Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?)

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Abstract

It is argued that the Allais paradox reveals a certain property of the decision scheme we use to determine the preference of one lottery over another. The decision scheme is based on the use of similarity relations on the probability and prize spaces.

It is proved that for every pair of similarity relations there is essentially only one preference consistent with the decision scheme and the similarities. It is claimed that the result shows a basic difficulty in reconciling utility theory with experimental data.

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I benefitted from discussions with Peter Fishburn, Andreu Mas-Colell, Amos Tversky, Cathy Weinberger, Asher Wolinsky, Menachem Yaari, and especially Nitza Kasir and Uzi Segal, whom I would like to thank. I also thank Mark Machina for many comments which helped me to integrate the paper into the literature.

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