Expected utility hypothesis

Expected Utility Hypothesis: Definition, Formula, Example, and FAQs

What Is Expected Utility Hypothesis?

The Expected Utility Hypothesis (EUH) is a foundational concept within decision-making under uncertainty, primarily associated with the field of behavioral finance. It posits that individuals make choices in uncertain situations by evaluating the expected value of utility derived from various possible outcomes, rather than simply the expected monetary value. This means a decision-maker chooses the option that maximizes their subjective utility – a measure of satisfaction or happiness – across all potential results, weighted by their respective probability. The Expected Utility Hypothesis serves as a cornerstone of rational choice theory in economics.

History and Origin

The conceptual roots of the Expected Utility Hypothesis can be traced back to the 18th century. Daniel Bernoulli, a Swiss mathematician, introduced the idea in 1738 as a resolution to the St. Petersburg Paradox. He proposed that people evaluate the "moral worth" (utility) of wealth, which typically increases at a decreasing rate, rather than its face value. This groundbreaking insight suggested that individuals exhibit risk aversion and assign diminishing marginal utility to additional increments of wealth.

Th⁵e modern formulation of the Expected Utility Hypothesis was rigorously developed by John von Neumann and Oskar Morgenstern in their 1944 work, "Theory of Games and Economic Behavior." The⁴ir axiomatic framework demonstrated that if an individual's preferences satisfy certain rationality axioms (such as completeness, transitivity, continuity, and independence), then their decision-making under uncertainty can be represented as maximizing the expected value of a utility function. This formalization made the Expected Utility Hypothesis a central tenet of modern economic theory and game theory.

Key Takeaways

• The Expected Utility Hypothesis suggests that individuals make decisions under uncertainty by maximizing the weighted average of the utility of all possible outcomes.
• Utility represents the subjective satisfaction or happiness derived from an outcome, which may not be directly proportional to its monetary value.
• It accounts for risk aversion, where individuals typically prefer a certain outcome over a risky one with the same expected value.
• The hypothesis forms a core part of traditional rational choice theory in economics.
• Despite its theoretical elegance, the Expected Utility Hypothesis faces criticisms from behavioral economics for not fully capturing observed human behavior.

Formula and Calculation

The Expected Utility Hypothesis does not have a single "formula" in the traditional sense of a numerical calculation like return on investment. Instead, it posits a decision rule for choosing among risky alternatives. If an individual is faced with a choice between several gambles or prospects, each with multiple possible outcomes and associated probabilities, they will choose the prospect that yields the highest expected utility.

For a prospect (L) with (n) possible outcomes ((x_1, x_2, \ldots, x_n)) and corresponding probabilities ((p_1, p_2, \ldots, p_n)), the expected utility (E(U)) is calculated as:

Where:

• (E(U(L))) is the expected utility of prospect (L).
• (p_i) is the probability of outcome (x_i) occurring.
• (U(x_i)) is the utility derived from outcome (x_i).

This formula aggregates the utility of each possible outcome, weighted by its likelihood, to arrive at a single value representing the overall desirability of the risky prospect.

Interpreting the Expected Utility Hypothesis

The Expected Utility Hypothesis provides a framework for understanding how individuals make choices when the outcomes are not certain. The key to interpreting the Expected Utility Hypothesis lies in understanding that people don't just look at the monetary value of a gamble or investment. Instead, they consider how much satisfaction or "utility" that money will bring them.

For example, a person with low wealth might derive significantly more utility from an extra $1,000 than a billionaire would. This concept of diminishing marginal utility explains why individuals typically prefer a guaranteed $500 over a 50% chance of winning $1,000 and a 50% chance of winning $0, even though both have the same expected value of $500. The guaranteed $500 provides a higher certain utility, whereas the utility of gaining $1,000 is less than double the utility of $500, and the utility of gaining $0 is zero. The Expected Utility Hypothesis dictates that individuals will choose the option that maximizes their subjective satisfaction, reflecting their individual risk tolerance.

Hypothetical Example

Consider an investor, Alice, who has $100,000. She is considering two investment options:

• Option A: A safe bond. This bond guarantees a return, increasing her wealth to $105,000 with 100% probability.
• Option B: A speculative stock. This stock has a 50% chance of increasing her wealth to $120,000 and a 50% chance of decreasing her wealth to $90,000.

To apply the Expected Utility Hypothesis, Alice needs to determine her utility for each level of wealth. Let's assume Alice has a utility function, (U(W) = \sqrt{W}), which reflects risk aversion (utility increases with wealth, but at a decreasing rate).

1. Calculate Expected Utility for Option A:

   • Outcome: $105,000
   • Utility: (U(105,000) = \sqrt{105,000} \approx 324.04)
   • Expected Utility: (1.00 \times 324.04 = 324.04)

2. Calculate Expected Utility for Option B:

   • Outcome 1: $120,000 (with 0.50 probability)
     • Utility: (U(120,000) = \sqrt{120,000} \approx 346.41)
   • Outcome 2: $90,000 (with 0.50 probability)
     • Utility: (U(90,000) = \sqrt{90,000} = 300)
   • Expected Utility: ((0.50 \times 346.41) + (0.50 \times 300) = 173.205 + 150 = 323.205)

According to the Expected Utility Hypothesis, Alice would choose Option A (the safe bond) because its expected utility (324.04) is higher than that of Option B (323.205), even though Option B has a higher expected value (0.50 * $120,000 + 0.50 * $90,000 = $105,000 for Option A vs. $105,000 for Option B). This demonstrates how utility considerations can lead to choices different from those based purely on monetary expectations.

Practical Applications

The Expected Utility Hypothesis has numerous practical applications across finance, economics, and various forms of decision-making under uncertainty:

• Insurance Markets: The hypothesis helps explain why individuals purchase insurance. They pay a certain premium to avoid the low-probability, high-loss event, even if the expected monetary value of the insurance is negative (due to administrative costs and profit margins). The utility gained from avoiding a large loss outweighs the utility lost from paying the premium. This reflects the deep-seated human tendency towards risk aversion.
• ³ Investment Decisions: In portfolio management, the Expected Utility Hypothesis guides the construction of portfolios tailored to an investor's risk tolerance. An investor with higher risk aversion will prefer a portfolio with lower volatility and more predictable returns, even if it means sacrificing some expected value.
• Public Policy and Regulation: Governments and regulatory bodies often consider the expected utility of different policies, especially those involving public safety, health, or social welfare programs. For instance, designing social security or unemployment benefits might involve weighing the utility of stable income against potential disincentives to work, based on how people value guaranteed funds versus uncertain opportunities.
• Gambling and Lotteries: The hypothesis can explain why people participate in lotteries (where expected monetary value is negative) or gamble. While seemingly irrational from a purely monetary perspective, some individuals might derive significant positive utility from the small chance of a very large prize or from the entertainment value of the activity itself, which can be incorporated into their utility function.

Limitations and Criticisms

Despite its widespread use, the Expected Utility Hypothesis has faced significant challenges, particularly from the field of behavioral economics. These criticisms highlight instances where human decision-making systematically deviates from the predictions of the Expected Utility Hypothesis:

• Violations of Axioms: Experiments have shown that individuals often violate the rationality axioms underlying the hypothesis, such as transitivity (if A is preferred to B, and B to C, then A should be preferred to C) or the independence axiom (the preference between two gambles should not change if both are combined with an identical third gamble).
• Framing Effects: Decisions can be influenced by how options are presented (framed), even if the underlying probabilities and outcomes are identical. The Expected Utility Hypothesis assumes such framing should not affect rational choices.
• Reference Dependence: People often evaluate outcomes relative to a reference point (e.g., their current wealth or an aspiration level) rather than in terms of absolute final wealth, which the Expected Utility Hypothesis traditionally assumes. This is a core idea in Prospect theory.
• Loss Aversion: A key finding in behavioral research is that individuals tend to feel the pain of a loss much more intensely than the pleasure of an equivalent gain. The Expected Utility Hypothesis, in its classic form, does not adequately capture this asymmetric response to gains and losses. Thi²s insight was central to the work that earned Daniel Kahneman a Nobel Prize, recognizing how psychological insights challenge traditional economic assumptions about rational choice theory.

Th¹ese limitations demonstrate that while the Expected Utility Hypothesis provides a robust normative framework for how rational agents should behave, it often falls short as a descriptive model of how real people actually make decisions.

Expected Utility Hypothesis vs. Prospect Theory

The Expected Utility Hypothesis and Prospect theory are both models of decision-making under uncertainty, but they differ significantly in their assumptions and descriptive power.

While the Expected Utility Hypothesis provides a powerful benchmark for ideal rational choice theory, Prospect theory offers a more realistic account of how individuals actually behave in risky situations by incorporating psychological factors.

FAQs

What is the main idea behind the Expected Utility Hypothesis?

The main idea is that when people face choices with uncertain outcomes, they don't just consider the average monetary value. Instead, they try to maximize their total satisfaction or "utility," accounting for how much joy or pain each possible outcome would bring them, weighted by its likelihood. This explains why someone might prefer a guaranteed smaller sum over a gamble with a higher average payout, due to risk aversion.

Who developed the modern Expected Utility Hypothesis?

The modern, axiomatic formulation of the Expected Utility Hypothesis was developed by mathematician John von Neumann and economist Oskar Morgenstern in their 1944 book, "Theory of Games and Economic Behavior." This provided a rigorous mathematical foundation for how rational choice theory could apply to decisions involving uncertainty.

How does the Expected Utility Hypothesis explain why people buy insurance?

The Expected Utility Hypothesis explains insurance by suggesting that individuals are generally risk aversion. They prefer a certain small loss (the insurance premium) over a small chance of a very large loss (the insured event). The utility gained from avoiding the potential large loss is greater than the utility lost by paying the premium, even if the expected value of the premium is higher than the expected payout from the insurer.

What are the criticisms of the Expected Utility Hypothesis?

Major criticisms, largely from behavioral economics, point out that people's actual decision-making often deviates from the hypothesis's predictions. These deviations include phenomena like framing effects (how a choice is presented), loss aversion (losses felt more strongly than equivalent gains), and reference dependence (evaluating outcomes relative to a starting point rather than absolute wealth).