One of the challenges of decision theory is figuring out exactly what the utility function is. The utility of money, for example, is notoriously nonlinear for most people

In fact, the behaviour of many people cannot be captured by a coherent utility function, as illustrated by the Allais paradox, which runs as follows.

Many people prefer A to B, and, at the same time, D to C. Prove that these preferences are inconsistent with any utility function U(x) for money.