On some aspects of decision theory under uncertainty: rationality, price-probabilities and the Dutch book argument
- 59 Downloads
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.
KeywordsUncertainty Rationality Probability Reservation prices Dutch book argument
- Bernoulli, D. (1738, 1954). Specimen theoriae novae de mensura sortis. Commentarii Academiae Scientiarum Imperialis Petropolitanae, 175–192. English translation: Exposition of a new theory on the measurement of risk. Econometrica 22, 23–26.Google Scholar
- de Finetti, B. (1937). La prévision: ses lois logiques, ses sources subjectives. Annales de l’Institut Henri Poincaré, 7, 1–68.Google Scholar
- Debreu, G. (1959). Theory of value. New York: Wiley.Google Scholar
- Ellsberg, D. (2001). Risk, ambiguity and decision. New York: Routledge.Google Scholar
- Kahneman, D. & Tversky, A. (2000/1984). Choices, values, and frames. In D. Kahneman & A. Tversky (Eds.), Choices, values, and frames (pp. 1–16). Cambridge: Cambridge University Press (Originally published in American Psychologist 39, 341–50).Google Scholar
- Montesano, A. (2006). The paretian theory of ophelimity in closed and open cycles. History of Economic Ideas, 14, 77–100.Google Scholar
- Pareto, V. (1906, 1909, 2014). Manuale di economia politica. Milano: Società editrice Libraria. Manuel d’économie politique. Paris: V. Giard & E. Brière. English translation: A. Montesano, A. Zanni, L. Bruni, J.S. Chipman & M. McLure (Eds.) Manual of political economy. A critical and variorum edition. Oxford: Oxford University Press.Google Scholar
- Richter, M. K. (1971). Rational choice. In J. S. Chipman, L. Hurwicz, M. K. Richter, & H. F. Sonnenschein (Eds.), Preferences, utility, and demand (pp. 29–58). New York: Harcourt Brave Jovanovich.Google Scholar
- Savage, J. (1954). Foundations of statistics. New York: Wiley.Google Scholar
- Simon, H. (1957). A behavioral model of rational choice. In Models of man, social and rational: Mathematical essays on rational human behavior in a social setting. New York: Wiley.Google Scholar
- von Neumann, J., & Morgenstern, O. (1947). Theory of games and economic behavior. Princeton: Princeton University Press. (1st ed. 1944, 2nd ed. 1947, 3rd ed. 1953).Google Scholar
- Zappia, C. (2015). Daniel Ellsberg on the Ellsberg paradox. http://www.siecon.org/online/wp-content/uploads/2015/10/Zappia.pdf.