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We study computational aspects of three prominent voting rules that use approval ballots to elect multiple winners. These rules are satisfaction approval voting, proportional approval voting, and reweighted approval voting. We first show that computing the winner for proportional approval voting is NP-hard, closing a long standing open problem. As none of(More)
We investigate the computational complexity of finding optimal bribery schemes in voting domains where the candidate set is the Cartesian product of a set of variables and voters use CP-nets, an expressive and compact way to represent preferences. To do this, we generalize the traditional bribery problem to take into account several issues over which agents(More)
We investigate the computational complexity of finding optimal bribery schemes in voting domains where the candidate set is the Cartesian product of a set of variables and agents' preferences are represented as CP-nets. We show that, in most cases, the bribery problem is easy. This also holds for some cases of k-approval, where bribery is difficult in(More)
We propose various models for lobbying in a probabilistic environment , in which an actor (called " The Lobby ") seeks to influence the voters' preferences of voting for or against multiple issues when the voters' preferences are represented in terms of probabilities. In particular, we provide two evaluation criteria and three bribery methods to formally(More)
We study the impact on strategic voting of tie-breaking by means of considering the order of tied candidates within a random vote. We compare this to another non-deterministic tie-breaking rule where we simply choose candidate uniformly at random. In general, we demonstrate that there is no connection between the computational complexity of computing a(More)
We study the computational complexity of optimal bribery and manipulation schemes for sports tournaments with uncertain information: cup; challenge or caterpillar; and round robin. Our results carry over to the equivalent voting rules: sequential pair-wise elections, cup, and Copeland, when the set of candidates is exactly the set of voters. This(More)
In this paper we present a twofold generalization of conditional preference networks (CP-nets) that incorporates uncertainty. CP-nets are a formal tool to model qualitative conditional statements (cp-statements) about preferences over a set of objects. They are inherently static structures, both in their ability to capture dependencies between objects and(More)
A Markov Decision Process (MDP) policy presents, for each state, an action, which preferably maximizes the expected reward accrual over time. In this paper, we present a novel system that generates, in real time, natural language explanations of the optimal action, recommended by an MDP while the user interacts with the MDP policy. We rely on natural(More)
The probabilistic serial (PS) rule is a prominent randomized rule for assigning indivisible goods to agents. Although it is well known for its good fairness and welfare properties, it is not strategyproof. In view of this, we address several fundamental questions regarding equilibria under PS. Firstly, we show that Nash deviations under the PS rule can(More)