Publications (150)48.85 Total impact

Article: Complexity of manipulation and bribery in judgment aggregation for uniform premisebased quota rules
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ABSTRACT: Endriss et al. (2012) initiated the complexitytheoretic study of problems related to judgment aggregation. We extend their results on the manipulation of two specific judgment aggregation procedures to a whole class of such procedures, namely to uniform premisebased quota rules. In addition, we consider incomplete judgment sets and the notions of toprespecting and closenessrespecting preferences introduced by Dietrich and List (2007). This complements previous work on the complexity of manipulation in judgment aggregation that focused on Hammingdistancerespecting preferences only, which we also study here. Furthermore, inspired by work on bribery in voting Faliszewski and Rothe (in press), we introduce and study the closely related issue of bribery in judgment aggregation.  [Show abstract] [Hide abstract]
ABSTRACT: We study the computational complexity of the existence and the verification problem for wonderfully stable partitions (WSPE and WSPV) and of the existence problem for strictly core stable coalition structures (SCSCS) in enemyoriented hedonic games. In this note, we show that WSPV is NPcomplete and both WSPE and SCSCS are DPhard, where DP is the second level of the boolean hierarchy, and we discuss an approach for classifying the latter two problems in terms of their complexity. 
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ABSTRACT: Peer reviewing is the key ingredient of evaluating the quality of scientific work. Based on the review scores assigned by individual reviewers to papers, program committees of conferences and journal editors decide which papers to accept for publication and which to reject. A similar procedure is part of the selection process of grant applications and, among other fields, in sports. It is well known that the reviewing process suffers from measurement errors due to a lack of agreement among multiple reviewers of the same paper. And if not all papers are reviewed by all reviewers, the naive approach of averaging the scores is biased. Several statistical methods are proposed for aggregating review scores, which all can be realized by standard statistical software. The simplest method uses the wellknown fixedeffects twoway classification with identical variances, while a more advanced method assumes different variances. As alternatives a mixed linear model and a generalized linear model are employed. The application of these methods implies an evaluation of the reviewers, which may help to improve reviewing processes. An application example with real conference data shows the potential of these statistical methods. 
Article: Minimizing envy and maximizing average Nash social welfare in the allocation of indivisible goods
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ABSTRACT: Envyfreeness is a desirable criterion when one wishes to fairly distribute a finite set of goods among two or more agents. Unfortunately, allocations satisfying this criterion may not exist in the setting where the goods are assumed to be indivisible. In this case, it is useful to settle for allocations with envy as small as possible. Adapting the framework of Chevaleyre etal. (2007), we propose a multiplicative form of the degree of envy of a given allocation and then study the approximability of the corresponding envy minimization problems. We show that these problems are APXhard to approximate in general, but admit an FPTAS for a fixed number of agents with additive utility functions. We also present a polynomialtime algorithm for the case when the number of agents is equal to the number of goods to be distributed. In addition, we study the problem of maximizing social welfare by the average Nash product. We provide a fast greedy approximation algorithm for this problem when the agents' utility functions are (sub)additive, and we design a PTAS for the case when all agents have the same additive utility function.  [Show abstract] [Hide abstract]
ABSTRACT: Control in elections models situations in which an external actor tries to change the outcome of an election by restructuring the election itself. The corresponding decision problems have been shown NPhard for a variety of voting systems. In particular, in our companion paper [16], we have shown that fallback and Bucklin voting are resistant (in terms of NPhardness) to almost all of the common types of control. While NPhardness results for manipulation (another way of tampering with the outcomes of elections) have been challenged experimentally (see, e.g., the work of Walsh and ), such an experimental approach is sorely missing for control. We for the first time tackle NPhard control problems in an experimental setting. Our experiments allow a more finegrained analysis and comparison—across various control scenarios, vote distribution models, and voting systems—than merely stating NPhardness for all these control problems.  [Show abstract] [Hide abstract]
ABSTRACT: Electoral control models ways of changing the outcome of an election via such actions as adding, deleting, or partitioning either candidates or voters. To protect elections from such control attempts, computational complexity has been used to establish socalled resistance results. We show that fallback voting, an election system proposed by Brams and Sanver [12] to combine Bucklin with approval voting, displays the broadest control resistance currently known to hold among natural election systems with a polynomialtime winner problem. We also study the control complexity of Bucklin voting and show that it performs almost as well as fallback voting in terms of control resistance. Furthermore, we investigate the parameterized control complexity of Bucklin and fallback voting, according to several parameters that are often likely to be small for typical instances. In a companion paper [28], we challenge our worstcase complexity results from an experimental point of view.  [Show abstract] [Hide abstract]
ABSTRACT: Falsename manipulation refers to the question of whether a player in a weighted voting game can increase her power by splitting into several players and distributing her weight among these false identities. Relatedly, the beneficial merging problem asks whether a coalition of players can increase their power in a weighted voting game by merging their weights. For the problems of whether merging or splitting players in weighted voting games is beneficial in terms of the Shapley–Shubik and the normalized Banzhaf index, merely NPhardness lower bounds are known, leaving the question about their exact complexity open. For the Shapley–Shubik and the probabilistic Banzhaf index, we raise these lower bounds to hardness for PP, "probabilistic polynomial time," a class considered to be by far a larger class than NP. For both power indices, we provide matching upper bounds for beneficial merging and, whenever the new players’ weights are given, also for beneficial splitting, thus resolving previous conjectures in the affirmative. Relatedly, we consider the beneficial annexation problem, asking whether a single player can increase her power by taking over other players’ weights. It is known that annexation is never disadvantageous for the Shapley–Shubik index, and that beneficial annexation is NPhard for the normalized Banzhaf index. We show that annexation is never disadvantageous for the probabilistic Banzhaf index either, and for both the Shapley–Shubik index and the probabilistic Banzhaf index we show that it is NPcomplete to decide whether annexing another player is advantageous. Moreover, we propose a general framework for merging and splitting that can be applied to different classes and representations of games. 
Conference Paper: Bribery in MultipleAdversary PathDisruption Games is Hard for the Second Level of the Polynomial Hierarchy (Extended Abstract)
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ABSTRACT: Pathdisruption games, a class of cooperative games introduced by Bachrach and Porat [1], model situations where the players, sitting on the vertices of a given graph, try to prevent  by blocking all possible paths  their adversaries from traveling from a set of source vertices to a set of target vertices. Rey and Rothe[3] studied bribery in these games and showed that when costs are assigned to the vertices, the corresponding problem is NPcomplete in the singleadversary case, and is in $\Sigma_2^p = \mathrm{NP}^{\mathrm{NP}}$, the second level of the polynomial hierarchy, in the multipleadversary case. They left open whether the latter problem is $\Sigma_2^p$complete. In this note, we solve this open question in the affirmative.  [Show abstract] [Hide abstract]
ABSTRACT: An important task in multiagent resource allocation, which provides mechanisms to allocate bundles of (indivisible and nonshareable) resources to agents, is to maximize social welfare. We study the computational complexity of exact social welfare optimization by the Nash product, which can be seen as a sensible compromise between the wellknown notions of utilitarian and egalitarian social welfare. When utilitiy functions are represented in the bundle or the kadditive form, for k ≥ 3, we prove that the corresponding computational problems are DPcomplete (where DP denotes the second level of the boolean hierarchy over NP), thus confirming two conjectures raised by Roos and Rothe [10]. We also study the approximability of social welfare optimization problems. 
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ABSTRACT: We define a family of rules for dividing m indivisible goods among agents, parameterized by a scoring vector and a social welfare aggregation function. We assume that agents' preferences over sets of goods are additive, but that the input is ordinal: each agent simply ranks single goods. Similarly to (positional) scoring rules in voting, a scoring vector s = (s1,⋯,sm) consists of m nonincreasing nonnegative weights, where si is the score of a good assigned to an agent who ranks it in position i. The global score of an allocation for an agent is the sum of the scores of the goods assigned to her. The social welfare of an allocation is the aggregation of the scores of all agents, for some aggregation function ∗ such as, typically, + or min. The rule associated with s and ∗ maps a profile to (one of) the allocation(s) maximizing social welfare. After defining this family of rules, and focusing on some key examples, we investigate some of the socialchoicetheoretic properties of this family of rules, such as various kinds of monotonicity, separability, envyfreeness, and Pareto efficiency. 
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ABSTRACT: We consider the problem of fairly distributing a number of indivisible goods among agents with additive utility functions. Among the common criteria of fairness, we focus on envyfreeness and its weaker notions. Instead of concentrating on envyfree allocations (which might not always exist), we seek to find an allocation with minimum envy. Based on a notion introduced by Chevaleyre et al. [7], we define several problems of minimizing the degree of envy and study their approximability. 
Article: Complexity of Manipulation, Bribery, and Campaign Management in Bucklin and Fallback Voting
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ABSTRACT: A central theme in computational social choice is to study the extent to which voting systems computationally resist manipulative attacks seeking to influence the outcome of elections, such as manipulation (i.e., strategic voting), control, and bribery. Bucklin and fallback voting are among the voting systems with the broadest resistance (i.e., NPhardness) to control attacks. However, only little is known about their behavior regarding manipulation and bribery attacks. We comprehensively investigate the computational resistance of Bucklin and fallback voting for many of the common manipulation and bribery scenarios; we also complement our discussion by considering several campaign management problems for Bucklin and fallback.  [Show abstract] [Hide abstract]
ABSTRACT: We discuss what behavioral social choice can contribute to computational social choice. An important trademark of behavioral social choice is to switch perspective away from a traditional sampling approach in the social choice literature and ... 
Conference Paper: Envyratio and averagenash social welfare optimization in multiagent resource allocation
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ABSTRACT: The resource allocation problem deals with distributing a number of indivisible, nonshareable resources among a set of agents so as to optimizing social welfare. Assuming all agents to have additive utility functions and focusing on two particular measures of social welfare, envyratio and averageNash product, we investigate the two resulting optimization problems. We give the first hardness of approximation result for a factor better than 3/2 for the problem of minimum envyratio, and we design an FPTAS for the case when the number of agents is fixed. For the special case when the number of agents and the number of resources are equal, we show that the problem is even solvable in polynomial time. Next, we propose the first approximation algorithm for maximizing the averageNash product in the general case, and we prove that this problem admits a PTAS if all agents' utility functions are the same. Finally, we study the problem of how hard it is to design a truthful mechanism for these two optimization problems. 
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ABSTRACT: We study computational aspects of various forms of manipulation and control in judgment aggregation, with a focus on the premisebased procedure. For manipulation, we in particular consider incomplete judgment sets and the notions of toprespecting and closenessrespecting preferences introduced by Dietrich and List [13]. This complements previous work on the complexity of manipulation in judgment aggregation that focused on Hammingdistanceinduced preferences [14,6], which we also study here. Regarding control, we introduce the notion of control by bundling judges and show that the premisebased procedure is resistant to it in terms of NPhardness. 
Conference Paper: Campaigns for lazy voters: Truncated ballots
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ABSTRACT: We study elections in which voters may submit partial ballots consisting of truncated lists: each voter ranks some of her top candidates (and possibly some of her bottom candidates) and is indifferent among the remaining ones. Holding elections with such votes requires adapting classical voting rules (which expect complete rankings as input) and these adaptations create various opportunities for candidates who want to increase their chances of winning. We provide complexity results regarding planning various kinds of campaigns in such settings, and we study the complexity of the possible winner problem for the case of truncated votes.
Publication Stats
1k  Citations  
48.85  Total Impact Points  
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Institutions

19702015

HeinrichHeineUniversität Düsseldorf
 • Institute for Theoretical Physics I.
 • Mathematisches Institut
Düsseldorf, North RhineWestphalia, Germany


19972000

Friedrich Schiller University Jena
 • Faculty of Mathematics and Computer Science
 • Department of Computer Science
Jena, Thuringia, Germany


19981999

University of Rochester
 Department of Computer Science
Rochester, NY, United States
