Jörg Rothe

Heinrich-Heine-Universität Düsseldorf, Düsseldorf, North Rhine-Westphalia, Germany

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Publications (125)7.63 Total impact

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    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 well-known notions of utilitarian and egalitarian social welfare. When utilitiy functions are represented in the bundle or the k-additive form, for k ≥ 3, we prove that the corresponding computational problems are DP-complete (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.
    Autonomous Agents and Multi-Agent Systems 03/2014; · 0.79 Impact Factor
  • Special Session on Computational Social Choice at the 13th International Symposium on Artificial Intelligence and Mathematics, Fort Lauderdale; 01/2014
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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., NP-hardness) 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.
    07/2013;
  • Judy Goldsmith, Jörg Rothe
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    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 ...
    Annals of Mathematics and Artificial Intelligence 07/2013; 68(1-3):3-4. · 0.20 Impact Factor
  • Trung Thanh Nguyen, Jörg Rothe
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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, envy-ratio and average-Nash 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 envy-ratio, 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 average-Nash 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.
    Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems; 05/2013
  • Anja Rey, Jörg Rothe
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    ABSTRACT: False-name 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. Analogously to this splitting problem, the beneficial merging problem asks whether a coalition of players can increase their power in a weighted voting game by merging their weights. Aziz et al. [ABEP11] analyze the problem of whether merging or splitting players in weighted voting games is beneficial in terms of the Shapley-Shubik and the normalized Banzhaf index, and so do Rey and Rothe [RR10] for the probabilistic Banzhaf index. All these results provide merely NP-hardness lower bounds for these problems, 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", and provide matching upper bounds for beneficial merging and, whenever the number of false identities is fixed, also for beneficial splitting, thus resolving previous conjectures in the affirmative. It follows from our results that beneficial merging and splitting for these two power indices cannot be solved in NP, unless the polynomial hierarchy collapses, which is considered highly unlikely.
    03/2013;
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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.
    Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2; 06/2012
  • Jörg Rothe, Lena Schend
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    ABSTRACT: Walsh [23,22], Davies et al. [9], and Narodytska et al. [20] studied various voting systems empirically and showed that they can often be manipulated effectively, despite their manipulation problems being NP-hard. Such an experimental approach is sorely missing for NP-hard control problems, where control refers to attempts to tamper with the outcome of elections by adding/delet-ing/partitioning either voters or candidates. We experimentally tackle NP-hard control problems for Bucklin and fallback voting, which among natural voting systems with efficient winner determination are the systems currently known to display the broadest resistance to control in terms of NP-hardness [12,11]. We also investigate control resistance experimentally for plurality voting, one of the first voting systems analyzed with respect to electoral control [1,18]. Our findings indicate that NP-hard control problems can often be solved effectively in practice. Moreover, our experiments allow a more fine-grained analysis and comparison--across various control scenarios, vote distribution models, and voting systems--than merely stating NP-hardness for all these control problems.
    11th International Symposium on Experimental Algorithms (SEA 2012); 06/2012
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    Joerg Rothe, Lena Schend
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    ABSTRACT: Walsh [Wal10, Wal09], Davies et al. [DKNW10, DKNW11], and Narodytska et al. [NWX11] studied various voting systems empirically and showed that they can often be manipulated effectively, despite their manipulation problems being NP-hard. Such an experimental approach is sorely missing for NP-hard control problems, where control refers to attempts to tamper with the outcome of elections by adding/deleting/partitioning either voters or candidates. We experimentally tackle NP-hard control problems for Bucklin and fallback voting. Among natural voting systems with efficient winner determination, fallback voting is currently known to display the broadest resistance to control in terms of NP-hardness, and Bucklin voting has been shown to behave almost as well in terms of control resistance [ER10, EPR11, EFPR11]. We also investigate control resistance experimentally for plurality voting, one of the first voting systems analyzed with respect to electoral control [BTT92, HHR07]. Our findings indicate that NP-hard control problems can often be solved effectively in practice. Moreover, our experiments allow a more fine-grained analysis and comparison-across various control scenarios, vote distribution models, and voting systems-than merely stating NP-hardness for all these control problems.
    03/2012;
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    ABSTRACT: Previous work on voter control, which refers to situations where a chair seeks to change the outcome of an election by deleting, adding, or partitioning voters, takes for granted that the chair knows all the voters' preferences and that all votes are cast simultaneously. However, elections are often held sequentially and the chair thus knows only the previously cast votes and not the future ones, yet needs to decide instantaneously which control action to take. We introduce a framework that models \emph{online voter control in sequential elections}. We show that the related problems can be much harder than in the standard (non-online) case: For certain election systems, even with efficient winner problems, online control by deleting, adding, or partitioning voters is PSPACE-complete, even if there are only two candidates. In addition, we obtain completeness for coNP in the deleting/adding cases with a bounded deletion/addition limit, and for NP in the partition cases with only one candidate. Finally, we show that for plurality, online control by deleting or adding voters is in P, and for partitioning voters is coNP-hard.
    03/2012;
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    ABSTRACT: All previous work on "candidate-control" manipulation of elections has been in the model of full-information, simultaneous voting. This is a problem, since in quite a few real-world settings---from TV singing/dancing talent shows to university faculty-hiring processes---candidates are introduced, and appraised by the voters, in sequence. We provide a natural model for sequential candidate evaluation, a framework for evaluating the computational complexity of controlling the outcome within that framework, and some initial results on the range such complexity can take on. We hope our work will lead to further examination of temporally involved candidate control.
    02/2012;
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    ABSTRACT: Most work on manipulation assumes that all preferences are known to the manipulators. However, in many settings elections are open and sequential, and manipulators may know the already cast votes but may not know the future votes. We introduce a framework, in which manipulators can see the past votes but not the future ones, to model online coalitional manipulation of sequential elections, and we show that in this setting manipulation can be extremely complex even for election systems with simple winner problems. Yet we also show that for some of the most important election systems such manipulation is simple in certain settings. This suggests that when using sequential voting, one should pay great attention to the details of the setting in choosing one's voting rule. Among the highlights of our classifications are: We show that, depending on the size of the manipulative coalition, the online manipulation problem can be complete for each level of the polynomial hierarchy or even for PSPACE. We obtain the most dramatic contrast to date between the nonunique-winner and unique-winner models: Online weighted manipulation for plurality is in P in the nonunique-winner model, yet is coNP-hard (constructive case) and NP-hard (destructive case) in the unique-winner model. And we obtain what to the best of our knowledge are the first P^NP[1]-completeness and P^NP-completeness results in the field of computational social choice, in particular proving such completeness for, respectively, the complexity of 3-candidate and 4-candidate (and unlimited-candidate) online weighted coalition manipulation of veto elections.
    02/2012;
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    ABSTRACT: Multiagent resource allocation provides mechanisms to allocate bundles of resources to agents, where resources are assumed to be indivisible and nonshareable. A central goal is to maximize social welfare of such allocations, which can be measured in terms of the sum of utilities realized by the agents (utilitarian social welfare), in terms of their minimum (egalitarian social welfare), and in terms of their product (Nash product social welfare). Unfortunately, social welfare optimization is a computationally intractable task in many settings. We survey recent approximability and inapproximability results on social welfare optimization in multiagent resource allocation, focusing on the two most central representation forms for utility functions of agents, the bundle form and the k-additive form. In addition, we provide some new (in)approximability results on maximizing egalitarian social welfare and social welfare with respect to the Nash product when restricted to certain special cases.
    International Symposium on Artificial Intelligence and Mathematics (ISAIM 2012), Fort Lauderdale, Florida, USA, January 9-11, 2012; 01/2012 · 0.20 Impact Factor
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    Jörg Rothe, Lena Schend
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    ABSTRACT: In the context of voting, manipulation and control refer to attempts to influence the outcome of elections by either setting some of the votes strategically (i.e., by reporting untruthful preferences) or by altering the structure of elections via adding, deleting, or partitioning either candidates or voters. Since by the celebrated Gibbard–Satterthwaite theorem (and other results expanding its scope) all reasonable voting systems are manipulable in principle and since many voting systems are in principle susceptible to many control types modeling natural control scenarios, much work has been done to use computational complexity as a shield to protect elections against manipulation and control. However, most of this work has merely yielded NP-hardness results, showing that certain voting systems resist certain types of manipulation or control only in the worst case. Various approaches, including studies of the typical case (where votes are given according to some natural distribution), pose serious challenges to such worst-case complexity results and might allow successful manipulation or control attempts, despite the NP-hardness of the corresponding problems. We survey and discuss some recent results on these challenges to complexity results for manipulation and control, including typical-case analyses and experiments, fixed-parameter tractability, domain restrictions (single-peakedness), and approximability.
    International Symposium on Artificial Intelligence and Mathematics (ISAIM 2012), Fort Lauderdale, Florida, USA, January 9-11, 2012; 01/2012 · 0.20 Impact Factor
  • Anja Rey, Jörg Rothe
    European Starting AI Researcher Symposium; 01/2012
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    ABSTRACT: The original possible winner problem is: Given an unweighted election with partial preferences and a distinguished candidate c, can the preferences be extended to total ones such that c wins? We introduce a novel variant of this problem in which not some of the voters' preferences are uncertain but some of their weights. Not much has been known previously about the weighted possible winner problem. We present a general framework to study this problem, both for integer and rational weights, with and without upper bounds on the total weight to be distributed, and with and without ranges to choose the weights from. We study the complexity of these problems for important voting systems such as scoring rules, Copeland, ranked pairs, plurality with runoff, and (simplified) Bucklin and fall-back voting.
    Proceedings of the 20th European Conference on Artificial Intelligence; 01/2012
  • Anja Rey, Jörg Rothe
    European Conference on Artificial Intelligence, Montpellier; 01/2012
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    International Symposium on Artificial Intelligence and Mathematics (ISAIM 2012), Fort Lauderdale, Florida, USA, January 9-11, 2012; 01/2012
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    Dorothea Baumeister, Joerg Rothe
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    ABSTRACT: The Possible Winner problem asks, given an election where the voters' preferences over the candidates are specified only partially, whether a designated candidate can become a winner by suitably extending all the votes. Betzler and Dorn [1] proved a result that is only one step away from a full dichotomy of this problem for the important class of pure scoring rules in the case of unweighted voters and an unbounded number of candidates: Possible Winner is NP-complete for all pure scoring rules except plurality, veto, and the scoring rule with vector (2,1,...,1,0), but is solvable in polynomial time for plurality and veto. We take the final step to a full dichotomy by showing that Possible Winner is NP-complete also for the scoring rule with vector (2,1,...,1,0).
    08/2011;
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    ABSTRACT: Electoral control models ways of changing the outcome of an election via such actions as adding/deleting/partitioning either candidates or voters. To protect elections from such control attempts, computational complexity has been investigated and the corresponding NP-hardness results are termed "resistance." It has been a long-running project of research in this area to classify the major voting systems in terms of their resistance properties. We show that fallback voting, an election system proposed by Brams and Sanver (2009) to combine Bucklin with approval voting, is resistant to each of the common types of control except to destructive control by either adding or deleting voters. Thus fallback voting displays the broadest control resistance currently known to hold among natural election systems with a polynomial-time winner problem. We also study the control complexity of Bucklin voting and show that it performs at least almost as well as fallback voting in terms of control resistance. As Bucklin voting is a special case of fallback voting, each resistance shown for Bucklin voting strengthens the corresponding resistance for fallback voting. Such worst-case complexity analysis is at best an indication of security against control attempts, rather than a proof. In practice, the difficulty of control will depend on the structure of typical instances. 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. Our results, though still in the worst-case complexity model, can be interpreted as significant strengthenings of the resistance demonstrations based on NP-hardness.
    Computing Research Repository - CORR. 03/2011;