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A social choice function implementable via backward induction with values in the ultimate uncovered set

Author

Listed:
  • Michel Le Breton

    () (CORE, Voie du Roman Pays, 34, B-1348, Louvain-la-Neuve, Belgium)

  • Peter J. Coughlan

    () (Harvard University, Graduate School of Business Administration, Morgan Hall 217, Soldiers Field Road, Boston, MA 02163, USA)

Abstract

We prove the existence of a social choice function implementable via backward induction which always selects within the ultimate uncovered set. Whereas the uncovered set is the set of maximal elements of the covering relation, the ultimate uncovered set is the set obtained by iterative application of this covering operation. Dutta and Sen (1993) showed that any social choice function which is the solution of a generalized binary voting procedure is implementable via backward induction. Our result follows from Dutta and Sen's theorem, in that we construct a binary voting procedure always selecting within the ultimate uncovered set. We use the classical multistage elimination procedure, which always selects an alternative within the uncovered set. When this procedure is also used to select among all of the possible agendas or orderings of alternatives within the procedure, the alternative selected (from the agenda selected) will be within the uncovered set of the uncovered set. Our result follows from repeated application of this construction. Intuitively, the procedure constructed consists of requiring agents to vote on how they should vote and so on.

Suggested Citation

  • Michel Le Breton & Peter J. Coughlan, 1999. "A social choice function implementable via backward induction with values in the ultimate uncovered set," Review of Economic Design, Springer;Society for Economic Design, vol. 4(2), pages 153-160.
  • Handle: RePEc:spr:reecde:v:4:y:1999:i:2:p:153-160
    Note: Received: 7 April 1997 / Accepted: 15 October 1998
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    Keywords

    Implementation via backward induction; Condorcet social choice function; ultimate uncovered set; binary voting procedure; majority-rule tournament;

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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