arXiv subjects

Jörg Rothe

Publications and source records attributed to Jörg Rothe.

At least 19 recordsLinked to original sources

arXiv2026

Navigating the Complexity Landscape of Nominee Selection in Schulze Voting

We study the Possible President problem and the Necessary President problem for Schulze voting, a rule that, due to its many desirable axiomatic properties, is popular in practice. In both problems, we are given an election with the candidates partitioned into a set of parties, and we are interested in questions about a given distinguished party. In the Possible President problem, we ask whether it is possible for the parties to each nominate exactly one candidate such that the nominee of the distinguished party is a Schulze winner of the resulting election with only the nominees running. In the Necessary President problem, we ask whether the distinguished party's nominee is a Schulze winner of the resulting election, irrespective of the nomination from the other parties. Rothe and Woitaschik have shown that Possible President is NP-complete and Necessary President is coNP-complete for Schulze elections. We complement and improve their results by a more fine-grained analysis: we determine the parameterized complexity of both problems with respect to all possible parameterizations, where we consider each of three natural parameters -- the number of voters, the maximum party size, and the number of parties -- to be either a constant, a parameter, or unbounded. In particular, we obtain dichotomies regarding the number of voters for both problems.

cs.GT↗

arXiv2026

How to Tamper with a Parliament: Strategic Campaigns in Apportionment Elections

In parliamentary elections, parties compete for a limited, typically fixed number of seats. Most parliaments are assembled using apportionment methods that distribute the seats based on the parties' vote counts. Common apportionment methods include divisor sequence methods (like D'Hondt or Sainte-Laguë), the largest-remainder method, and first-past-the-post. In many countries, an electoral threshold is implemented to prevent very small parties from entering the parliament. Further, several countries have apportionment systems that incorporate multiple districts. We study how computationally hard it is to change the election outcome (i.e., to increase or limit the influence of a distinguished party) by convincing a limited number of voters to change their vote. We refer to these bribery-style attacks as \emph{strategic campaigns} and study the corresponding problems in terms of their computational (both classical and parameterized) complexity. We also run extensive experiments on real-world election data and study the effectiveness of optimal campaigns, in particular as opposed to using heuristic bribing strategies and with respect to the influence of the threshold and the influence of the number of districts. For apportionment elections with threshold, finally, we propose -- as an alternative to the standard top-choice mode -- the second-chance mode where voters of parties below the threshold receive a second chance to vote for another party, and we establish computational complexity results also in this setting.

cs.GT↗

arXiv2025

Skating System Unveiled: Exploring Preference Aggregation in Ballroom Tournaments

The Skating System, which originated from the scrutineering system in dance sport tournaments, can be formulated as a voting system: We introduce and formalize the Skating System Single (SkS, for short), a new voting system embedded into the framework of computational social choice. Although SkS has similarities with Bucklin voting, it differs from it because it is subject to additional constraints when determining the election winners. Through an analysis of the axiomatic properties of SkS and of its vulnerability to manipulative and electoral control attacks, we compare SkS with Bucklin voting and provide insights into its potential strengths and weaknesses. In particular, we show that SkS satisfies nondictatorship as well as the majority criterion, positive responsiveness, monotonicity, and citizens' sovereignty but violates the Condorcet criterion, strong monotonicity, independence of clones, consistency, participation, resoluteness, and strategy-proofness. Further, we study manipulation, i.e., where (groups of) voters vote strategically to improve the outcome of an election in their favor, showing that the constructive coalitional weighted manipulation problem for SkS is NP-complete, while the destructive variant can be solved in polynomial time. Lastly, we initiate the study of electoral control, where an external agent attempts to change the election outcome by interfering with the structure of the election. Here, we show NP-completeness for constructive and destructive control by deleting candidates as well as for constructive control by adding voters, whereas we show that the problem of destructive control by adding voters can be solved in polynomial time.

cs.GT↗

arXiv2025

Solving Four Open Problems about Core Stability in Altruistic Hedonic Games

Hedonic games -- at the interface of cooperative game theory and computational social choice -- are coalition formation games in which the players have preferences over the coalitions they can join. Kerkmann et al. [13] introduced altruistic hedonic games where the players' utilities depend not only on their own but also on their friends' valuations of coalitions. The complexity of the verification problem for core stability has remained open in four variants of altruistic hedonic games: namely, for the variants with average- and minimum-based "equal-treatment" and "altruistic-treatment" preferences. We solve these four open questions by proving the corresponding problems coNP-complete; our reductions rely on rather intricate gadgets in the related networks of friends.

cs.GT↗

arXiv2025

Control by Deleting Players from Weighted Voting Games Is NP^PP-Complete for the Penrose-Banzhaf Power Index

Weighted voting games are a popular class of coalitional games that are widely used to model real-life situations of decision-making. They can be applied, for instance, to analyze legislative processes in parliaments or voting in corporate structures. Various ways of tampering with these games have been studied, among them merging or splitting players, fiddling with the quota, and controlling weighted voting games by adding or deleting players. While the complexity of control by adding players to such games so as to change or maintain a given player's power has been recently settled, the complexity of control by deleting players from such games (with the same goals) remained open. We show that when the players' power is measured by the probabilistic Penrose-Banzhaf index, some of these problems are complete for NP^PP -- the class of problems solvable by NP machines equipped with a PP ("probabilistic polynomial time") oracle. Our results optimally improve the currently known lower bounds of hardness for much smaller complexity classes, thus providing protection against SAT-solving techniques in practical applications.

cs.GT↗

arXiv2024

Control by Adding Players to Change or Maintain the Shapley-Shubik or the Penrose-Banzhaf Power Index in Weighted Voting Games Is Complete for NP^PP

Weighted voting games are a well-known and useful class of succinctly representable simple games that have many real-world applications, e.g., to model collective decision-making in legislative bodies or shareholder voting. Among the structural control types being analyzing, one is control by adding players to weighted voting games, so as to either change or to maintain a player's power in the sense of the (probabilistic) Penrose-Banzhaf power index or the Shapley-Shubik power index. For the problems related to this control, the best known lower bound is PP-hardness, where PP is "probabilistic polynomial time," and the best known upper bound is the class NP^PP, i.e., the class NP with a PP oracle. We optimally raise this lower bound by showing NP^PP-hardness of all these problems for the Penrose-Banzhaf and the Shapley-Shubik indices, thus establishing completeness for them in that class. Our proof technique may turn out to be useful for solving other open problems related to weighted voting games with such a complexity gap as well.

cs.GT↗

arXiv2024

Toward Completing the Picture of Control in Schulze and Ranked Pairs Elections

Both Schulze and ranked pairs are voting rules that satisfy many natural, desirable axioms. Many standard types of electoral control (with a chair seeking to change the outcome of an election by interfering with the election structure) have already been studied. However, for control by replacing candidates or voters and for (exact) multimode control that combines multiple standard attacks, many questions remain open. We solve a number of these open cases for Schulze and ranked pairs. In addition, we fix a flaw in the reduction of Menton and Singh [IJCAI 2013] showing that Schulze is resistant to constructive control by deleting candidates and re-establish a vulnerability result for destructive control by deleting candidates. In some of our proofs, we study variants of s-t vertex cuts in graphs that are related to our control problems.

cs.GT↗

arXiv2023

Cutting a Cake Is Not Always a 'Piece of Cake': A Closer Look at the Foundations of Cake-Cutting Through the Lens of Measure Theory

Cake-cutting is a playful name for the fair division of a heterogeneous, divisible good among agents, a well-studied problem at the intersection of mathematics, economics, and artificial intelligence. The cake-cutting literature is rich and edifying. However, different model assumptions are made in its many papers, in particular regarding the set of allowed pieces of cake that are to be distributed among the agents and regarding the agents' valuation functions by which they measure these pieces. We survey the commonly used definitions in the cake-cutting literature, highlight their strengths and weaknesses, and make some recommendations on what definitions could be most reasonably used when looking through the lens of measure theory.

cs.GT↗

arXiv2023

Altruism in Coalition Formation Games

Nguyen et al. [1] introduced altruistic hedonic games in which agents' utilities depend not only on their own preferences but also on those of their friends in the same coalition. We propose to extend their model to coalition formation games in general, considering also the friends in other coalitions. Comparing our model to altruistic hedonic games, we argue that excluding some friends from the altruistic behavior of an agent is a major disadvantage that comes with the restriction to hedonic games. After introducing our model and showing some desirable properties, we additionally study some common stability notions and provide a computational analysis of the associated verification and existence problems.

cs.GT↗

arXiv2021

Stability of Special Graph Classes

Frei et al. [6] showed that the problem to decide whether a graph is stable with respect to some graph parameter under adding or removing either edges or vertices is $Θ_2^{\text{P}}$-complete. They studied the common graph parameters $α$ (independence number), $β$ (vertex cover number), $ω$ (clique number), and $χ$ (chromatic number) for certain variants of the stability problem. We follow their approach and provide a large number of polynomial-time algorithms solving these problems for special graph classes, namely for graphs without edges, complete graphs, paths, trees, forests, bipartite graphs, and co-graphs.

cs.CC↗

arXiv2020

Complexity of Stability

Graph parameters such as the clique number, the chromatic number, and the independence number are central in many areas, ranging from computer networks to linguistics to computational neuroscience to social networks. In particular, the chromatic number of a graph (i.e., the smallest number of colors needed to color all vertices such that no two adjacent vertices are of the same color) can be applied in solving practical tasks as diverse as pattern matching, scheduling jobs to machines, allocating registers in compiler optimization, and even solving Sudoku puzzles. Typically, however, the underlying graphs are subject to (often minor) changes. To make these applications of graph parameters robust, it is important to know which graphs are stable for them in the sense that adding or deleting single edges or vertices does not change them. We initiate the study of stability of graphs for such parameters in terms of their computational complexity. We show that, for various central graph parameters, the problem of determining whether or not a given graph is stable is complete for Θ_2^p, a well-known complexity class in the second level of the polynomial hierarchy, which is also known as "parallel access to NP."

cs.CC↗

arXiv2020

Signatures of technetium oxidation states: a new approach

A general strategy for the determination of Tc oxidation state by new approach involving X-ray absorption near edge spectroscopy (XANES) at the Tc L3 edge is shown. A comprehensive series of 99Tc compounds, ranging from oxidation states I to VII, was measured and subsequently simulated within the framework of crystal-field multiplet theory. The observable trends in the absorption edge energy shift in combination with the spectral shape allow for a deeper understanding of complicated Tc coordination chemistry. This approach can be extended to numerous studies of Tc systems as this method is one of the most sensitive methods for accurate Tc oxidation state and ligand characterization.

physics.chem-ph↗

arXiv2019

The Complexity of Online Bribery in Sequential Elections (Extended Abstract)

Prior work on the complexity of bribery assumes that the bribery happens simultaneously, and that the briber has full knowledge of all voters' votes. But neither of those assumptions always holds. In many real-world settings, votes come in sequentially, and the briber may have a use-it-or-lose-it moment to decide whether to bribe/alter a given vote, and at the time of making that decision, the briber may not know what votes remaining voters are planning on casting. In this paper, we introduce a model for, and initiate the study of, bribery in such an online, sequential setting. We show that even for election systems whose winner-determination problem is polynomial-time computable, an online, sequential setting may vastly increase the complexity of bribery, in fact jumping the problem up to completeness for high levels of the polynomial hierarchy or even PSPACE. On the other hand, we show that for some natural, important election systems, such a dramatic complexity increase does not occur, and we pinpoint the complexity of their bribery problems in the online, sequential setting.

cs.GT↗

arXiv2013

Complexity of Manipulation, Bribery, and Campaign Management in Bucklin and Fallback Voting

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.

cs.GT↗

arXiv2013

False-Name Manipulation in Weighted Voting Games is Hard for Probabilistic Polynomial Time

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.

cs.GT↗

arXiv2012

Control Complexity in Bucklin and Fallback Voting

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.

cs.CC↗

arXiv2011

Structural characterization of Nd-doped calcium aluminosilicate glasses designed for the preparation of zirconolite (CaZrTi2O7) -based glass-ceramic

This work concerns glasses belonging to SiO2-Al2O3-CaO-ZrO2-TiO2-Nd2O3 system that lead to zirconolite crystallization in their bulk after nucleation + crystal growth thermal treatments and that could find application as nuclear waste form. The understanding of crystallization processes in glasses implied to investigate their structure. The environment around Ti, Zr (nucleating agents) and Nd was characterized for various Nd2O3 loadings. Electron spin resonance study of the small amount of Ti3+ occurring in glasses enabled to identify two types of sites for titanium. EXAFS showed that Zr occupied a quite well defined 6-7-fold site coordinated by oxygen at 2.20 Å, with second neighbors that could correspond to Ca/Ti and Zr around 3.5 Å. This short range order presents some similarities with zirconolite, which could predispose glass to zirconolite nucleation. Nd environment was probed by optical spectroscopies, ESR and EXAFS. Results showed that the environment around Nd was very constrained by the glassy network and significantly differed from the one in zirconolite. Nd occupied a highly distorted 8-9-fold coordinated site in glass with oxygen atoms at 2.53 Å. No second neighbors were clearly identified by EXAFS around Nd, but the study of Nd optical fluorescence decays suggested a strong interaction between Nd ions.

cond-mat.mtrl-sci↗

arXiv2011

The Complexity of Probabilistic Lobbying

We propose models for lobbying in a probabilistic environment, in which an actor (called "The Lobby") seeks to influence voters' preferences of voting for or against multiple issues when the voters' preferences are represented in terms of probabilities. In particular, we provide two evaluation criteria and two bribery methods to formally describe these models, and we consider the resulting forms of lobbying with and without issue weighting. We provide a formal analysis for these problems of lobbying in a stochastic environment, and determine their classical and parameterized complexity depending on the given bribery/evaluation criteria and on various natural parameterizations. Specifically, we show that some of these problems can be solved in polynomial time, some are NP-complete but fixed-parameter tractable, and some are W[2]-complete. Finally, we provide approximability and inapproximability results for these problems and several variants.

cs.CC↗