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Preliminaries • A social decision scheme (SDS) is a function that maps a preference profile to a lottery over the alternatives. Formally, an SDS is a function f : í µí³¡ í µí³•(í µí³) → ∆(A). • An SDS is majoritarian if it only depends on the (unweighted) majority comparisons between alternatives. • We compare lotteries using stochastic dominance (SD). A(More)
We consider randomized mechanisms with optional participation. Preferences over lotteries are modeled using skew-symmetric bilinear (SSB) utility functions, a generalization of classic von Neumann-Morgenstern utility functions. We show that every welfare-maximizing mechanism entices participation and that the converse holds under additional assumptions. Two(More)
Efficiency—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—are two cornerstones of economics and ubiquitous in important areas such as voting, auctions, or matching markets. Within the context of random assignment, Bogo-molnaia and(More)
Perhaps one of the most fundamental notions in economics is that of Pareto efficiency. We study Pareto efficiency in a setting that involves two kinds of uncertainty: Uncertainty over the possible outcomes is modeled using probability distributions (lotteries) whereas uncertainty over the agents' preferences over lotteries is modeled using sets of plausible(More)
Two fundamental axioms in social choice theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non-probabilistic social choice, these axioms are incompatible with each other. We show that in the context of prob-abilistic social choice, these axioms(More)
Coalition formation provides a versatile framework for analyzing cooperative behavior in multi-agent systems. In particular , hedonic coalition formation has gained considerable attention in the literature. An interesting class of hedonic games recently introduced by Aziz et al. [3] are fractional hedonic games. In these games, the utility an agent assigns(More)
Two important requirements when aggregating the preferences of multiple agents are that the outcome should be economically efficient and the aggrega-tion mechanism should not be manipulable. In this paper, we provide a computer-aided proof of a sweeping impossibility using these two conditions for randomized aggregation mechanisms. More precisely, we show(More)