๐ What is Expected Utility Theory?
Expected Utility Theory (EUT) is a normative theory in economics and psychology that explains how individuals make rational decisions when faced with uncertain outcomes. It posits that people don't simply maximize expected monetary value but instead maximize their personal 'utility,' which represents the satisfaction or value they derive from different outcomes. This utility is then weighted by the probability of each outcome occurring.
๐ A History of Expected Utility Theory
The roots of Expected Utility Theory can be traced back to the 18th century:
- ๐ฒ Early Probabilistic Reasoning: The initial seeds were sown with studies of probability and games of chance.
- ๐งฎ Daniel Bernoulli (1738): Published 'Exposition of a New Theory on the Measurement of Risk.' He introduced the concept that people value gains and losses differently, suggesting that utility is not linear with monetary value. Bernoulli proposed that individuals maximize expected utility rather than expected monetary value, famously solving the St. Petersburg Paradox. This paradox demonstrated that people are generally risk-averse.
- ๐ Ramsey (1926) and von Neumann & Morgenstern (1947): These figures formalized the theory. Ramsey's work on subjective probability and utility provided a philosophical grounding, while von Neumann and Morgenstern's 'Theory of Games and Economic Behavior' provided a rigorous axiomatic foundation for EUT. They showed that if preferences satisfy certain axioms (completeness, transitivity, continuity, and independence), then a utility function can be constructed to represent those preferences.
- ๐ง Savage (1954): Extended EUT to situations with subjective probabilities in 'The Foundations of Statistics.' He developed Subjective Expected Utility (SEU) where probabilities are not objectively given but are instead personal beliefs.
- ๐งช Kahneman & Tversky (1979): Challenged EUT with 'Prospect Theory.' They provided empirical evidence demonstrating that people systematically violate the axioms of EUT, particularly concerning losses and gains. Prospect Theory incorporates concepts like loss aversion and framing effects to better describe actual decision-making behavior.
๐ Key Principles of Expected Utility Theory
- โ๏ธ Expected Value: The weighted average of possible outcomes, where the weights are the probabilities of those outcomes. For example, if there is a 50% chance of winning $100 and a 50% chance of winning $0, the expected value is $$\$50$$.
- ๐ Utility Function: Represents an individual's preferences over different outcomes. It assigns a numerical value to each outcome, reflecting the individual's level of satisfaction. The utility function is typically assumed to be increasing (more is better) but can be concave (risk-averse), convex (risk-seeking), or linear (risk-neutral).
- ๐ Risk Aversion: Most individuals are risk-averse, meaning they prefer a certain outcome to a gamble with the same expected value. This is reflected in a concave utility function.
- ๐ฏ Axioms of Rational Choice: EUT relies on several axioms:
- โ
Completeness: Individuals can compare and rank any two options.
- โก๏ธ Transitivity: If an individual prefers A to B and B to C, then they must prefer A to C.
- โ๏ธ Independence: If an individual prefers A to B, then they must also prefer a gamble involving A and a third option C to a gamble involving B and C, provided the probabilities are the same.
- ๐ Continuity: For any three outcomes A, B, and C, where A is preferred to B, and B is preferred to C, there exists a probability p such that the individual is indifferent between B and a gamble that yields A with probability p and C with probability (1-p).
๐ Real-world Examples
- ๐ฐ Investment Decisions: Investors use EUT to decide which assets to invest in, considering the potential returns and the associated risks. A risk-averse investor might choose a lower-risk investment with a lower expected return over a higher-risk investment with a higher expected return.
- ๐ฅ Medical Treatment: Patients use EUT to evaluate different treatment options, weighing the probabilities and utilities of possible outcomes (e.g., success, side effects, death).
- ๐ฐ Insurance: Individuals purchase insurance because the utility loss from a large financial setback is greater than the utility gain from the small premium they pay.
- ๐ผ Career Choices: People often weigh the risks and rewards of different job opportunities. A stable job with a lower salary might be preferred over a high-paying but unstable freelance career.
โญ Conclusion
Expected Utility Theory provides a valuable framework for understanding how individuals make decisions under uncertainty. While it has been challenged by behavioral economics, it remains a cornerstone of economic and decision-making theory. By considering both the probabilities and utilities of different outcomes, EUT helps explain and predict a wide range of choices in economics, finance, health, and beyond.