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.
Abstract: We 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.
Citations
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TL;DR: In this article , the authors introduce three position-based matching models, which minimize the "dissatisfaction score", which measures matchings from different perspectives, and present diverse complexity results for these three models, among others, polynomial-time solvability for the first model.
Abstract: Many models have been proposed for computing a one-to-one matching between two equal-sized sets/sides of agents, each assigned with one preference list of the agents in the opposite side. The most prominent one might be the Stable Matching model. Re-cently, the Stable Matching model has been extended to the multimodal setting [6, 13, 29], where each agent has more than one preference lists, each representing a criterion based on which the agents of the opposite side are evaluated. We use a layer to denote the set of preference lists of agents, which are based on the same criterion. Thus, the single modal matching problem has only one layer. This setting finds applications in many real-world scenarios. However, it turns out that stable matchings might not exist with multi-modal preferences and the determination is NP-hard and W-hard with respect to several natural parameters. Here, we introduce three position-based matching models, which minimize the “dissatisfaction score”. We define four dissatisfaction scores, which measure matchings from different perspectives. The first model minimizes the total respective dissatisfaction score over all layers, while the second minimizes the maximum of the respective score over all layers. The third model seeks for a matching 𝑀 which is Layer Pareto-optimal, meaning that there does not exist a matching 𝑀 ′ , which is at least as good as 𝑀 with respect to the respective dissatisfaction score in all layers, but is strictly better in at least one layer. We present diverse complexity results for these three models, among others, polynomial-time solvability for the first model. We also investigate the generalization which given an upper bound on the dissatisfaction score, computes a matching involving subsets of agents and a subset of layers. Hereby, we mainly focus on the parameterized complexity with respect to parameters such as the size of agent subsets, or the size of the layer subset and achieve fixed-parameter tractability as well as intractability results.
2 citations
16 May 2022
TL;DR: In this paper , the complexity of stable matching problems with multilayer approval preferences was studied and eleven stability notions derived from three well-established stability notions for stable matchings with ties and four adaptions proposed by Chen et al.
Abstract: We study stable matching problems where agents have multilayer preferences: There are ℓ layers each consisting of one preference relation for each agent. Recently, Chen et al. [EC ’18] studied such problems with strict preferences, establishing four multilayer adaptions of classical notions of stability. We follow up on their work by analyzing the computational complexity of stable matching problems with multilayer approval preferences. We consider eleven stability notions derived from three well-established stability notions for stable matchings with ties and the four adaptions proposed by Chen et al. For each stability notion, we show that the problem of finding a stable matching is either polynomial-time solvable or NP-hard. Furthermore, we examine the influence of the number of layers and the desired “degree of stability” on the problems’ complexity. Somewhat surprisingly, we discover that assuming approval preferences instead of strict preferences does not consider-ably simplify the situation (and sometimes even makes polynomial-time solvable problems NP-hard).
TL;DR: In this article , the distortion in attribute approval committee elections is studied, where each candidate satisfies a variety of attributes in different categories (e.g., academic degree, work experience, lo-cation).
Abstract: In attribute approval elections, the task is to select sets of winning candidates, while each candidate satisfies a variety of attributes in different categories (e.g., academic degree, work experience, lo-cation). Every voter specifies, which attributes in each category are desirable for a candidate, whereas each candidate might satisfy only some of the attributes. In this paper, we study questions of distortion in attribute approval committee elections. We introduce different methods to derive approval ballots, ordinal preferences, or cardinal preferences from a given attribute approval ballot. Then for a given voting method, assuming only a derived preference is provided, we compute the ratio of the voters’ satisfaction for the worst possible committee, with the satisfaction of the actual winning committee, given the attribute approval ballots.
TL;DR: In this paper , the authors considered a new model of election control that by assigning different rules to the votes from different layers, makes the special candidate p being the winner of the election (a rule can be assigned to different layers).
Abstract: We study the election control problem with multi-votes, where each voter can present a single vote according different views (or layers, we use"layer"to represent"view"). For example, according to the attributes of candidates, such as: education, hobby or the relationship of candidates, a voter may present different preferences for the same candidate set. Here, we consider a new model of election control that by assigning different rules to the votes from different layers, makes the special candidate p being the winner of the election (a rule can be assigned to different layers). Assuming a set of candidates C among a special candidate"p", a set of voters V, and t layers, each voter gives t votes over all candidates, one for each layer, a set of voting rules R, the task is to find an assignment of rules to each layer that p is acceptable for voters (possible winner of the election). Three models are considered (denoted as sum-model, max-model, and min-model) to measure the satisfaction of each voter. In this paper, we analyze the computational complexity of finding such a rule assignment, including classical complexity and parameterized complexity. It is interesting to find out that 1) it is NP-hard even if there are only two voters in the sum-model, or there are only two rules in sum-model and max-model; 2) it is intractable with the number of layers as parameter for all of three models; 3) even the satisfaction of each vote is set as dichotomous, 1 or 0, it remains hard to find out an acceptable rule assignment. Furthermore, we also get some other intractable and tractable results.
References
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TL;DR: This work proposes a practical and polynomial-time algorithm for diverse committee selection that draws on the idea of using soft bounds and satisfies natural axioms.
Abstract: Committee selection with diversity or distributional constraints is a ubiquitous problem. However, many of the formal approaches proposed so far have certain drawbacks including (1) computational intractability in general, and (2) inability to suggest a solution for instances where the hard constraints cannot be met. We propose a cubic-time algorithm for diverse committee selection that satisfies natural axioms and draws on the idea of using soft bounds.
18 citations
"Committee selection with multimodal..." refers background or methods in this paper
...Theorem 1 Max-k-Borda is NP-hard and W[1]-hard w....
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...We provide a polynomial time reduction from the W[1]hard problem Independent Set (IS) [12]....
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...Proposition 5 Min-k-Borda is NP-hard and W[1]-hard w....
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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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...[3] proved that Egalitarian-k-Borda is W[1]-hard w....
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24 Sep 2007
TL;DR: This paper addresses the problem of multimedia content retrieval by first defining a novel preference-based representation particularly adapted to the fusion problem, and then investigating the RankBoost algorithm to combine those preferences and a learn multimodal retrieval model.
Abstract: Representing and fusing multimedia information is a key issue to discover semantics in multimedia. In this paper we address more specifically the problem of multimedia content retrieval by first defining a novel preference-based representation particularly adapted to the fusion problem, and then, by investigating the RankBoost algorithm to combine those preferences and a learn multimodal retrieval model. The approach has been tested on annotated images and on the complete TRECVID 2005 corpus and compared with SVM-based fusion strategies. The results show that our approach equals SVM performance but, contrary to SVM, is parameter free and faster.
14 citations
"Committee selection with multimodal..." refers background in this paper
..., in the context of matching [10] and information retrieval [8]....
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Posted Content•
TL;DR: This work identifies several natural subclasses of committee scoring rules, namely, weakly separable, representation-focused, top-$k$-counting, OWA-based, and decomposable rules, and characterize SNTV, Bloc, and $k$--Courant as the only nontrivial rules in pairwise intersections of these classes.
Abstract: 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-$k$-counting, 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.
10 citations
"Committee selection with multimodal..." refers methods in this paper
...So, as some CSRs are NP-hard, we inherit their hardness to our models; in particular, we observe this phenomenon when we consider the NP-hard multiwinner CSR Chamberlin– Courant (CC)....
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...R score is at least R. Remark 1 Our adaptations of CSRs to the multimodal setting differ by the way in which we define voter satisfaction w.r.t. the different layers....
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...3.2 Pareto-R and Vector-R We consider a further kind of an adaptation of CSRs to our model, based on the concept of Pareto dominance....
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...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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...Next we discuss our different adaptations of CSRs to our multimodal model....
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Proceedings Article•
25 Apr 2018TL;DR: An experimental evaluation of two novel heuristics for computing approximate results of multiwinner elections under arbitrary committee scoring rules uses the two-dimensional Euclidean domain to compare the visual representations of the outputs of the algorithms.
Abstract: Committee scoring rules form an important class of multiwinner voting rules. As computing winning committees under such rules is generally intractable, in this paper we investigate efficient heuristics for this task. We design two novel heuristics for computing approximate results of multiwinner elections under arbitrary committee scoring rules; notably, one of these heuristics uses concepts from cooperative game theory. We then provide an experimental evaluation of our heuristics (and two others, known from the literature): we compare the scores of the committees output by our algorithms to the scores of the optimal committees, and also use the two-dimensional Euclidean domain to compare the visual representations of the outputs of our algorithms.
10 citations
"Committee selection with multimodal..." refers background in this paper
...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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01 Aug 2019
TL;DR: The computational complexity of computing such committees is analyzed and an experimental evaluation of the compromise levels that can be achieved between several well-known rules, including k-Borda, SNTV, Bloc, and the Chamberlin–Courant rule is provided.
Abstract: We study the problem of computing committees that perform well according to several different criteria, which are expressed as committee scoring rules. We analyze the computational complexity of computing such committees and provide an experimental evaluation of the compromise levels that can be achieved between several well-known rules, including k-Borda, SNTV, Bloc, and the Chamberlin--Courant rule.
10 citations
"Committee selection with multimodal..." refers background in this paper
...[23], in which the dimensions of optimization are different voting rules....
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