Is expected utility theory positively or normatively valid?
Expected utility theory (EUT) has two lives. It is presented as a positive theory describing how people choose under uncertainty, and as a normative theory prescribing how rational people ought to choose. EUT has poor positive validity as a predictive theory. Its normative validity is not established by its representation theorem or by internal consistency alone.
When EUT fails descriptively, its normative status is often upheld independently: people may not behave as predicted, but they should. This implies an assessment of people’s decision-making as irrational. Ergodicity economics reveals that consistency with EUT is a poor definition of rational behaviour.
Does EUT have positive validity?
Positive validity asks whether EUT describes or predicts how people actually behave. There is strong evidence that it performs poorly as a predictive theory. Utility functions are generally inferred from observed choices, which makes it easy to accommodate observations after the fact but scientific positive merit is judged by prediction out-of-sample. In Risky Curves: On the Empirical Failure of Expected Utility, Daniel Friedman, R. Mark Isaac, Duncan James, and Shyam Sunder review decades of empirical work with EUT models and conclude that “Their power to predict out-of-sample is in the poor-to-non-existent range.”
This failure is usually framed as human irrationality: people ought to follow EUT but often do not. That moves the argument from positive to normative validity.
Does EUT have normative validity?
Normative validity asks whether people ought to maximise expected utility. The prevailing view is stated without ambiguity in the Stanford Encyclopedia of Philosophy: EUT “holds that a decision-maker ought to maximize expected utility.” But this restates the prescription; it does not justify it. Why ought a decision maker to follow EUT?
The conventional defence appeals to axioms of consistency and the representation theorems built from them. Preferences over lotteries that satisfy the von Neumann–Morgenstern axioms can be represented as maximising the expectation of a utility function. Stronger defences add that violations can expose a decision maker to a money pump or that expected-utility maximisation performs well over repeated trials.
But this mathematical result is often asked to carry more weight than it can bear. A representation theorem says that certain preferences can be represented in expected-utility form. It does not establish that following those preferences maximises wealth, survival, experienced utility, or any other quantity through time. As Gigerenzer puts it: “By itself, a representation theorem does not imply a prescription of what people should do.” He also points out that the normative interpretation of the axioms and of expected-utility maximisation is absent from all three editions of von Neumann and Morgenstern’s Theory of Games and Economic Behavior. The theorem was turned into a prescription later.
Consistency is a property of a decision rule, not an objective. A person can consistently follow a self-harming rule. If consistency merely guarantees that the harm follows a coherent pattern, it gives us no reason to call the rule rational. To justify EUT normatively, one must show that following it helps the decision maker achieve an objective. Internal consistency alone cannot do that.
There is a further problem with the normative defence. Berg and Gigerenzer observe that neoclassical and behavioural economics both “refer to a common set of axiomatic norms without subjecting them to empirical investigation.” Behavioural economics has documented many deviations from those norms, but almost no evidence that the deviations cause lower earnings, happiness, health, predictive accuracy, or longevity. Berg and Gigerenzer therefore argue for an empirical normative analysis: examine real decision processes and ask which strategies succeed in which environments. They call this matching of strategies to environments ecological rationality.
What is the ergodicity economics critique of EUT?
Ergodicity economics supplies the missing external criterion. It asks what a decision rule achieves along a trajectory through time. When ensemble averages and time averages differ, maximising expected utility need not maximise the utility actually experienced over time. It may systematically reduce it. The decision rule can be internally consistent while defeating the decision maker’s stated objective.
This is not a claim that EUT is always wrong. If the relevant observable is ergodic, the expectation value represents what happens over time. EUT can also reproduce time-optimal behaviour when the utility function is the ergodicity transformation appropriate to the specified dynamics. The time interpretation of expected utility theory develops this special correspondence. The dynamics determine whether the expectation is relevant; relevance cannot simply be assumed.
Rationality requires an objective and an environment
The positive and normative claims for EUT should be assessed separately, but both require the relevant dynamics. Positive validity requires genuine predictive performance. Normative validity requires showing that the rule achieves an objective in the environment where it is used.
This conclusion is close in spirit to ecological rationality: a decision strategy cannot be judged independently of its environment. Our joint open project with Gerd Gigerenzer explores this connection. Ergodicity economics makes a complementary point mathematically precise. A strategy that maximises an ensemble average is rational for an individual only when the dynamics justify using that average as a guide to what happens through time.
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