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

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.