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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 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 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)
The probabilistic serial (PS) rule is one of the most prominent randomized rules for the assignment problem. It is well-known for its desirable fairness and welfare properties. However, PS is not immune to manipulative behaviour by the agents. We initiate the study of the computational complexity of an agent manipulating the PS rule. We show that computing(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)
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)
Positional scoring rules in voting compute the score of an alternative by summing the scores for the alternative induced by every vote. This summation principle ensures that all votes contribute equally to the score of an alternative. We relax this assumption and, instead, aggregate scores by taking into account the rank of a score in the ordered list of(More)