http://worldcat.org/entity/work/id/2230764

The Logic of decision

This book uses elementary logical and mathematical means to a philosophical end: elucidation of the notions of subjective probability and subjective desirability or utility which form the core of Bayesian decision theory. Most of the book is devoted to a new theory of preference between propositions, within which a Bayesian agent's probability and utility functions are determined by features of his preference ranking. Here the elementary logical operations on propositions (denial, conjunction, disjunction) do the work which is done by the operation of forming gambles in the 'classical' theory of Ramsey and Savage. Classically, the agent's preference ranking of gambles determines his utility function up to a linear transformation with positive coefficient, and determines his probability function completely; but here the preference ranking of propositions determines the utility function only up to a fractional linear transformation with positive determinant, and determines the probability function only to within a certain quantization. The classical case is obtained here if the preference ranking is of the sort that can only be represented by a utility function that is unbounded both above and below; and it is shown that the present theory is immune to the St. Petersburg paradox, so that one can reasonably be a Bayesian in the present sense and still have an unbounded utility function.

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