Axiomatic characterization of committee scoring rules (original) (raw)
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Committee Scoring Rules: Axiomatic Characterization and Hierarchy
arXiv (Cornell University), 2018
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.
Strategy-proof consensus rules for committee elections
Mathematical and Computer Modelling
committee election problem is to choose from a finite set S of candidates a nonempty subset of committee members as the consequence of an election in which each voter expresses a preference for a candidate in S. We use ideas of vote concentration to formulate families of committee election rules, which may exhibit several natural, intuitively appealing properties. One concept of vote concentration, a typification of committee strength, ensures that the associated committee election rule is strategy-proof and so is not subject to voter manipulation. (~
Committee Scoring Rules: Axiomatic Classification and Hierarchy
2016
We consider several natural classes of committee scoring rules, namely, weakly separable, representation-focused, top-k-counting, OWA-based, and decomposable rules. We study some of their axiomatic properties, especially properties of monotonicity, and concentrate on containment relations between them. We characterize SNTV, Bloc, and k-approval Chamberlin-Courant, as the only rules in certain intersections of these classes. We introduce decomposable rules, describe some of their applications, and show that the class of decomposable rules strictly contains the class of OWA-based rules.
Multiwinner analogues of the plurality rule: axiomatic and algorithmic perspectives
Social Choice and Welfare, 2018
We characterize the class of committee scoring rules that satisfy the fixedmajority criterion. We argue that rules in this class are multiwinner analogues of the single-winner Plurality rule, which is uniquely characterized as the only single-winner scoring rule that satisfies the simple majority criterion. We define top-k-counting committee scoring rules and show that the fixed-majority consistent rules are a subclass of the top-k-counting rules. We give necessary and sufficient conditions for a top-kcounting rule to satisfy the fixed-majority criterion. We show that, for many top-kcounting rules, the complexity of winner determination is high (formally, we show that the problem of deciding if there exists a committee with at least a given score is NPhard), but we also show examples of rules with polynomial-time winner determination procedures. For some of the computationally hard rules, we provide either exact FPT algorithms or approximate polynomial-time algorithms.
Multiwinner Analogues of Plurality Rule: Axiomatic and Algorithmic Perspectives
arXiv (Cornell University), 2016
We characterize the class of committee scoring rules that satisfy the fixed-majority criterion. In some sense, the committee scoring rules in this class are multiwinner analogues of the singlewinner Plurality rule, which is uniquely characterized as the only single-winner scoring rule that satisfies the simple majority criterion. We define top-k-counting committee scoring rules and show that the fixed majority consistent rules are a subclass of the top-k-counting rules. We give necessary and sufficient conditions for a top-k-counting rule to satisfy the fixed-majority criterion. We find that, for most of the rules in our new class, the complexity of winner determination is high (that is, the problem of computing the winners is NP-hard), but we also show examples of rules with polynomial-time winner determination procedures. For some of the computationally hard rules, we provide either exact FPT algorithms or approximate polynomial-time algorithms.
K. May characterized majority rule as a function satisfying anonymity, neutrality, and responsiveness. Recent work criticized his characterization and opened the way to the introduction of properties defined by taking into account an entire set of societies. Following this approach, this paper presents a new axiomatization of majority rule that appeals, besides a variant of May's responsiveness, to new properties I will call bnull societyQ and bsubsets decomposabilityQ. D
A new axiomatic approach to the impartial nomination problem
Games and Economic Behavior, 2021
Abstract In this paper we introduce a new set of axioms that characterize uniform random dictatorship (URD) as a randomized impartial nomination rule. Unlike earlier work we use a variable population model which allows us to employ axioms that reflect consistency and proportionality–axioms that ensure that the rule behaves well with respect to the combinatorial structure of the nomination profile. Earlier work characterizing URD employed strong symmetry axioms and so it is surprising that our axioms characterize the same rule.
Multi-winner scoring election methods: Condorcet consistency and paradoxes
Public Choice, 2016
The goal of this paper is to propose a comparison of four multi-winner voting rules, k-Plurality, k-Negative Plurality, k-Borda, and Bloc, which can be considered as generalisations of well-known single-winner scoring rules. The first comparison is based on the Condorcet committee efficiency which is defined as the conditional probability that a given voting rule picks out the Condorcet committee, given that such a committee exists. The second comparison is based on the likelihood of two paradoxes of committee elections: The Prior Successor Paradox and the Leaving Member Paradox which occur when a member of an elected committee leaves. In doing so, using the well-known Impartial Anonymous Culture condition, we extend the results of Kamwa and Merlin (2015) in two directions. First, our paper is concerned with the probability of the paradoxes no matter the ranking of the leaving candidate. Second, we do not only focus on the occurrence of these paradoxes when one wishes to select a committee of size k = 2 out of m = 4 candidates but we consider more values of k and m.
Properties of multiwinner voting rules
The goal of this paper is to propose and study properties of multiwinner voting rules which can be consider as generalisations of single-winner scoring voting rules. We consider SNTV, Bloc, k-Borda, STV, and several variants of Chamberlin-Courant's and Monroe's rules and their approximations. We identify two broad natural classes of multiwinner score-based rules, and show that many of the existing rules can be captured by one or both of these approaches. We then formulate a number of desirable properties of multiwinner rules, and evaluate the rules we consider with respect to these properties.
An axiomatic characterization of different majority concepts
European journal of operational research, 2007
A lot of decision support systems use some kind of aggregation procedure based on the concept of majority, but not always the same one; it can be simple majority, weak majority or one of the many other kinds of majority. This paper attempts to present the main variants of majority and to characterize them in a uniform way. Consequently, it is now easier to compare different kinds of majority and to understand the dissimilarities (or similarities) between them. This should help decision analysts willing to use a majority procedure to choose the right one for their problem and context.