The previous chapter presented the main ideas of expected utility analysis. This chapter defends those ideas against objections and generalizes them for cases where options and states are not independent.

OBJECTIONS

One of the main objections to expected utility analysis challenges the assumption that a partition of states yields a suitable separation of pros and cons. The objection claims that a partition of states separates pros and cons in a way that omits some relevant considerations, in particular, risk. Here by risk I mean the epistemic possibility of gain or loss. This is the ordinary meaning enlarged to include the possibility of gain as well as loss, and refined to take risk specifically as an epistemic rather than a physical phenomenon. The objection claims that the risk involved in an option depends on the set of possible outcomes and does not appear in the possible outcomes themselves. As a result, expected utility calculations ignore some considerations bearing on an option's utility.

Allais's paradox (1953) clearly displays this line of argument. Simplified, the paradox goes as follows. It is not irrational (a) to prefer $3,000 for sure to a 4/5 chance for $4,000, and simultaneously (b) to prefer a 1/5 chance for $4,000 to a 1/4 chance for $3,000.