On some aspects of decision theory under uncertainty: rationality, price-probabilities and the Dutch book argument

Abstract

Choice under uncertainty is treated in economics by different approaches. We can distinguish three of them, two of which concern individual choice, while the third frames individual choices within the analysis of the social system. The first approach can determine how a rational decision-maker must choose; the second one how a real decision-maker behaves; and the third one how decision-makers are represented in the general economic theory. The main theories that result from these approaches are briefly presented. This paper considers, in particular, the third approach, which is the most general since it represents preferences by means of a continuous (ordinal) utility function of the possible outcomes, without any specification with regard to uncertainty. The link between the reservation prices of bets on events and their subjective probabilities is examined. It is shown as the additivity condition for these price-probabilities is not required by the Dutch book argument if preferences are represented by a continuous utility function that is not differentiable.