Glossary

3.1 Expected Utility Theory vs. Prospect Theory

4 min read•july 31, 2024

and are two key models for understanding decision-making under risk. While Expected assumes rational choices based on probabilities, Prospect Theory factors in psychological biases and reference points.

The theories differ in their predictions about risk attitudes and . Prospect Theory explains phenomena like and framing effects, which Expected Utility can't account for. Understanding these models helps us grasp real-world financial and consumer behaviors.

Expected Utility vs Prospect Theory

Key Assumptions and Predictions

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  • Expected Utility Theory assumes rational decision-making based on probability-weighted average of all possible outcomes while Prospect Theory incorporates psychological factors and cognitive biases
  • Expected Utility Theory predicts people maximize expected utility whereas Prospect Theory suggests evaluation of outcomes relative to a
  • Prospect Theory's features S-shaped and asymmetric curve indicating loss aversion and to gains and losses
  • Prospect Theory introduces probability weighting where people overweight small probabilities and underweight moderate to high probabilities (lottery tickets, insurance)
  • Expected Utility Theory assumes risk aversion across all domains while Prospect Theory predicts risk-seeking behavior in the domain of losses
  • Prospect Theory incorporates where people overweight certain outcomes relative to probable ones
  • in Prospect Theory suggests presentation of choices significantly influences decision-making, not addressed in Expected Utility Theory
    • Example: Describing a medical treatment as "90% survival rate" vs "10% mortality rate" can affect patient choices

Mathematical Representations

  • Expected Utility Theory formula: EU=∑i=1npi∗u(xi)EU = \sum_{i=1}^n p_i * u(x_i)
    • EU represents expected utility
    • pip_i represents probability of outcome i
    • u(xi)u(x_i) represents utility of outcome i
  • Prospect Theory value function: v(x)={xαif x≥0−λ(−x)βif x<0v(x) = \begin{cases} x^\alpha & \text{if } x \geq 0 \\ -\lambda(-x)^\beta & \text{if } x < 0 \end{cases}
    • α\alpha and β\beta represent diminishing sensitivity to gains and losses
    • λ\lambda represents loss aversion coefficient
  • Prospect Theory probability weighting function: w(p)=pγ(pγ+(1−p)γ)1/γw(p) = \frac{p^\gamma}{(p^\gamma + (1-p)^\gamma)^{1/\gamma}}
    • γ\gamma represents the degree of probability distortion

Prospect Theory's Limitations

Addressing Paradoxes

  • Resolves by accounting for certainty effect explaining violations of independence axiom in Expected Utility Theory
  • Addresses by incorporating ambiguity aversion explaining preference for known probabilities over unknown ones
  • Value function accounts for loss aversion explaining higher sensitivity to losses than equivalent gains
    • Example: People feel more upset about losing 100thantheyfeelhappyaboutgaining100 than they feel happy about gaining 100
  • Reference point dependence explains preference reversals and violations of invariance in Expected Utility Theory
    • Example: Framing a decision as a gain or loss can reverse preferences (Asian disease problem)

Overcoming Assumptions

  • Probability weighting function addresses overweighting of small probabilities explaining behaviors like playing lotteries and buying insurance
  • Incorporation of helps explain violations of fungibility assumption in Expected Utility Theory
    • Example: People may have separate "mental accounts" for vacation money and emergency funds
  • Framing effects account for preference inconsistencies unexplained by Expected Utility Theory's assumption of description invariance
    • Example: Presenting the same financial option as a potential gain or loss can lead to different choices

Implications of Prospect Theory

Financial Decision-Making

  • Explains in financial markets where investors hold losing stocks too long and sell winning stocks too quickly
  • Provides insights into consumer behavior such as higher sensitivity to price increases than equivalent price decreases
    • Example: A 5increaseina5 increase in a 50 product feels more significant than a $5 decrease
  • Loss aversion concept explains where people place higher value on owned items compared to identical unowned items
    • Example: People demand more money to sell a mug they own than they would pay to buy the same mug

Marketing and Policy

  • Framing effects have implications for marketing and advertising strategies explaining why different presentations of same information lead to different consumer choices
    • Example: Advertising a product as "95% fat-free" instead of "5% fat" can increase sales
  • Probability weighting function explains behaviors in insurance markets such as buying insurance for low-probability high-impact events (natural disasters)
  • Provides framework for understanding risk-taking behavior in various domains including entrepreneurship medical decision-making and policy choices
    • Example: Entrepreneurs may be more willing to take risks due to overweighting small probabilities of success
  • Reference point dependence has implications for negotiation strategies and outcomes in business and diplomatic contexts
    • Example: Setting an initial offer as a reference point can influence the final negotiation outcome

Empirical Evidence for Prospect Theory

Experimental Studies

  • Numerous laboratory experiments consistently demonstrate violations of Expected Utility Theory's axioms providing support for Prospect Theory's alternative framework
  • Field studies in financial markets show evidence of disposition effect supporting Prospect Theory's predictions about risk-seeking behavior in domain of losses
  • Neuroimaging studies provide biological evidence for asymmetric processing of gains and losses aligning with Prospect Theory's value function
    • Example: fMRI studies show different brain regions activate for potential gains versus losses

Meta-Analyses and Cross-Cultural Research

  • Meta-analyses of decision-making experiments consistently find Prospect Theory outperforms Expected Utility Theory in predicting choices under risk
  • Studies in behavioral economics demonstrate robustness of framing effects across various contexts supporting Prospect Theory's emphasis on context-dependent preferences
  • Research in neuroeconomics provides evidence for separate neural systems processing gains and losses consistent with Prospect Theory's asymmetric value function
  • Cross-cultural studies show general principles of Prospect Theory hold across different cultures and societies while specific parameters may vary
    • Example: Loss aversion observed in both Western and Eastern cultures, but magnitude may differ

Key Terms to Review (23)

Allais Paradox: The Allais Paradox is a situation in decision theory that demonstrates how people's choices can violate the expected utility theory, highlighting inconsistencies in human behavior regarding risk and probability. It reveals that individuals often make choices based on perceived outcomes rather than strictly following the mathematical principles of expected utility, suggesting that emotions and cognitive biases can heavily influence decision-making. This paradox is particularly relevant in understanding the differences between traditional expected utility theory and more modern approaches like prospect theory, which account for how people actually behave under risk.
Amos Tversky: Amos Tversky was a pioneering cognitive psychologist known for his groundbreaking work in decision-making and behavioral economics, particularly in collaboration with Daniel Kahneman. His research highlighted how people often deviate from traditional economic theories and rationality due to cognitive biases, which has reshaped our understanding of human decision-making processes.
Bounded rationality: Bounded rationality refers to the concept that individuals make decisions based on limited information and cognitive limitations, rather than striving for complete rationality. This means that while people aim to make the best choices, they often rely on heuristics and simplified models, leading to decisions that may be satisfactory but not necessarily optimal.
Certainty Effect: The certainty effect refers to the phenomenon where individuals disproportionately favor certain outcomes over probable ones, even when the expected utility is lower. This behavior highlights a key difference in decision-making between rational choice models and actual human behavior, revealing how people often make choices based on perceived certainty rather than statistical probabilities.
Choice Overload: Choice overload refers to the phenomenon where having too many options leads to feelings of anxiety and indecision, ultimately impairing the decision-making process. When individuals are faced with an overwhelming number of choices, they may struggle to evaluate each option adequately, which can result in dissatisfaction or the avoidance of making a choice altogether.
Daniel Kahneman: Daniel Kahneman is a renowned psychologist known for his work in behavioral economics, particularly in understanding how psychological factors influence economic decision-making. His research challenges traditional economic theories by highlighting the cognitive biases and heuristics that impact people's choices, ultimately reshaping the way we think about rationality in economics.
Diminishing Sensitivity: Diminishing sensitivity refers to the psychological phenomenon where individuals experience a decreasing emotional response to changes in wealth or outcomes as they move further from a reference point. This means that as gains or losses increase, the perceived impact of those changes on a person’s utility or satisfaction becomes less significant. It plays a crucial role in understanding how people make decisions, particularly when contrasting theories like expected utility and prospect theory.
Disposition Effect: The disposition effect is a behavioral finance phenomenon where investors are more likely to sell assets that have increased in value while holding onto assets that have decreased in value. This tendency reflects emotional biases in decision-making, often leading to suboptimal investment choices and impacting overall portfolio performance.
Ellsberg Paradox: The Ellsberg Paradox illustrates people's preference for known probabilities over unknown probabilities, even when the expected outcomes are the same. It challenges traditional economic theories that assume individuals make decisions solely based on calculated risks, highlighting a discrepancy between expected utility theory and actual human behavior.
Endowment Effect: The endowment effect is a cognitive bias where individuals value an item more highly simply because they own it. This phenomenon impacts how people make economic decisions, leading to irrational behaviors that deviate from traditional economic theories.
Expected Utility Theory: Expected utility theory is a foundational concept in economics and decision-making that describes how individuals make choices under uncertainty by calculating the expected outcomes of different actions and assigning values to them. This theory assumes that people evaluate risky options based on their expected utility, which is derived from the probabilities of potential outcomes and their respective utilities. By comparing these expected utilities, individuals can choose the option that maximizes their perceived satisfaction or benefit.
Framing effect: The framing effect refers to the phenomenon where people's decisions are influenced by how information is presented or 'framed,' rather than just by the information itself. This can significantly alter perceptions and choices, impacting economic decisions, as different presentations can lead to different interpretations and outcomes.
Loss Aversion: Loss aversion refers to the psychological phenomenon where people prefer to avoid losses rather than acquire equivalent gains, implying that the pain of losing is psychologically more impactful than the pleasure of gaining. This concept connects deeply with how individuals make economic decisions, influencing behaviors across various contexts such as risk-taking, investment choices, and consumer behavior.
Mental Accounting: Mental accounting refers to the cognitive process by which individuals categorize, evaluate, and track their financial resources. This concept highlights how people create separate 'accounts' in their minds for different types of expenses or incomes, which can lead to irrational financial behaviors and decisions.
Preference Reversal: Preference reversal refers to the phenomenon where individuals change their preferences between options when the method of evaluation is altered. This inconsistency in choice reveals how people can value outcomes differently based on contextual factors, like framing or presentation, rather than on the actual utility of the outcomes themselves. Understanding this behavior is crucial for exploring the contrasts between expected utility theory, which assumes rational decision-making, and prospect theory, which recognizes the influence of psychological factors on decision-making.
Probability Weighting: Probability weighting refers to the cognitive bias that causes individuals to perceive probabilities differently than they are mathematically represented, often leading them to overweight low probabilities and underweight high probabilities. This concept is crucial for understanding how people make choices under uncertainty, as it influences decision-making processes in contexts involving risk and reward, challenging traditional economic theories of rationality.
Prospect Theory: Prospect theory is a behavioral economic theory that describes how individuals evaluate potential losses and gains when making decisions under risk. It highlights the way people perceive gains and losses differently, leading to decisions that often deviate from expected utility theory, particularly emphasizing the impact of loss aversion and reference points in their choices.
Reference Point: A reference point is a baseline or standard that individuals use to evaluate outcomes, decisions, or changes in value. This concept is crucial in understanding how people perceive gains and losses, as well as their decision-making process regarding uncertain outcomes. Reference points shape expectations and can significantly influence choices, highlighting the difference between objective value and perceived value in economic decisions.
Risk preference: Risk preference refers to an individual's or group's attitude towards risk when making decisions, indicating whether they prefer to take risks or avoid them. This concept plays a crucial role in understanding how people evaluate potential outcomes, weighing the probabilities and consequences of different choices. Risk preference influences economic decisions, particularly in contexts where uncertainty is present, such as investments, insurance, and gambling.
Sunk Cost Fallacy: The sunk cost fallacy refers to the tendency for individuals to continue investing in a decision based on the cumulative prior investment (time, money, resources) rather than on current or future benefits. This irrational decision-making process often leads to further losses as people feel compelled to justify their earlier investments.
Utility: Utility refers to the satisfaction or benefit derived from consuming goods and services. In decision-making contexts, it represents how individuals evaluate choices based on the expected pleasure or value they will receive, guiding their preferences and actions. Understanding utility is crucial for analyzing choices under risk and uncertainty, as it connects to how people weigh potential outcomes against their desires and expectations.
Utility Function: A utility function is a mathematical representation that assigns a numerical value to the satisfaction or happiness an individual derives from consuming goods or services. It serves as a crucial tool in economic decision-making by illustrating how choices reflect personal preferences and helping to predict how individuals will behave under uncertainty. Utility functions are foundational in both Expected Utility Theory and Prospect Theory, highlighting the differences in how individuals assess risk and make decisions.
Value Function: The value function is a core component of Prospect Theory, representing how individuals evaluate potential gains and losses relative to a reference point rather than in absolute terms. It highlights that people perceive losses more intensely than gains of the same size, illustrating the concept of loss aversion. This function plays a crucial role in understanding economic behaviors, especially when comparing traditional Expected Utility Theory, which assumes individuals make decisions based purely on expected outcomes without considering reference points.
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