Aggregation of Semi-Orders: Intransitive Indifference Makes a Difference

Abstract : A semiorder can be thought of as a binary relation P for which there is a utilityu representing it in the following sense: xPy iffu(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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Economic Theory, Springer Verlag, 1995, Vol.5, issue 1, pp. 109-126. 〈10.1007/BF01213647〉
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Itzhak Gilboa, Robert Lapson. Aggregation of Semi-Orders: Intransitive Indifference Makes a Difference. Economic Theory, Springer Verlag, 1995, Vol.5, issue 1, pp. 109-126. 〈10.1007/BF01213647〉. 〈hal-00753141〉

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