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Proceedings ArticleDOI

Committee selection with multimodal preferences

01 Jan 2020-Vol. 325, pp 123-130

TL;DR: This work designs efficient algorithms for certain cases of committee selection with multimodal preferences and discusses applications of the model and the computational complexity of several generalizations of known committee scoring rules to this setting.

AbstractWe study committee selection with multimodal preferences: Assuming a set of candidatesA, a set of voters V , and ` layers, where each voter v ∈ V has ordinal preferences over the alternatives for each layer separately, the task is to select a committee S ⊆ A of size k. We discuss applications of our model and study the computational complexity of several generalizations of known committee scoring rules (specifically, k-Borda and Chamberlin–Courant) to our setting, as well as discuss domain restrictions for our model. While most problems we encounter are computationally intractable in general, we nevertheless design efficient algorithms for certain cases.

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Journal ArticleDOI
Abstract: When a decision is reached by voting or is arrived at by a group all of whose members are not in complete accord, there is no part of economic theory which applies. This paper is intended to help fill this gap; to provide a type of reasoning which will contribute to the development of the theory of tradeunions, the firm, and the cartel; and to provide the basis for a theory of the equilibrium distribution of taxation or of public expenditure. Still other uses of the theory might be not less important. For reasons of space we avoid discussion of many points that demand fuller treatment and only attempt to indicate the course of the argument.

2,033 citations


"Committee selection with multimodal..." refers background in this paper

  • ...A particularly popular domain restriction is the single-peaked domain, originally proposed by Black [6]....

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Journal ArticleDOI
TL;DR: This work shows that INDEPENDENT SET is complete for W, and the W Hierarchy of parameterized problems was defined, and complete problems were identified for the classes W [ t ] for t ⩾ 2.
Abstract: For many fixed-parameter problems that are trivially solvable in polynomial-time, such as k -DOMINATING SET, essentially no better algorithm is presently known than the one which tries all possible solutions. Other problems, such as FEEDBACK VERTEX SET, exhibit fixed-parameter tractability : for each fixed k the problem is solvable in time bounded by a polynomial of degree c , where c is a constant independent of k . In a previous paper, the W Hierarchy of parameterized problems was defined, and complete problems were identified for the classes W [ t ] for t ⩾ 2. Our main result shows that INDEPENDENT SET is complete for W [1].

617 citations


"Committee selection with multimodal..." refers methods in this paper

  • ...We provide a polynomial time reduction from the W[1]hard problem Independent Set (IS) [12]....

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  • ...Towards this, we give a reduction from the W[1]-hard problem Independent Set (IS) [12], in which given a graph G and an integer t; we shall decide the existence of a t-sized set X ⊆ V (G) containing only nonadjacent vertices....

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Journal ArticleDOI
TL;DR: This work investigates two systems of fully proportional representation suggested by Chamberlin & Courant and Monroe and investigates the parameterized complexity of winner determination of the two classical and two new rules with respect to several parameters.
Abstract: We investigate two systems of fully proportional representation suggested by Chamberlin & Courant and Monroe. Both systems assign a representative to each voter so that the "sum of misrepresentations" is minimized. The winner determination problem for both systems is known to be NP-hard, hence this work aims at investigating whether there are variants of the proposed rules and/or specific electorates for which these problems can be solved efficiently. As a variation of these rules, instead of minimizing the sum of misrepresentations, we considered minimizing the maximal misrepresentation introducing effectively two new rules. In the general case these "minimax" versions of classical rules appeared to be still NP-hard. We investigated the parameterized complexity of winner determination of the two classical and two new rules with respect to several parameters. Here we have a mixture of positive and negative results: e.g., we proved fixed-parameter tractability for the parameter the number of candidates but fixed-parameter intractability for the number of winners. For single-peaked electorates our results are overwhelmingly positive: we provide polynomial-time algorithms for most of the considered problems. The only rule that remains NP-hard for single-peaked electorates is the classical Monroe rule.

197 citations


"Committee selection with multimodal..." refers background or methods in this paper

  • ...We adapt the corresponding algorithm for CC [5]: We guess a clustering of the voters (i....

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  • ...Due to Proposition 2, and NP-hardness and W[2]-hardness of EgalitarianCC with respect to the committee size k [5], we obtain:...

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  • ...[5] for Max-CC and Min-CC under Global-SP; unfortunately,...

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  • ...In particular, a polynomial time algorithm, computing winning committees under CC for single-peaked profiles is known [5]....

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  • ...k [5], we obtain the following result....

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Journal ArticleDOI
TL;DR: It is demonstrated that winner selection in two prominent proportional representation voting systems is a computationally intractable problem—implying that these systems are impractical when the assembly is large, and in settings where the size of the Assembly is constant, the problem can be solved in polynomial time.
Abstract: We demonstrate that winner selection in two prominent proportional representation voting systems is a computationally intractable problem—implying that these systems are impractical when the assembly is large. On a different note, in settings where the size of the assembly is constant, we show that the problem can be solved in polynomial time.

195 citations


"Committee selection with multimodal..." refers background in this paper

  • ...Due to Proposition 4 and the fact that Egalitarian-CC is NP-hard and W[2]-hard w.r.t. the committee size k [5], we have following result....

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  • ...In particular, while finding winning committees under kBorda can be done in polynomial time (one has to select k candidates with the highest individual Borda scores), CC is NP-hard [26] but FPTfor certain parameters, admit approximation algorithms, and certain heuristics are known to be effective for it [5, 20, 28, 15]....

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  • ...Due to Proposition 3 and the fact that CC is NP-hard and W[2]-hard w.r.t. k [5], we obtain the following result....

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  • ...Corollary 8 Min-CC, Sum-CC, and Vector-CC are NP-hard and W[2]-hard w.r.t. k even for Local-SP, and n = 1 We next study the computational complexity of Max-CC for Global-SP profiles, and obtain intractability....

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  • ...Due to Proposition 2, and NP-hardness and W[2]-hardness of EgalitarianCC with respect to the committee size k [5], we obtain: Corollary 4 Min-CC is NP-hard and W[2]-hard w.r.t. k even for n = 1....

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Proceedings Article
25 Jan 2015
TL;DR: The problem is hard in general, but a number of tractability results for its natural special cases are shown.
Abstract: We consider the following problem: There is a set of items (e.g., movies) and a group of agents (e.g., passengers on a plane); each agent has some intrinsic utility for each of the items. Our goal is to pick a set of K items that maximize the total derived utility of all the agents (i.e., in our example we are to pick K movies that we put on the plane's entertainment system). However, the actual utility that an agent derives from a given item is only a fraction of its intrinsic one, and this fraction depends on how the agent ranks the item among the chosen, available, ones. We provide a formal specification of the model and provide concrete examples and settings where it is applicable. We show that the problem is hard in general, but we show a number of tractability results for its natural special cases.

171 citations


"Committee selection with multimodal..." refers methods in this paper

  • ...Related Work In this paper we generalize several (ordinal) OWArules3 [27] – which is a subclass of the more general class of CSRs [19, 18] – to the setting of multimodal committee elections....

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  • ...Related Work In this paper we generalize several (ordinal) OWArules(3) [27] – which is a subclass of the more general class of CSRs [19, 18] – to the setting of multimodal committee elections....

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