What Is Generalized Expected Utility?
Generalized expected utility (GEU) refers to a class of decision theory models that extend the traditional expected utility theory (EUT) to account for observed discrepancies between theoretical predictions and actual human choices under risk and uncertainty. As a significant concept within behavioral economics, GEU theories aim to provide more descriptively accurate representations of how individuals make decisions when outcomes are not certain. Instead of strictly adhering to the linearity in probabilities assumed by EUT, generalized expected utility models incorporate various modifications to the utility function or the weighting of probabilities to better reflect observed behaviors, such as those demonstrated in the Allais paradox and Ellsberg paradox. These modifications acknowledge that human preferences often deviate from the perfectly rational axioms of earlier economic theories.
History and Origin
The foundation of expected utility theory dates back to the 18th century with Daniel Bernoulli's resolution of the St. Petersburg Paradox, and was formally axiomatized in the 20th century by John von Neumann and Oskar Morgenstern. For decades, EUT served as the dominant framework for analyzing decision making under uncertainty, resting on assumptions like the von Neumann-Morgenstern axioms. However, starting in the 1950s, empirical and experimental evidence, notably from Maurice Allais and others, began to reveal systematic violations of EUT's core assumptions, particularly the independence axiom. These violations highlighted that individuals do not always behave as if their preferences are linear in probabilities, leading to a need for more flexible models.16
In response to these challenges, economists and psychologists developed alternative "non-expected utility" models in the late 1970s and 1980s. Key developments include prospect theory by Daniel Kahneman and Amos Tversky (1979) and rank-dependent utility theory. A general analytical approach, termed "generalized expected utility analysis," was prominently advanced by Mark J. Machina. His seminal work, such as "Choice Under Uncertainty: Problems Solved and Unsolved," published in the Journal of Economic Perspectives, provided a framework to analyze preferences without strictly adhering to the independence axiom, while still retaining many of the analytical tools of traditional expected utility analysis.14, 15 This marked a significant shift in economic theory, pushing the field toward models that better captured observed human behavior.
Key Takeaways
- Generalized expected utility (GEU) represents a broad category of models designed to explain deviations from classical expected utility theory.
- GEU theories often modify the way probabilities are weighted or how outcomes are valued to reflect human cognitive biases and risk attitudes.
- The development of GEU was largely driven by empirical observations that contradicted the assumptions of traditional EUT, such as the Allais paradox.
- These models are central to behavioral economics, providing more realistic frameworks for understanding decision making under uncertainty.
- GEU allows for more nuanced representations of individual preferences, including varying degrees of risk aversion and risk-seeking behavior.
Interpreting Generalized Expected Utility
Interpreting generalized expected utility involves understanding that individuals do not always evaluate risky choices purely based on objective probabilities and a linear utility scale. Instead, GEU models suggest that people might overweight small probabilities, underweight large probabilities, or value gains and losses differently depending on their starting point or reference level.
For instance, in traditional expected utility theory, the utility of a gamble is a straightforward weighted average of the utilities of its possible outcomes, with the weights being their respective probabilities. In GEU frameworks, this linearity can be relaxed. The "generalized" aspect means that the preference relation over uncertain prospects might not conform to all the axioms of standard EUT. This allows for decision-makers to exhibit behaviors like preferring a certain smaller gain over a risky larger one, even if the latter has a higher expected value, or conversely, taking on significant risk to avoid a guaranteed small loss. The interpretation of generalized expected utility thus moves beyond mere rationality maximization to encompass a more psychologically informed view of choice under uncertainty.
Hypothetical Example
Consider an investor, Sarah, who is faced with two investment opportunities, Investment A and Investment B.
- Investment A: Offers a 70% chance of gaining $10,000 and a 30% chance of gaining $1,000.
- Investment B: Offers a 50% chance of gaining $15,000 and a 50% chance of gaining nothing ($0).
Under standard expected utility theory, a rational investor would calculate the expected monetary value (EMV) and then their expected utility for each option.
- EMV of A = (0.70 * $10,000) + (0.30 * $1,000) = $7,000 + $300 = $7,300
- EMV of B = (0.50 * $15,000) + (0.50 * $0) = $7,500 + $0 = $7,500
A strictly rational investor focused only on expected monetary value would choose Investment B. However, under a generalized expected utility framework, Sarah's subjective valuation of these outcomes, potentially influenced by risk aversion or the feeling of a potential loss, might lead her to choose Investment A. For example, she might place a higher subjective weight on the certainty of a positive outcome in Investment A, or disproportionately value the avoidance of a $0 outcome in Investment B, even if the expected monetary gain is lower. Her personal utility function, as generalized in GEU, would better capture this nuanced preference, showing that she might derive more subjective satisfaction or perceive less risk from Investment A, despite its lower mathematical expectation.
Practical Applications
Generalized expected utility models find practical applications across various fields, particularly where decision making under uncertainty is critical. In finance, these models help explain investor behavior that deviates from predictions of classical economic theory, such as why individuals might hold seemingly suboptimal portfolios or engage in patterns like selling winners too early and holding onto losers for too long. They inform the design of financial products and advisory services that better align with actual investor preferences and psychological biases.
Beyond finance, generalized expected utility is applied in public policy and regulatory contexts. For instance, understanding how individuals respond to different framings of risks and rewards can influence the design of public health campaigns, environmental policies, or savings programs. Governments and organizations, including the OECD, increasingly leverage insights from behavioral economics to craft more effective policies.13 For example, insights derived from generalized expected utility frameworks can inform how information about retirement savings or health insurance choices is presented to encourage participation, accounting for observed non-linear responses to probability and outcome valuation.
Limitations and Criticisms
While generalized expected utility theories offer a more realistic account of human decision making under risk and uncertainty than traditional models, they are not without limitations and criticisms. One challenge is their increased complexity compared to expected utility theory. The flexibility introduced by allowing non-linear probability weighting or more complex utility functions means that there isn't a single, universally accepted generalized expected utility model, but rather a family of models (e.g., prospect theory, rank-dependent utility). This can make them more challenging to apply and test empirically.12
Critics also point out that while these models explain observed deviations from rationality, they may still struggle to predict behavior consistently across all contexts. Some argue that the very act of generalizing the utility function or probability weighting can make the models less parsimonious and more difficult to falsify. Furthermore, some deviations from EUT are still not fully captured by GEU models, suggesting the need for even more nuanced frameworks.10, 11 Despite their advancements, the ongoing debate underscores the complexity of human preference and the continuous evolution of decision theory. As George A. Akerlof discusses in "Rationality and the Behavioral Foundations of Economics," understanding human behavior requires moving beyond purely rational assumptions.9
Generalized Expected Utility vs. Expected Utility Theory
The core distinction between generalized expected utility (GEU) and expected utility theory (EUT) lies in their underlying assumptions about how individuals process probabilities and value outcomes when making decisions under uncertainty.
| Feature | Expected Utility Theory (EUT) | Generalized Expected Utility (GEU) |
|---|---|---|
| Probability Processing | Linear weighting of objective probabilities. | Non-linear weighting of probabilities (e.g., small probabilities overweighted, large ones underweighted). |
| Utility Function | Assumes a fixed, often concave, utility function where preferences are linear in probabilities.8 | Allows for more flexible utility functions, potentially incorporating reference points, loss aversion, or varying risk attitudes across different domains (gains vs. losses). |
| Behavioral Fit | Often fails to predict real-world choices, especially in paradoxes like the Allais paradox.6, 7 | Aims to provide a more accurate descriptive model of actual human decision making, explaining paradoxes. |
| Axiomatic Structure | Built on strong axioms, including the independence axiom.5 | Relaxes or modifies some classical axioms, particularly the independence axiom, to accommodate observed irrationalities.3, 4 |
| Applications | Forms the basis of classical economic theory and normative models of choice. | Central to behavioral economics and prescriptive models that account for psychological factors. |
While EUT provides a normative benchmark for ideal rational behavior, generalized expected utility seeks to describe how people actually behave, recognizing that psychological factors often lead to deviations from strict rationality. This distinction is crucial for disciplines like behavioral economics that aim to understand and predict human economic behavior more accurately.
FAQs
Why was generalized expected utility developed?
Generalized expected utility was developed because traditional expected utility theory (EUT) often failed to accurately describe how people make decisions in real-world situations involving risk and uncertainty. Empirical observations, particularly experimental paradoxes like the Allais paradox, showed that human choices systematically deviated from EUT's predictions, prompting the need for more descriptively accurate models.
Is there one universal formula for generalized expected utility?
No, there isn't one universal formula for generalized expected utility. Instead, "generalized expected utility" refers to a class of theories that extend or modify the standard expected utility framework. These theories propose different mathematical forms for the utility function or how probability is weighted, such as those found in prospect theory or rank-dependent utility models.2
How does generalized expected utility account for risk aversion?
Generalized expected utility models can account for risk aversion in more nuanced ways than traditional EUT. While EUT uses the curvature of the utility function to represent risk aversion, GEU models can incorporate additional factors, such as overweighting the probability of negative outcomes or having different sensitivities to gains versus losses, which provides a richer explanation for observed risk-taking behaviors.
What is the primary goal of generalized expected utility models?
The primary goal of generalized expected utility models is to provide a more descriptively accurate framework for decision making under uncertainty. They aim to bridge the gap between theoretical predictions of economic theory and actual human behavior by incorporating psychological insights and relaxing some of the restrictive assumptions of traditional expected utility theory.1
How does generalized expected utility relate to behavioral finance?
Generalized expected utility is a fundamental concept in behavioral economics and, by extension, behavioral finance. It provides the theoretical underpinning for understanding many observed anomalies in financial markets and investor behavior, such as deviations from rational asset pricing and seemingly irrational investment choices, by offering models that better reflect how individuals perceive and respond to risk.