Expected Utility Theory and Its Critiques

Rational Choice Under Uncertainty

How does one make decisions under uncertainty? Expected Utility Theory (von Neumann, Morgenstern, 1944): a rational agent maximizes the mathematical expectation of their utility function. This is a normative theory: how a rational agent ought to behave.

Expected value vs. expected utility. Example: a lottery — 50% chance to win 200 rubles, 50% chance to win nothing. Expected value = 100 rubles. But most people will agree to sell this ticket for less than 100 rubles — they are risk-averse. This is explained by decreasing marginal utility of money: an additional 200 rubles is less valuable to a wealthy person than to a poor person.

St. Petersburg paradox (Bernoulli, 1738): a coin is flipped until the first heads appears. If heads appears on the n-th flip, payout is $2^n$ rubles. Expected value is infinite. But no one will pay a large sum to participate in this game. Why? Diminishing marginal utility, limited ability of the casino to pay.

Allais and Ellsberg Paradoxes

Maurice Allais (1953) showed: people systematically violate expected utility theory. The “Allais paradox”: most people prefer A (100% to receive 1 million) over B (89% to receive 1 million, 10% — 5 million, 1% — nothing) — and simultaneously prefer C (10% to receive 5 million) over D (11% to receive 1 million). These preferences are incompatible with expected utility theory.

Ellsberg paradox (1961): “risk” (known probability) vs. “uncertainty” (unknown probability). People systematically avoid uncertainty — even when it is irrational according to the theory. “Ambiguity aversion”: we fear the unknown more than calculated risk.

This opened the door for behavioral economics: Kahneman and Tversky, prospect theory, which describes how people actually make decisions.

Question for discussion: You make decisions under uncertainty every day. Do you have situations where you systematically avoid “unknown” uncertainty (ambiguity) even at the expense of rational calculation?