A decision‑theoretic model for choices under risk in which an agent's preferences over lotteries (probabilistic outcomes) are represented by the expectation of a utility function; agents choose the option with the highest expected utility, subject to the theory's axioms (completeness, transitivity, independence, continuity).

Principle

Risk attitudes map to the curvature of the utility function: concave utility implies risk aversion, linear utility risk neutrality, and convex utility risk seeking; the independence axiom ensures preference linearity in probabilities so expected utility aggregates outcomes by weighted utilities.

Demonstration

Situation: An agent must choose between a certain $50 and a lottery paying $100 with 0.6 probability and $0 with 0.4. Recognition: Compute expected utilities under a specified utility function u(·). Action: Choose the alternative with higher expected utility. Consequence: The agent's risk posture (via u) determines choice consistently across comparable lotteries.

Misapplication

Assuming Expected Utility Theory is a descriptive law of actual human choice in all contexts; the semantic error is treating normative axioms (like independence) as empirically universal rather than as premises for coherent decision representation—empirical violations (preference reversals) are possible without negating the model's normative role.

Consequence

EUT provides a coherent normative benchmark for pricing risk, insurance, and portfolio selection and underlies much economic modeling of risk; when used descriptively, deviations motivate alternative models and adjustments to policy or design that account for observed behavior.

Reversal

When probabilities are ambiguous or decision makers systematically violate axioms (e.g., independence), alternative representations (rank‑dependent utility, prospect theory, ambiguity models) may better describe choice; EUT's prescriptions require known probabilities and stable preferences.

Boundary

Clearly within: choices among lotteries with known probabilities and stable, transitive preferences. Boundary case: decision under ambiguity where probabilities are imprecise. Clearly outside: situations with dynamic inconsistency, preference formation during choice, or common‑knowledge failures about probabilities.

Semantic Tension

Tension between normative coherence (axiomatic rationality) and empirical descriptiveness (observed deviations); operationally the tension is whether to use EUT as a prescriptive standard or as a literal behavioral model.

Synthesis

EUT furnishes a compact normative calculus linking risk attitudes to a utility function's shape and provides tractable comparative statics; empirical departures do not nullify its role as a benchmark but motivate enriched models when descriptive accuracy is required.