A PROBABILISTIC THEORY OF UTILITY

Abstract

MOST MATHEMATICAL FORMULATIONS of individual decision making - utility theories - have been based upon non-probabilistic preference relations, usually postulated to be weak orders. Few authors have been satisfied with the assumption that preference is transitive, which is easily demonstrated to be at variance with fact. Yet this assumption has been retained as an approximation to reality because of its attractive mathematical properties; for example, only such preference relations can be completely represented by order preserving numerical functions. Nonetheless, a number of people have voiced a desire for a probabilistic theory, mainly, I would judge, so as to be able better to handle empirical data; and several attempts to formulate such 1 This work was supported in part by the Office of Naval Research through funds extended to the Behavioral Models Project, Bureau of Applied Social Research, and to the Department of Mathematical Statistics, Columbia University, and in part by a grant from the National Science Foundation. Reproduction in whole or in part is permitted for any purpose of the United States Government. The paper may be identified as publication A-195 of the Bureau of Applied Social Research.

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