

Deemen

Vergunst

1998

Empirical Studies in Comparative Politics

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Abstract.In this paper we analyze four national elections held in 1982, 1986, 1989 and 1994 in the Netherlands on the occurrence of the Condorcet paradox. In addition, we investigate these elections on the occurrence of three so-called majority-plurality paradoxes. The first paradox states that a party having a majority over another party may receive less seats. The second states that a Condorcet winner may not receive the largest number of seats and even may not receive a seat at all. The third says that the majority relation may be the reverse of the ranking of parties in terms of numbers of seats.

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“…The impartial culture is usually defined as a uniform distribution over all linear orders (DeMeyer and Plott, 1970;Gehrlein and Fishburn, 1976) and occasionally defined as a uniform distribution over weak orders (Jones et al, 1995;Van Deemen, 1999). The most canonical generalization of the impartial culture to an arbitrary set of binary relations is therefore a uniform distribution over that set of relations.…”

Section: Generalizing the Impartial Culture And Related Cultures Ofmentioning

confidence: 99%

A general concept of majority rule

Regenwetter

Marley

Grofman

2002

Mathematical Social Sciences

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We develop a general concept of majority rule for finitely many choice alternatives that is consistent with arbitrary binary preference relations, real-valued utility functions, probability distributions over binary preference relations, and random utility representations. The underlying framework is applicable to virtually any type of choice, rating, or ranking data, not just the linear orders or paired comparisons assumed by classic majority rule social welfare functions. Our general definition of majority rule for arbitrary binary relations contains the standard definition for linear orders as a special case. 

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The Probability of a Cyclical Majority

Cited by 113 publications

References 7 publications

On the Discriminative Power of Tournament Solutions

On the Discriminative Power of Tournament Solutions

Empirical evidence of paradoxes of voting in Dutch elections

A general concept of majority rule

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