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

Coughlan, Peter J. and Le Breton, Michel (1999) A social choice function implementable via backward induction with values in the ultimate uncovered text. Review of Economic Design, 4 (2). pp. 153-160. ISSN 1434-4742. doi:10.1007/s100580050030.

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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.

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Additional Information:© Springer-Verlag Berlin Heidelberg 1999. Received: 7 April 1997; Accepted: 15 October 1998. We would like to thank Tom Palfrey, Richard McKelvey, Micah Altman, and Doug Creutz for their input during an informal research meeting at Caltech. We would also like to thank Jean Francois Laslier and an anonymous referee for additional comments. Formerly SSWP 1024.
Subject Keywords:Implementation via backward induction, Condorcet social choice function, ultimate uncovered set, binary voting procedure, majority-rule tournament
Issue or Number:2
Classification Code:JEL: D70, D71, D78
Record Number:CaltechAUTHORS:20171128-161758988
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83555
Deposited By: Jacquelyn Bussone
Deposited On:29 Nov 2017 20:11
Last Modified:15 Nov 2021 20:12

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