Computations of volumes and Ehrhart series in four candidates elections

Bruns, Winfried; Ichim, Bogdan; Söger, Christof

doi:10.1007/s10479-019-03152-y

Cited by 20 publications

(32 citation statements)

References 28 publications

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“…This package works with the same general procedure that was implemented in Cervone et al (2005) and recently used in other studies, e.g., Diss and Doghmi (2016), Gehrlein (2015, 2012), Gehrlein et al (2015) and Moyouwou and Tchantcho (2017). This technique is used in this paper in order to obtain all our exact results for m = 3 and m = 4, except for the probabilities displayed in Table 11 for which we used Normaliz (Bruns et al, 2017(Bruns et al, , 2019 which works with the same procedure as Convex. However, the two methods are not efficient when, as in this paper, the number of candidates is equal to 5 and 6.…”

Section: Methodsmentioning

confidence: 99%

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On Some k -scoring Rules for Committee Elections: Agreement and Condorcet Principle

Diss¹,

Kamwa²,

Tlidi³

2020

Revue d'Économie Politique

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Given a collection of individual preferences on a set of candidates and a desired number of winners, a multi-winner voting rule outputs groups of winners, which we call committees. In this paper, we consider five multi-winner voting rules widely studied in the literature of social choice theory: the k-Plurality rule, the k-Borda rule, the k-Negative Plurality rule, the Bloc rule, and the Chamberlin-Courant rule. The objective of this paper is to provide a comparison of these multi-winner voting rules according to many principles by taking into account a probabilistic approach using the well-known Impartial Anonymous Culture (IAC) assumption. We first evaluate the probability that each pair of the considered voting rules selects the same unique committee in order to identify which multi-winner rules are the most likely to agree for a given number of candidates and a fixed target size of the committee. In this matter, our results show that the Chamberlin-Courant rule and the k-Plurality rule on one side, and the k-Borda rule and the Bloc rule on the other side, are the pairs of rules that most agree in comparison to other pairs. Furthermore, we evaluate the probability of every multi-winner voting rule selecting the Condorcet committee à la Gehrlein when it exists. The Condorcet committee à la Gehrlein is a fixed-size committee such that every member defeats every non-member in

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Section: Methodsmentioning

confidence: 99%

“…We emphasize that this paper is one of the rare contributions in the literature giving exact results under the Impartial Anonymous Culture (IAC) condition for the case of four candidates. To the best of our knowledge, the only papers in this category are: Bruns et al (2019), Bubboloni et al (2018), Doghmi (2016), andEl Ouafdi et al (2018).…”

Section: Introductionmentioning

confidence: 99%

On Some k -scoring Rules for Committee Elections: Agreement and Condorcet Principle

Diss¹,

Kamwa²,

Tlidi³

2020

Revue d'Économie Politique

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“…However, recent developments within the polytope theory allow us to obtain exact results for the case of four candidates with the algorithm Normaliz (Bruns et al, 2017a) which is, to the best of our knowledge, the only program able to compute the number of voting situations in polytopes corresponding to elections with up to four candidates. The reader is referred to Bruns et al (2017b) who describe several results obtained in four-candidate elections with Normaliz. Notice that this software needs relatively high memory when the number of voters increases.…”

Section: More Than Three Candidatesmentioning

confidence: 99%

Social acceptability of Condorcet committees

Diss¹,

Mahajne

2020

Mathematical Social Sciences

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We define and examine the concept of social acceptability of committees, in multi-winner elections context. We say that a committee is socially acceptable if each member in this committee is socially acceptable, i.e., the number of voters who rank her in their top half of the candidates is at least as large as the number of voters who rank her in the least preferred half, otherwise she is unacceptable. We focus on the social acceptability of Condorcet committees, where each committee member beats every nonmember by a majority, and we show that a Condorcet committee may be completely unacceptable, i.e., all its members are unacceptable. However, if the preferences of the voters are single-peaked or singlecaved and the committee size is not "too large" then a Condorcet committee must be socially acceptable, but if the preferences are single-crossing or group-separable, then a Condorcet committee may be socially acceptable but may not. Furthermore, we evaluate the probability for a Condorcet committee, when it exists, to be socially (un)acceptable under Impartial Anonymous Culture (IAC) assumption. It turns to be that, in general, Condorcet committees are significantly exposed to social unacceptability.. AbstractWe define and examine the concept of social acceptability of committees, in multi-winner elections context. We say that a committee is socially acceptable if each member in this committee is socially acceptable, i.e., the number of voters who rank her in their top half of the candidates is at least as large as the number of voters who rank her in the least preferred half, otherwise she is unacceptable.We focus on the social acceptability of Condorcet committees, where each committee member beats every non-member by a majority, and we show that a Condorcet committee may be completely unacceptable, i.e., all its members are unacceptable. However, if the preferences of the voters are single-peaked or single-caved and the committee size is not "too large" then a Condorcet committee must be socially acceptable, but if the preferences are single-crossing or group-separable, then a Condorcet committee may be socially acceptable but may not. Furthermore, we evaluate the probability for a Condorcet committee, when it exists, to be socially (un)acceptable under Impartial Anonymous Culture (IAC) assumption. It turns to be that, in general, Condorcet committees are significantly exposed to social unacceptability.

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“…A Maple procedure is also available from authors upon request. Of course, there is an abundant literature on volume computations with very efficient algorithms and packages such as Büeler et al (2000) and Lawrence (1991) for Maple users or Bruns and Ichim (2010) and Bruns et al (2019Bruns et al ( , 2018.…”

Section: B Computation Details For Propositionmentioning

confidence: 99%