Elsevier

Journal of Economic Theory

Volume 34, Issue 2, December 1984, Pages 252-261
Journal of Economic Theory

Median-based extensions of an ordering over a set to the power set: An axiomatic characterization

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Abstract

In this paper we consider the problem of inducing an ordering over the set of all non-empty subsets of a finite set X of alternatives, given an ordering R over X. Assuming R to be antisymmetric and X to have at least six elements, we provide a set of independent, necessary, and sufficient conditions for the induced ordering to be “median-based” (so that every non-empty subset of X is “indifferent” to its own median set defined in terms of R).

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We are extremely grateful to B. Peleg, who suggested to us a version of Axiom WD used in this paper, and to S. Barbera and R. Holzman for several helpful comments. Much of the work on this paper was done when both of us were Fellows of the Institute for Advanced Studies, the Hebrew University, Jerusalem, and a part of the work was done when one of us was at the Southern Methodist University. We are grateful to both of these institutions for a very congenial environment for work.

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