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Weighted voting is a classic model of cooperation among agents in decision-making domains. In such games, each player has a weight, and a coalition of players wins the game if its total weight meets or exceeds a given quota. A player's power in such games is usually not directly proportional to his weight, and is measured by a power index, the most(More)
—Weighted voting games are mathematical models , used to analyse situations where voters with variable voting weight vote in favour of or against a decision. They have been applied in various political and economic organizations. Similar combinatorial models are also encountered in neuroscience, threshold logic, reliability theory and distributed systems.(More)
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)
In social choice settings with linear preferences, random dictatorship is known to be the only social decision scheme satisfying strategyproofness and ex post efficiency. When also allowing indifferences, random serial dictatorship (RSD) is a well-known generalization of random dictatorship that retains both properties. RSD has been particularly successful(More)
We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or ran-domized allocations to systematically define varying notions of proportionality and envy-freeness for discrete assignments. The(More)
Two fundamental notions in microeconomic theory are ef-ficiency—no agent can be made better off without making another one worse off—and strategyproofness—no agent can obtain a more preferred outcome by misrepresenting his preferences. When social outcomes are probability distributions (or lotteries) over alternatives, there are varying degrees of these(More)
We present computational results concerning stable partitions in additively separable hedonic games. First, we propose a polynomial-time algorithm to compute a contractually individually stable partition. This contrasts with previous results such as NP-hardness of computing individually stable or Nash stable partitions. Secondly, we prove that checking(More)
Cooperative games provide an appropriate framework for fair and stable resource allocation in multiagent systems. This paper focusses on monotone cooperative games, a class which comprises a variety of games that have enjoyed special attention within AI, in particular, skill games, connectiv-ity games, flow games, voting games, and matching games. Given a(More)