Approximation and Hardness of Shift-Bribery

In the Shift-Bribery problem we are given an election, a preferred candidate, and the costs of shifting this preferred candidate up the voters' preference orders. The goal is to find such a set of shifts that ensures that the preferred candidate wins the election. We give the first polynomial-time approximation scheme for the Shift-Bribery problem for the case of positional scoring rules, and for the Copeland rule we show strong inapproximability results.Comment: An extended abstract of this work appears in AAAI'1

Schulze and Ranked-Pairs Voting are Fixed-Parameter Tractable to Bribe, Manipulate, and Control

Schulze and ranked-pairs elections have received much attention recently, and the former has quickly become a quite widely used election system. For many cases these systems have been proven resistant to bribery, control, or manipulation, with ranked pairs being particularly praised for being NP-hard for all three of those. Nonetheless, the present paper shows that with respect to the number of candidates, Schulze and ranked-pairs elections are fixed-parameter tractable to bribe, control, and manipulate: we obtain uniform, polynomial-time algorithms whose degree does not depend on the number of candidates. We also provide such algorithms for some weighted variants of these problems

Broadening the Complexity-theoretic Analysis of Manipulative Attacks in Group Identification

In the Group Identification problem, we are given a set of individuals and are asked to identify a socially qualified subset among them. Each individual in the set has an opinion about who should be considered socially qualified. There are several different rules that can be used to determine the socially qualified subset based on these mutual opinions. In a manipulative attack, an outsider attempts to exploit the way the used rule works, with the goal of changing the outcome of the selection process to their liking. In recent years, the complexity of group control and bribery based manipulative attacks in Group Identification has been the subject of intense research. However, the picture is far from complete, and there remain many open questions related to what exactly makes certain problems hard, or certain rules immune to some attacks. Supplementing previous results, we examine the complexity of group microbribery on so-called protective problem instances; that is, instances where all individuals from the constructive target set are already socially qualified initially. In addition, we study a relaxed variant of group control by deleting individuals for the consent rules, the consensus-start-respecting rule, and the liberal-start-respecting rule. Based on existing literature, we also formalize three new social rules of the iterative consensus type, and we provide a comprehensive complexity-theoretic analysis of group control and bribery problems for these rules.Comment: 93 pages, 8 figures, 3 table

A deep exploration of the complexity border of strategic voting problems

Voting has found applications in a variety of areas. Unfortunately, in a voting activity there may exist strategic individuals who have incentives to attack the election by performing some strategic behavior. One possible way to address this issue is to use computational complexity as a barrier against the strategic behavior. The point is that if it is NP-hard to successfully perform a strategic behavior, the strategic individuals may give up their plan of attacking the election. This thesis is concerned with strategic behavior in restricted elections, in the sense that the given elections are subject to some combinatorial restrictions. The goal is to find out how the complexity of the strategic behavior changes from the very restricted case to the general case.Abstimmungen werden auf verschiedene Gebiete angewendet. Leider kann es bei einer Abstimmung einzelne Teilnehmer geben, die Vorteile daraus ziehen, die Wahl durch strategisches Verhalten zu manipulieren. Eine Möglichkeit diesem Problem zu begegnen ist es, die Berechnungskomplexität als Hindernis gegen strategisches Verhalten zu nutzen. Die Annahme ist, dass falls es NP-schwer ist, um strategisches Verhalten erfolgreich anzuwenden, der strategisch Handelnde vielleicht den Plan aufgibt die Abstimmung zu attackieren. Diese Arbeit befasst sich mit strategischem Vorgehen in eingeschränkten Abstimmungen in dem Sinne, dass die vorgegebenen Abstimmungen kombinatorischen Einschränkungen unterliegen. Ziel ist es herauszufinden, wie sich die Komplexität des strategischen Handelns von dem sehr eingeschränkten zu dem generellen Fall ändert

Collecting, Classifying, Analyzing, and Using Real-World Elections

We present a collection of $7582$ real-world elections divided into $25$ datasets from various sources ranging from sports competitions over music charts to survey- and indicator-based rankings. We provide evidence that the collected elections complement already publicly available data from the PrefLib database, which is currently the biggest and most prominent source containing $701$ real-world elections from $36$ datasets. Using the map of elections framework, we divide the datasets into three categories and conduct an analysis of the nature of our elections. To evaluate the practical applicability of previous theoretical research on (parameterized) algorithms and to gain further insights into the collected elections, we analyze different structural properties of our elections including the level of agreement between voters and election's distances from restricted domains such as single-peakedness. Lastly, we use our diverse set of collected elections to shed some further light on several traditional questions from social choice, for instance, on the number of occurrences of the Condorcet paradox and on the consensus among different voting rules