Aggregation of Semiorders: Intransitive Indifference Makes a Difference

Itzhak Gilboa and Robert Lapson

Economic Theory, 1995, vol. 5, issue 1, 109-26

Abstract: A semiorder can be thought of as a binary relation P for which there is a utility "u" representing it in the following sense: xPy iff u(x)-u(y) > 1. We argue that weak orders (for which indifference is transitive) can not be considered a successful approximation of semiorders; for instance, a utility function representing a semiorder in the manner mentioned above is almost unique, i.e. cardinal and not only ordinal. In this paper we deal with semiorders on a product space and their relation to given semiorders on the original spaces. Following the intuition of Rubinstein we find surprising results: with the appropriate framework, it turns out that a Savage-type expected utility requires significantly weaker axioms than it does in the context of weak orders.

Date: 1995
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Working Paper: Aggregation of Semi-Orders: Intransitive Indifference Makes a Difference (1995)
Working Paper: Aggregation of Semiorders: Intransitive Indifference Makes a Difference (1990)
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