This paper discusses two problems. (a) What happens to the conditional risk premium that a decision maker is willing to pay out of the middle prize in a lottery to avoid uncertainty concerning the middle prize outcome, when the probabilities of other prizes change? (b) What happens to the increase that a decision maker is willing to accept in the probability of an unpleasant outcome in order to avoid ambiguity concerning this probability, when this probability increases? We discuss both problems by using anticipated utility theory, and show that the same conditions on this functional predict behavioral patterns that are consistent both with a natural extension of the concept of diminishing risk aversion and with some experimental findings.
Expected utility theory used to be the most widely used theory of decision making under uncertainty. It owes much of its popularity to its simplicity. Every contingent outcome is evaluated by the utility indicator and then multiplied by its own probability, without any dependence on other parts of the lottery. The separability of outcomes and linearity in the probabilities are at the heart of this theory. However, if the theory, due to the linearity or separability, fails to account for empirical phenomenan, an alternative theory must be used.
In this paper we consider two cases. The first one cannot be dealt with by expected utility theory because of the separability of outcomes, while the other one contradicts the linearity assumption. These two cases seem to be totally independent, but as is shown by our analysis, they are correlated. In the first case the following question is asked: How will the attitude of decision makers towards one prize in a lottery depend upon the levels and probabilities of the other prizes in the lottery?
We are grateful to Larry Epstein and Mark Machina for their comments and suggestions. Support from SSHRC Grant #410-87-1375 is gratefiflly acknowledged.