Achieving fully proportional representation by clustering voters

Faliszewski, Piotr; Slinko, Arkadii; Stahl, Kolja; Talmon, Nimrod

doi:10.1007/s10732-018-9376-y

Cited by 14 publications

(9 citation statements)

References 24 publications

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“…Indeed, this is the case for each of α-CC (Procaccia, Rosenschein, and Zohar 2008), β-CC (Lu and Boutilier 2011), and PAV (Skowron, Faliszewski, and Slinko 2015;Aziz et al 2015). Yet, there are various workarounds for these hardness results, including approximation algorithms (Lu and Boutilier 2011;Skowron, Faliszewski, and Lang 2016;Skowron, Faliszewski, and Slinko 2015), heuristics (Faliszewski et al 2018c;2018a), and algorithms for restricted preference domains (Betzler, Slinko, and Uhlmann 2013;Peters 2018).…”

Section: For Approval Utilities and Owa-vectors Of The Formmentioning

confidence: 99%

Parameterized Algorithms for Finding a Collective Set of Items

Bredereck

Faliszewski

Kaczmarczyk

et al. 2020

AAAI

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We extend the work of Skowron et al. (AIJ, 2016) by considering the parameterized complexity of the following problem. We are given a set of items and a set of agents, where each agent assigns an integer utility value to each item. The goal is to find a set of k items that these agents would collectively use. For each such collective set of items, each agent provides a score that can be described using an OWA (ordered weighted average) operator and we seek a set with the highest total score. We focus on the parameterization by the number of agents and we find numerous fixed-parameter tractability results (however, we also find some W[1]-hardness results). It turns out that most of our algorithms even apply to the setting where each agent has an integer weight.

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Section: For Approval Utilities and Owa-vectors Of The Formmentioning

confidence: 99%

Parameterized Algorithms for Finding a Collective Set of Items

Bredereck

Faliszewski

Kaczmarczyk

et al. 2020

AAAI

Self Cite

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“…This is the variant of the rule originally proposed by Chamberlin and Courant [17], but, subsequently, other authors (e.g., Procaccia et al [65], Betzler at al. [9], and Faliszewski et al [34]) considered other ones, based on other single-winner scoring functions. In particular, we will be interested in the k-Approval Chamberlin-Courant rule, (α k -CC) which is defined through functions:…”

Section: Examples Of Committee Scoring Rulesmentioning

confidence: 99%

“…This fact was first shown by Procaccia et al [65] in the approval-based setting, and then by Lu and Boutilier [51] for β-CC. Since then, various means of computing the results under the Chamberlin-Courant rule and its variants were studied in quite some detail [9,20,75,78,59,34,48,28].…”

Section: Representation-focused Rulesmentioning

confidence: 99%

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Committee Scoring Rules: Axiomatic Characterization and Hierarchy

Faliszewski,

Skowron,

Slinko

et al. 2018

Preprint

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Committee scoring voting rules are multiwinner analogues of positional scoring rules which constitute an important subclass of single-winner voting rules. We identify several natural subclasses of committee scoring rules, namely, weakly separable, representation-focused, top-kcounting, OWA-based, and decomposable rules. We characterize SNTV, Bloc, and k-Approval Chamberlin-Courant as the only nontrivial rules in pairwise intersections of these classes. We provide some axiomatic characterizations for these classes, where monotonicity properties appear to be especially useful. The class of decomposable rules is new to the literature. We show that it strictly contains the class of OWA-based rules and describe some of the applications of decomposable rules.

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“…Winner determination for these rules, however, is NPhard [19], though it is possible to compute the winner when some parameters are small [2]; that is, winner determination for these rules is fixed-parameter tractable with respect to either the number of voters or the number of candidates. Further, efficient approximation algorithms are known [22] for these rules as well as heuristic algorithms based on clustering [12].…”

Section: Introductionmentioning

confidence: 99%

Proportional Representation in Vote Streams

Dey,

Talmon,

van Handel

2017

Preprint

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We consider elections where the voters come one at a time, in a streaming fashion, and devise space-efficient algorithms which identify an approximate winning committee with respect to common multiwinner proportional representation voting rules; specifically, we consider the Approval-based and the Borda-based variants of both the Chamberlin-Courant rule and the Monroe rule. We complement our algorithms with lower bounds. Somewhat surprisingly, our results imply that, using space which does not depend on the number of voters it is possible to efficiently identify an approximate representative committee of fixed size over vote streams with huge number of voters. CCS Concepts•Computing methodologies → Multi-agent systems;•Theory of computation → Streaming, sublinear and near linear time algorithms;

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Achieving fully proportional representation by clustering voters

Cited by 14 publications

References 24 publications

Parameterized Algorithms for Finding a Collective Set of Items

Parameterized Algorithms for Finding a Collective Set of Items

Committee Scoring Rules: Axiomatic Characterization and Hierarchy

Proportional Representation in Vote Streams

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