Expected Utility Theory

Von Neumann and Morgenstern (1944) formalised rational choice under uncertainty: maximise expected utility, not expected value. The formula is Σ (probability × utility). A 50% chance of $100 and 50% chance of $0 has expected value $50. But the rational decision depends on utility — how much satisfaction each outcome delivers. $100 means more to someone with $10K than to someone with $10M. Diminishing marginal utility: each additional dollar adds less satisfaction than the one before. Expected utility theory (EUT) says the rational actor multiplies each outcome by its probability, applies a utility function to each outcome, and chooses the option with the highest sum.

The distinction from expected value matters. A gamble with positive expected value can have negative expected utility if the downside is catastrophic relative to your wealth. A gamble with negative expected value can have positive expected utility if the upside delivers outsized satisfaction. EUT is normative — it describes how a rational agent should decide. Kahneman and Tversky's Prospect Theory (1979) showed we systematically violate it: we're loss-averse, we overweight small probabilities, we evaluate gains and losses asymmetrically. EUT remains the benchmark.

The strategic use: when outcomes are probabilistic, model decisions as expected utility. Estimate probabilities, assign utilities, multiply, sum. The discipline forces explicit treatment of risk and preference. Applied to investing, the Kelly Criterion is expected utility with logarithmic utility — bet size proportional to edge over odds. Applied to business, Amazon's "two-way door" is expected utility for reversible decisions: low downside, high upside, so expected utility favours action over delay. The model does not tell you what to do. It gives you a structure for deciding. The probabilities and utilities are yours to supply. The value is in making them explicit.

Diminishing marginal utility is central. $100 to someone with $10K delivers more utility than $100 to someone with $10M. The same dollar, different satisfaction. This is why expected value fails: it treats all dollars equally. Expected utility corrects for the fact that the first million changes your life and the tenth changes almost nothing. The utility function captures this. Without it, you're optimising the wrong thing.

The model is prescriptive, not descriptive. It tells you what to do, not what people do. Kahneman's Prospect Theory overturned EUT as a description of human behaviour — we violate the axioms routinely. But EUT remains the right standard for rational choice. When you catch yourself deviating from it, ask why. Sometimes the deviation is a bug (sunk cost fallacy, loss aversion). Sometimes it's a feature (you value something the model doesn't capture). The discipline is to know the difference.