Semiorders and a Theory of Utility Discrimination

In the theory of preferences underlying utility theory i t is generally assumed that the indifference relation is transitive, and this leads t o equivalence classes of indifferent elements or, equally, t o indifference curves. It has been pointed out that this assumption is contrary to experience and 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 t o be substantially equivalent t o 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.