Aggregation of Semiorders: Intransitive Indifference Makes a Difference
AbstractA 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.
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Bibliographic InfoPaper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 870.
Date of creation: Feb 1990
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- Gilboa, Itzhak & Lapson, Robert, 1995. "Aggregation of Semiorders: Intransitive Indifference Makes a Difference," Economic Theory, Springer, vol. 5(1), pages 109-26, January.
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