Utility representation via additive or multiplicative error functions

摘要

The aim of this article is to study two distinct cases of utility representations where the error functions are assumed to display characteristics different than usual. These characteristics depend respectively on the feasible set and the two alternatives compared. Thus, in the first case the error functions are additive and in the second they are multiplicative. Our study of additive error functions shows that a very narrow class of choice functions can be represented in this form. Also we introduce a new class of binary relations, called simple semiorders, to fill the relevant gap in the literature. As for the case of multiplicative error functions, we study the cases where the error function is directly and inversely proportional to the utility function. We show that these classes of binary relations display characteristics of interval orders, semiorder, or regular semiorders depending on the case studied.