Arkadii Slinko

Stanisław Szufa, Niclas Boehmer, Robert Bredereck et al.

Our main contribution is the introduction of the map of elections framework. A map of elections consists of three main elements: (1) a dataset of elections (i.e., collections of ordinal votes over given sets of candidates), (2) a way of measuring similarities between these elections, and (3) a representation of the elections in the 2D Euclidean space as points, so that the more similar two elections are, the closer are their points. In our maps, we mostly focus on datasets of synthetic elections, but we also show an example of a map over real-life ones. To measure similarities, we would have preferred to use, e.g., the isomorphic swap distance, but this is infeasible due to its high computational complexity. Hence, we propose polynomial-time computable positionwise distance and use it instead. Regarding the representations in 2D Euclidean space, we mostly use the Kamada-Kawai algorithm, but we also show two alternatives. We develop the necessary theoretical results to form our maps and argue experimentally that they are accurate and credible. Further, we show how coloring the elections in a map according to various criteria helps in analyzing results of a number of experiments. In particular, we show colorings according to the scores of winning candidates or committees, running times of ILP-based winner determination algorithms, and approximation ratios achieved by particular algorithms.

Yvo Desmedt, Arkadii Slinko

The study of Rational Secret Sharing initiated by Halpern and Teague regards the reconstruction of the secret in secret sharing as a game. It was shown that participants (parties) may refuse to reveal their shares and so the reconstruction may fail. Moreover, a refusal to reveal the share may be a dominant strategy of a party. In this paper we consider secret sharing as a sub-action or subgame of a larger action/game where the secret opens a possibility of consumption of a certain common good. We claim that utilities of participants will be dependent on the nature of this common good. In particular, Halpern and Teague scenario corresponds to a rivalrous and excludable common good. We consider the case when this common good is non-rivalrous and non-excludable and find many natural Nash equilibria. We list several applications of secret sharing to demonstrate our claim and give corresponding scenarios. In such circumstances the secret sharing scheme facilitates a power sharing agreement in the society. We also state that non-reconstruction may be beneficial for this society and give several examples.

Piotr Skowron, Piotr Faliszewski, Arkadii Slinko

We study the complexity of (approximate) winner determination under the Monroe and Chamberlin--Courant multiwinner voting rules, which determine the set of representatives by optimizing the total (dis)satisfaction of the voters with their representatives. The total (dis)satisfaction is calculated either as the sum of individual (dis)satisfactions (the utilitarian case) or as the (dis)satisfaction of the worst off voter (the egalitarian case). We provide good approximation algorithms for the satisfaction-based utilitarian versions of the Monroe and Chamberlin--Courant rules, and inapproximability results for the dissatisfaction-based utilitarian versions of them and also for all egalitarian cases. Our algorithms are applicable and particularly appealing when voters submit truncated ballots. We provide experimental evaluation of the algorithms both on real-life preference-aggregation data and on synthetic data. These experiments show that our simple and fast algorithms can in many cases find near-perfect solutions.

Ali Hameed, Arkadii Slinko

Beimel, Tassa and Weinreb (2008) and Farras and Padro (2010) partially characterized access structures of ideal weighted threshold secret sharing schemes in terms of the operation of composition. They classified indecomposable ideal weighted threshold access structures, and proved that any other ideal weighted threshold access structure is a composition of indecomposable ones. It remained unclear which compositions of indecomposable weighted threshold access structures are weighted. In this paper we fill the gap. Using game-theoretic techniques we determine which compositions of indecomposable ideal access structures are weighted, and obtain an if and only if characterization of ideal weighted threshold secret sharing schemes.