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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)
An important issue in multi-agent systems is the exploitation of synergies via coalition formation. We initiate the formal study of fractional hedonic games. In fractional he-donic games, the utility of a player in a coalition structure is the average value he ascribes to the members of his coalition. Among other settings, this covers situations in which(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)
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)
We consider the well-studied cake cutting problem in which the goal is to identify an envy-free allocation based on a minimal number of queries from the agents. The problem has attracted considerable attention within various branches of computer science, mathematics, and economics. Although, the elegant Selfridge-Conway envy-free protocol for three agents(More)
We consider the well-studied cake cutting problem in which the goal is to find an envy-free allocation based on queries from n agents. The problem has received attention in computer science, mathematics, and economics. It has been a major open problem whether there exists a discrete and bounded envy-free protocol. We resolve the problem by proposing a(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 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)