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Semiorders and a Theory of Utility Discrimination

R. Duncan Luce

Abstract

In the theory of preferences underlying utility theory it is generally assumed that the indifference relation is transitive, and this leads to equivalence classes of indifferent elements or, equally, to indifference curves. It has been pointed out that utility is not perfectly discriminable, as such a theory necessitates. In this paper intransitive indifference relations are admitted and a class of them are axiomatized. This class is shown to be substantially equivalent to a utility theory in which there are just noticeable difference functions which state for any value of utility the change in utility so that the change is just noticeable. In the case of risk represented by a linear utility function over a mixture space, the precise form of the function is examined in detail.