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Implementing Social Choice Functions: A New Look at Some Impossibility Results

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  • Matthew O. Jackson
  • Sanjay Srivastava

Abstract

For some solution concepts, such as dominant strategies, Nash equilibrium, and undominated strategies, only dictatorial social choice functions are implementable on a full domain of preferences with at least three alternatives. For other solution concepts, such as the iterative removal of weakly dominated strategies, undominated Nash equilibrium, and maximin, it is possible to implement non-dictatorial social choice functions. We begin by offering simple prrofs of several of the "impossibility" results. These proofs provide intuition into the properties of a solution concept which make it impossible to implement non-dictatorial social choice functions. This allows us to provide a characterization of solution concepts which lead to impossibility results, as well as two easily checked sufficient conditions.

Suggested Citation

  • Matthew O. Jackson & Sanjay Srivastava, 1990. "Implementing Social Choice Functions: A New Look at Some Impossibility Results," Discussion Papers 965, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:965
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    1. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April.
    2. Partha Dasgupta & Peter Hammond & Eric Maskin, 1979. "The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 185-216.
    3. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-1099, September.
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