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 InfoArticle provided by Springer in its journal Economic Theory.
Volume (Year): 5 (1995)
Issue (Month): 1 (January)
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Other versions of this item:
- Itzhak Gilboa & Robert Lapson, 1990. "Aggregation of Semiorders: Intransitive Indifference Makes a Difference," Discussion Papers 870, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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