The Complexity of Manipulating kk-Approval Elections

An important problem in computational social choice theory is the complexity of undesirable behavior among agents, such as control, manipulation, and bribery in election systems. These kinds of voting strategies are often tempting at the individual level but disastrous for the agents as a whole. Creating election systems where the determination of such strategies is difficult is thus an important goal. An interesting set of elections is that of scoring protocols. Previous work in this area has demonstrated the complexity of misuse in cases involving a fixed number of candidates, and of specific election systems on unbounded number of candidates such as Borda. In contrast, we take the first step in generalizing the results of computational complexity of election misuse to cases of infinitely many scoring protocols on an unbounded number of candidates. Interesting families of systems include $k$-approval and $k$-veto elections, in which voters distinguish $k$ candidates from the candidate set. Our main result is to partition the problems of these families based on their complexity. We do so by showing they are polynomial-time computable, NP-hard, or polynomial-time equivalent to another problem of interest. We also demonstrate a surprising connection between manipulation in election systems and some graph theory problems

How Hard Is It to Control an Election by Breaking Ties?

We study the computational complexity of controlling the result of an election by breaking ties strategically. This problem is equivalent to the problem of deciding the winner of an election under parallel universes tie-breaking. When the chair of the election is only asked to break ties to choose between one of the co-winners, the problem is trivially easy. However, in multi-round elections, we prove that it can be NP-hard for the chair to compute how to break ties to ensure a given result. Additionally, we show that the form of the tie-breaking function can increase the opportunities for control. Indeed, we prove that it can be NP-hard to control an election by breaking ties even with a two-stage voting rule.Comment: Revised and expanded version including longer proofs and additional result

Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context