Nonmanipulable decision mechanisms for economic environments
Gibbard (1973), Satterthwaite (1975) and, more recently, Barberà and Peleg (1990) have considered the existence of strategy-proof voting schemes for the case that the social alternatives are purely public. The results which these authors obtained were mostly negative. In the present paper, social decision problems are investigated when there are both public alternatives and private goods so that a conflict of interests arises with respect to the latter. Moreover, it is required that decision mechanisms be responsive to the individuals' preferences; these mechanisms need not always select Pareto optimal outcomes. The results of the present paper show that it is not the purely public character of the social alternatives that generated the impossibility results of Gibbard, Satterthwaite and many others. The existence of public components together with opposing interests among individuals yields the same negative conclusions. Two concepts used by the author have to be made more precise before the main results of the paper can be stated. Firstly, a mechanism is said to be responsive if at every preference profile, each person's utility is maximized conditionally, given the outcome assigned to all other individuals. Note that when the set of feasible alternatives is purely public, then every mechanism is vacuously responsive. The second concept is the notion of degree of conflict which provides a measure of the conflict of interests present in a set of alternatives. When the set of feasible alternatives is purely public, the range of a voting scheme contains a degree of conflict equal to its cardinality. If the range consists of just one alternative, there are no conflictive outcomes for the individuals. It is then said that there is a conflict of degree one. The negative result of Theorem 1 presupposes a conflict of degree greater than two. Theorem 1. For two individuals and under the condition that for each person, her set of admissible utility functions comprises all the continuous functions on her set of possible outcomes, every nonmanipulable responsive mechanism whose range contains a conflict of degree greater than two, is dictatorial. This result contains the Barberà and Peleg theorem as a special case for the situation of two individuals. Theorem 2. For any finite number of individuals and under the requirement of Theorem 1 with respect to the set of admissible utility functions, every nonmanipulable responsive mechanism whose range of public components contains more than two outcomes, is dictatorial. When the set of alternatives is purely public, the last result coincides with the Barberà and Peleg theorem.
scientific article; zbMATH DE number 617485