We propose a simple criterion to compare generalized median voter schemes according to their manipulability. We identify three necessary and sufficient conditions for the comparability of two generalized median voter schemes in terms of their vulnerability to manipulation. The three conditions are stated using the two associated families of monotonic fixed ballots and depend very much on the power each agent has to unilaterally change the outcomes of the two generalized median voter schemes. We perform a specific analysis of all median voter schemes: the anonymous subfamily of generalized median voter schemes.
We characterize the set of all obviously strategy-proof and onto social choice functions on the domain of single-peaked preferences. Since obvious strategyproofness implies strategy-proofness, and the set of strategy-proof and onto social choice functions on this domain coincides with the class of generalized median voter schemes, we focus on this class. We identify a condition on generalized median voter schemes for which the following characterization holds. A generalized median voter scheme is obviously strategy-proof if and only if it satis…es the increasing intersection property. Our proof is constructive; for each generalized median voter scheme that satis…es the increasing intersection property we de…ne an extensive game form that implements it in obviously dominant strategies.
We study cooperative and competitive solutions for a many-to-many generalization of Shapley and Shubik’s (1971) assignment game. We consider the Core, three other notions of group stability, and two alternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related to the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated with the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of matrices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view.
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