Probabilities of electoral outcomes: from three-candidate to four-candidate elections

Ouafdi, Abdelhalim El; Lepelley, Dominique

doi:10.1007/s11238-019-09724-5

Cited by 15 publications

(4 citation statements)

References 20 publications

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“…For three candidates elections a detailed study of the family of Borda paradoxes 12 is contained in 29 , while the case of four candidates is discussed in Section 2.5 4 . According to 22 , similar results were obtained independently in 27 .…”

Section: A Challenging Computational Problem Arising From Social Choicesupporting

confidence: 78%

“…In the case of four candidates the plurality voting versus plurality runoff problem was first computed by De Loera, Dutra, Köppe, Moreinis, Pinto and Wu in 25 using LattE Integrale 26 for the volume computation.The Condorcet efficiency of plurality voting was first computed by Schürmann in 3 , whereas the Condorcet efficiency of the runoff plurality voting was given in 4 . According to 22 , it was obtained independently in 4 and 27 . In Section 6 5 we additionally discuss the influence of a third ballot on the Condorcet efficiencies of plurality and negative plurality.…”

Section: A Challenging Computational Problem Arising From Social Choicementioning

confidence: 99%

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Computations of volumes in five candidates elections

Bruns

Ichim

2023

Sci Rep

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We describe several analytical (i.e., precise) results obtained in five candidates social choice elections under the assumption of the Impartial Anonymous Culture. These include the Condorcet and Borda paradoxes, as well as the Condorcet efficiency of plurality, negative plurality and Borda voting, including their runoff versions. The computations are done by Normaliz. It finds precise probabilities as volumes of polytopes in dimension 119, using its recent implementation of the Lawrence algorithm.

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Section: A Challenging Computational Problem Arising From Social Choicesupporting

confidence: 78%

Section: A Challenging Computational Problem Arising From Social Choicementioning

confidence: 99%

Computations of volumes in five candidates elections

Bruns

Ichim

2023

Sci Rep

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“…As we only deal with large electorates, we follow a procedure that was developed in Cervone et al (2005). This technique which is based on the computation of polytope volumes has recently been used in many research papers; see among others Diss andGehrlein (2015, 2012), Diss et al (2020Diss et al ( , 2018, El Ouafdi et al (2020), Gehrlein et al (2015), Kamwa (2019), Kamwa and Moyouwou (2021), Kamwa and Valognes (2017), Moyouwou and Tchantcho (2015). In the online supplementary material we report Propositions 8 to 10 which give the probability representations that we obtain from this technique.…”

Section: Computation Resultsmentioning

confidence: 99%

Scoring rules, ballot truncation, and the truncation paradox

Kamwa

2022

Public Choice

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A voting rule that permits some voters to favor a candidate by providing only the initial segment of their sincere rankings is said to be vulnerable to the truncation paradox. In this paper, we consider four models for counting truncated ballots, optimistic, pessimistic (the most common), averaged, and round-down. Under the impartial anonymous culture assumption, the choice of model generally has a real impact on truncation-paradox vulnerability, but there are exceptions. When the election is decided by a one-shot scoring rule, the optimistic model is invulnerable to the truncation paradox, but all other models are vulnerable. We identify new voting rules immune to the truncation paradox, such as the Modified Borda Count. To obtain a more complete picture of the impact of processing model, we assess the likelihood of the truncation paradox in three-candidate elections with large electorates, focusing not only on oneshot scoring rules but also scoring rules with one-by-one or below-average elimination. Our assessment confirms that the processing model for truncated ballots may really matter.

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“…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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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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Probabilities of electoral outcomes: from three-candidate to four-candidate elections

Cited by 15 publications

References 20 publications

Computations of volumes in five candidates elections

Computations of volumes in five candidates elections

Scoring rules, ballot truncation, and the truncation paradox

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

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