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

Multiwinner Analogues of Plurality Rule: Axiomatic and Algorithmic Perspectives

We characterize the class of committee scoring rules that satisfy the fixed-majority criterion. In some sense, the committee scoring rules in this class are multiwinner analogues of the single-winner Plurality rule, which is uniquely characterized as the only single-winner scoring rule that satisfies the simple majority criterion. We define top-$k$-counting committee scoring rules and show that the fixed majority consistent rules are a subclass of the top-$k$-counting rules. We give necessary and sufficient conditions for a top-$k$-counting rule to satisfy the fixed-majority criterion. We find that, for most of the rules in our new class, the complexity of winner determination is high (that is, the problem of computing the winners is NP-hard), but we also show examples of rules with polynomial-time winner determination procedures. For some of the computationally hard rules, we provide either exact FPT algorithms or approximate polynomial-time algorithms

Fixed-Parameter Algorithms for Computing Kemeny Scores - Theory and Practice

The central problem in this work is to compute a ranking of a set of elements which is "closest to" a given set of input rankings of the elements. We define "closest to" in an established way as having the minimum sum of Kendall-Tau distances to each input ranking. Unfortunately, the resulting problem Kemeny consensus is NP-hard for instances with n input rankings, n being an even integer greater than three. Nevertheless this problem plays a central role in many rank aggregation problems. It was shown that one can compute the corresponding Kemeny consensus list in f(k) + poly(n) time, being f(k) a computable function in one of the parameters "score of the consensus", "maximum distance between two input rankings", "number of candidates" and "average pairwise Kendall-Tau distance" and poly(n) a polynomial in the input size. This work will demonstrate the practical usefulness of the corresponding algorithms by applying them to randomly generated and several real-world data. Thus, we show that these fixed-parameter algorithms are not only of theoretical interest. In a more theoretical part of this work we will develop an improved fixed-parameter algorithm for the parameter "score of the consensus" having a better upper bound for the running time than previous algorithms.Comment: Studienarbei

Multivariate Analyis of Swap Bribery

We consider the computational complexity of a problem modeling bribery in the context of voting systems. In the scenario of Swap Bribery, each voter assigns a certain price for swapping the positions of two consecutive candidates in his preference ranking. The question is whether it is possible, without exceeding a given budget, to bribe the voters in a way that the preferred candidate wins in the election. We initiate a parameterized and multivariate complexity analysis of Swap Bribery, focusing on the case of k-approval. We investigate how different cost functions affect the computational complexity of the problem. We identify a special case of k-approval for which the problem can be solved in polynomial time, whereas we prove NP-hardness for a slightly more general scenario. We obtain fixed-parameter tractability as well as W[1]-hardness results for certain natural parameters.Comment: 20 pages. Conference version published at IPEC 201