Subjective expected utility

SEU is a different approach from the one put forward by von Neumann and Morgenstern in that it does not take (objective) probabilities (i.e., lotteries) as given. Instead, subjective probabilities are used, which are assumed to be consistent with choice behavior.

The main contribution to formalizing SEU was done by L. J. Savage in 1954 (see Savage's axioms), following previous work by Ramsey and von Neumann. Savage proved that, if the decision-maker preferences over acts satisfy some reasonable axioms, then their choices can be explained as arising from a utility function ${\displaystyle u(x_i)}$ combined with the subjective belief that there is a probability of each outcome ${\displaystyle P(x_i).}$ The subjective expected utility is the resulting expected value of the utility:

${\displaystyle \mathrm{E}[u(X)]=\sum _{i}u(x_i)P(x_i).}$

Experiments have shown that many individuals do not behave in a manner consistent with Savage's axioms of subjective expected utility, e.g. most prominently Allais (1953) and Ellsberg (1961).