Utility comparison and the theory of games

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Abstract
1. Interpersonal comparability of utility is generally regarded as an unsound basis on which to erect theories of multipersonal behavior. Nevertheless, it enters naturally—and, I believe, properly—as a nonbasic, derivative concept playing an important if sometimes hidden role in the theories of bargaining, group decisionmaking, and social welfare. The formal and conceptual framework of game theory is well adapted for a broad and unified approach to this group of theories, though it tends to slight the psychological aspects of group interaction in favor of the structural aspects—e.g., complementary physical resources, the channels of information and control, the threats and other strategic options open to the participants, etc. In this note I shall discuss two related topics in which game theory becomes creatively involved with questions of interpersonal utility comparison. The first topic concerns the nature of the utility functions that are admissible in a bargaining theory that satisfies certain minimal requirements. I shall show, by a simple argument, that while cardinal utilities are admissible, purely ordinal utilities are not. Some intriguing intermediate systems are not excluded. The argument does not depend on the injection of probabilities or uncertainty into the theory. The second topic concerns a method of solving general n-person games by making use of the interpersonal comparisons of utility that are implicit in the solution.

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