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

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

The G-20 and International Financial Institution Governance

This paper addresses the agenda for the Group of Twenty (G-20) leaders' meeting in Seoul, Korea in November 2010. This is an opportunity and challenge for Asian leaders in particular. Their test will be, first, to demonstrate that they can responsibly advance economic recovery. They must also deliver on institutional reform, in particular of the International Monetary Fund (IMF). Author Edwin M. Truman advocates a substantial expansion of the IMF's role as lender of last resort that is integrated with the surveillance role of the IMF in the form of comprehensive prequalification for IMF assistance and policy advice and a substantial increase in the IMF's financial resources. Truman also propose an approach to meaningful reform of the distribution of IMF quotas along with limiting European seats on the IMF executive board.International Monetary Fund, Group of Twenty G20, China, Korea, Asia, special drawing rights, economic growth, exchange rates

Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers

We introduce a new Condorcet consistent voting method, called Split Cycle. Split Cycle belongs to the small family of known voting methods satisfying independence of clones and the Pareto principle. Unlike other methods in this family, Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections. Thus, relative to other clone-independent Paretian methods, Split Cycle mitigates “spoiler effects” and “strong no show paradoxes.

Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers

We propose a Condorcet consistent voting method that we call Split Cycle. Split Cycle belongs to the small family of known voting methods that significantly narrow the choice of winners in the presence of majority cycles while also satisfying independence of clones. In this family, only Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections. Thus, in contrast to other clone-independent methods, Split Cycle mitigates both "spoiler effects" and "strong no show paradoxes."Comment: 71 pages, 15 figures. Added a new explanation of Split Cycle in Section 1, updated the caption to Figure 2, the discussion in Section 3.3, and Remark 4.11, and strengthened Proposition 6.20 to Theorem 6.20 to cover single-voter resolvability in addition to asymptotic resolvability. Thanks to Nicolaus Tideman for helpful discussio

Social choice on complex objects: A geometric approach

Marengo and Pasquali (2008) present a model of object construction in majority voting and show that, in general, by appropriate changes of such bundles, different social outcomes may be obtained. In this paper we extend and generalize this approach by providing a geometric model of individual preferences and social aggregation based on hyperplanes and their arrangements. As an application of this model we give a necessary condition for existence of a local social optimum. Moreover we address the question if a social decision rule depends also upon the number of voting agents. More precisely: are there social decision rules that can be obtained by an odd (even) number of voting agent which cannot be obtained by only three (two) voting agent? The answer is negative. Indeed three (or two) voting agent can produce all possible social decision rules.Social choice; object construction power; agenda power; intransitive cycles; arrangements; graph theory.

The Geometry of Manipulation — A Quantitative Proof of the Gibbard Satterthwaite Theorem

We prove a quantitative version of the Gibbard-Satterthwaite theorem. We show that a uniformly chosen voter profile for a neutral social choice function f of q ≥ 4 alternatives and n voters will be manipulable with probability at least 10−4∈2 n −3 q −30, where ∈ is the minimal statistical distance between f and the family of dictator functions. Our results extend those of [11], which were obtained for the case of 3 alternatives, and imply that the approach of masking manipulations behind computational hardness (as considered in [4,6,9,15,7]) cannot hide manipulations completely. Our proof is geometric. More specifically it extends the method of canonical paths to show that the measure of the profiles that lie on the interface of 3 or more outcomes is large. To the best of our knowledge our result is the first isoperimetric result to establish interface of more than two bodies