Extensions of the Simpson voting rule to the committee selection setting

Bubboloni, Daniela; Diss, Mostapha; Gori, Michele

doi:10.1007/s11127-019-00692-6

Cited by 14 publications

(6 citation statements)

References 46 publications

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“…As mentioned in the introduction, there has been a significant interest over the past three decades in developing representations for the probability of interesting voting events under the two aforementioned assumptions. The most significant part of the research on these probabilities make use of analytical and geometrical techniques in order to obtain exact theoretical probabilities of the studied voting events in the case of three-alternative elections and more recently in the case of four-alternative elections (see, for instance, Brandt et al, 2020aBrandt et al, , 2020bBruns and Söger, 2015;Bruns et al, 2019;Bubboloni et al, 2020;Diss el al., 2020;vEl Ouafdi et al, 2020aKamwa and Merlin, 2019). However, it turns out that in our framework the implementation of those techniques are difficult to manage.…”

Section: Computational Resultsmentioning

confidence: 99%

Majority properties of positional social preference correspondences

Diss¹,

Gori

2021

Theory Decis

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We characterize the positional social preference correspondences (spc) satisfying the qualified majority property for any given majority threshold. We also characterize the positional spcs satisfying the minimal majority property. We next evaluate the probability that the Borda, the Plurality and the Antiplurality spcs fulfil the two aforementioned properties under two assumptions on individuals' preferences in the presence of three and four alternatives for various sizes of the society. Our results show that the Borda spc is the positional spc which better behaves in relation with the qualified majority principle and the minimal majority principle. Finally, we propose some remarks on the concept of Condorcet consistency for social choice correspondences.

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Section: Computational Resultsmentioning

confidence: 99%

Majority properties of positional social preference correspondences

Diss¹,

Gori

2021

Theory Decis

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“…For more details on these algorithms and their use in social choice theory, the reader may refer to Cervone et al (2005) and Moyouwou and Tchantcho (2017). These techniques have recently been used under different forms by Bubboloni et al (2020), Doghmi (2016), El Ouafdi et al (2020), Kamwa (2019), Kamwa and Moyouwou (2020), Lepelley et al (2018), and Lepelley and Smaoui (2019), among others.…”

Section: Infinite Total Weightsmentioning

confidence: 99%

Inconsistent weighting in weighted voting games

Béal¹,

Deschamps²,

Diss³

et al. 2022

Public Choice

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In a weighted voting game, each voter has a given weight and a coalition of voters is successful if the sum of its weights exceeds a given quota. Such voting systems translate the idea that voters are not all equal by assigning them different weights. In such a situation, two voters are symmetric in a game if interchanging the two voters leaves the outcome of the game unchanged. Two voters with the same weight are naturally symmetric in every weighted voting game, but the converse statement is not necessarily true. We call this latter type of scenario inconsistent weighting. We investigate the conditions that give rise to such a phenomenon within the class of weighted voting games. We also study how the choice of the quota and the total weight can affect the probability of observing inconsistent weighting. Finally, we investigate various applications where inconsistent weighting is observed.

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“…The Copeland rule picks the candidate who fares better in pairwise comparisons the largest number of times: arg max i ( j r ij ) where r ij stands for the number of times candidate i fares better against candidate j in the voter preferences. Maximin, also known as Simpson's rule, picks the candidate for whom the candidate who fares the best against him/her in pairwise comparisons has the least pairwise score: arg min i (max j r ji ) [Bubboloni et al, 2020]. The Kemeny rule [Kemeny, 1959] first computes a ranking that maximizes the sum of all pairwise wins: σ * = arg max σ i σ j r ij , where i σ j means that candidate i is preferred against j according to ranking σ.…”

Section: Classical Voting Rulesmentioning

confidence: 99%

Learning to Elect

Anil,

Bao

2021

Preprint

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Voting systems have a wide range of applications including recommender systems, web search, product design and elections. Limited by the lack of general-purpose analytical tools, it is difficult to hand-engineer desirable voting rules for each use case. For this reason, it is appealing to automatically discover voting rules geared towards each scenario. In this paper, we show that set-input neural network architectures such as Set Transformers, fully-connected graph networks and DeepSets are both theoretically and empirically well-suited for learning voting rules. In particular, we show that these network models can not only mimic a number of existing voting rules to compelling accuracy -both position-based (such as Plurality and Borda) and comparison-based (such as Kemeny, Copeland and Maximin)but also discover near-optimal voting rules that maximize different social welfare functions. Furthermore, the learned voting rules generalize well to different voter utility distributions and election sizes unseen during training. IntroductionVoting systems are highly prevalent in our daily lives. Examples range from large scale democratic elections to company or family-wide decision making, recommender systems and product design [Boutilier et al., 2015].As with any social decision-making process, the goal of designing voting rules is to reconcile differences and maximize some collective objective. The area of research that studies different voting rules and the approaches to designing them is called voting theory.A vast number of voting rules have been proposed over the years. Among them is the widely applied plurality rule. Despite being simple and intuitive, the plurality rule is very limited in that it does not consider the strength of voters' preferences. Other examples of voting rules, such as Borda and Copeland, take into consideration the ranked preferences of the voters.Voting theorists have developed different approaches to designing voting rules. For example, the axiomatic approach constrains the voting rules to satisfy certain desired properties (axioms) such as anonymity (treating all voters equally) and neutrality (treating all candidates equally). The utilitarian approach, on the other hand, aims to maximize a pre-defined notion of social welfare -a scalar quantity that measures the quality of the elected candidate in the eyes of the electorate.There are major hurdles to overcome in the traditional way of designing and implementing voting rules. First, the celebrated Arrow's Theorem states the nonexistence of non-dictatorship voting rules that simultaneously satisfy a set of seemingly sensible axioms [Arrow et al., 1951]. Second, for some voting rules such as the ones based on pairwise comparisons, finding the winner can be computationally expensive, making them infeasible for large-scale applications. Last but not least, for the utilitarian approach, it is not obvious how to design voting rules that maximize a given notion * Equal contribution.Preprint. Under review.

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Extensions of the Simpson voting rule to the committee selection setting

Cited by 14 publications

References 46 publications

Majority properties of positional social preference correspondences

Majority properties of positional social preference correspondences

Inconsistent weighting in weighted voting games

Learning to Elect

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