Expected Utility Theory (EUT), formalized by von Neumann and Morgenstern in 1944 and anticipated by Daniel Bernoulli in 1738, states that a rational decision maker evaluates risky prospects (lotteries) by computing the expected value of a utility function over outcomes. Bernoulli's key insight was that the utility of money is not linear — a gain of $100 matters more to a pauper than to a millionaire — leading to the concave utility function that explains risk aversion.
The Expected Utility Formula
L = lottery (p₁, x₁; p₂, x₂; ...)
u(x) = utility function over outcomes
Choose L₁ over L₂ iff EU(L₁) > EU(L₂)
Utility Functions and Risk Attitudes
The curvature of the utility function determines risk attitude. A concave utility function (u″ < 0) implies risk aversion: the expected utility of a gamble is less than the utility of its expected value. A convex function implies risk seeking. A linear function implies risk neutrality. Common functional forms include logarithmic (u(x) = ln(x)), power (u(x) = xᵅ, α < 1), and exponential (u(x) = 1 − e^(−αx)) utility.
Limitations
Despite its normative appeal, EUT is systematically violated by human decision makers. The Allais paradox demonstrates violations of the independence axiom. Prospect theory replaces EUT with a descriptive model incorporating reference dependence, loss aversion, and probability weighting. Nevertheless, EUT remains the benchmark for rational choice and the starting point for all alternative theories.