💰Psychology of Economic Decision-Making Unit 3 – Prospect Theory: Decisions Under Risk

Key Concepts and Foundations

• Prospect theory is a behavioral economic theory that describes how people make decisions under risk and uncertainty
• Developed by Daniel Kahneman and Amos Tversky in 1979 as an alternative to expected utility theory
• Focuses on the subjective perception of gains and losses relative to a reference point rather than absolute outcomes
• Introduces the concept of loss aversion, the idea that people feel the pain of losses more intensely than the pleasure of equivalent gains
• Incorporates the diminishing sensitivity principle, which suggests that people are more sensitive to changes near their reference point than to changes further away
  • For example, the difference between a gain of $100 and$200 feels larger than the difference between a gain of $1,100 and$1,200
• Considers the role of probability weighting, where people tend to overweight small probabilities and underweight large probabilities
• Accounts for framing effects, demonstrating that the way a problem is presented can significantly influence the decision made
  • For instance, presenting a choice as a potential gain versus a potential loss can lead to different decisions, even if the outcomes are objectively equivalent

Historical Context and Development

• Expected utility theory, developed by John von Neumann and Oskar Morgenstern in 1944, was the dominant model for decision-making under risk before prospect theory
  • Expected utility theory assumes that people make rational decisions based on the expected value of outcomes, calculated by multiplying the probability of each outcome by its utility
• Kahneman and Tversky observed that people's actual decision-making often violated the assumptions of expected utility theory
  • For example, the Allais paradox demonstrates that people's preferences can be inconsistent with the independence axiom of expected utility theory
• Prospect theory was developed as a descriptive model to better capture how people actually make decisions under risk, rather than a normative model of how they should make decisions
• The original version of prospect theory, published in 1979, focused on decision-making under risk with known probabilities
• Cumulative prospect theory, introduced by Tversky and Kahneman in 1992, extended the original theory to include decision-making under uncertainty with unknown probabilities
• Prospect theory has become one of the most influential theories in behavioral economics and has been applied to various fields, including finance, insurance, and public policy

Components of Prospect Theory

• Reference point: the benchmark against which gains and losses are evaluated
  • Often based on the current state or status quo, but can also be influenced by expectations, goals, or social comparisons
• Value function: assigns subjective values to gains and losses relative to the reference point
  • Concave for gains, indicating diminishing sensitivity (e.g., the difference between a gain of $100 and$200 feels larger than the difference between a gain of $1,100 and$1,200)
  • Convex for losses, also indicating diminishing sensitivity
  • Steeper for losses than for gains, reflecting loss aversion (e.g., a loss of $100 feels more painful than a gain of$100 feels pleasant)
• Weighting function: transforms objective probabilities into decision weights
  • Overweights small probabilities and underweights large probabilities
  • Leads to the fourfold pattern of risk attitudes: risk-averse for high-probability gains and low-probability losses, risk-seeking for low-probability gains and high-probability losses
• Framing: the way a decision problem is presented can influence the perceived reference point and, consequently, the evaluation of gains and losses
  • Positive framing emphasizes potential gains, while negative framing emphasizes potential losses
  • For example, a medical treatment described as having an 80% survival rate (positive frame) is more appealing than one described as having a 20% mortality rate (negative frame), even though the outcomes are objectively equivalent

Decision-Making Process Under Risk

• Editing phase: the initial phase where the decision problem is simplified and reformulated
  • Coding: outcomes are categorized as gains or losses relative to the reference point
  • Combination: probabilities associated with identical outcomes are combined
  • Segregation: the decision problem is separated into a risk-free component and a risky component
  • Cancellation: common components of different prospects are discarded
  • Simplification: probabilities and outcomes are rounded
  • Detection of dominance: if one prospect dominates another, the dominated prospect is rejected
• Evaluation phase: the edited prospects are evaluated, and the prospect with the highest value is chosen
  • The value of each prospect is calculated by multiplying the value of each outcome (determined by the value function) by its decision weight (determined by the weighting function) and summing these products
• The decision-making process under prospect theory is influenced by various cognitive biases and heuristics, such as loss aversion, diminishing sensitivity, and probability weighting
• Prospect theory predicts that people will be risk-averse when choosing between gains and risk-seeking when choosing between losses
  • For example, when presented with a choice between a sure gain of $500 and a 50$1,000, most people prefer the sure gain (risk aversion)
  • However, when presented with a choice between a sure loss of $500 and a 50$1,000, most people prefer the gamble (risk-seeking)

Cognitive Biases and Heuristics

• Loss aversion: the tendency to feel the pain of losses more intensely than the pleasure of equivalent gains
  • Leads to a greater willingness to take risks to avoid losses than to achieve gains
  • Can result in the endowment effect, where people value items they own more highly than identical items they do not own
• Diminishing sensitivity: the tendency to be more sensitive to changes near the reference point than to changes further away
  • Contributes to the concavity of the value function for gains and the convexity for losses
  • Can lead to the isolation effect, where people focus on the differences between options rather than their overall value
• Probability weighting: the tendency to overweight small probabilities and underweight large probabilities
  • Leads to the fourfold pattern of risk attitudes and can explain the popularity of lottery tickets and insurance
  • Can result in the certainty effect, where people overvalue outcomes that are certain relative to outcomes that are merely probable
• Framing effects: the tendency to make different decisions based on how a problem is presented
  • Can influence the perceived reference point and the evaluation of gains and losses
  • Contributes to the reflection effect, where preferences between negative prospects are the mirror image of preferences between positive prospects
• Anchoring and adjustment: the tendency to rely heavily on an initial piece of information (the anchor) when making estimates or decisions
  • Can influence the perceived reference point and lead to insufficient adjustment away from the anchor
  • For example, when estimating the value of a house, the asking price can serve as an anchor that influences the final estimate

Applications in Economics and Finance

• Prospect theory has been applied to various economic and financial contexts to explain observed behavior that deviates from the predictions of expected utility theory
• In financial markets, prospect theory can help explain the disposition effect, where investors are more likely to sell assets that have increased in value (realizing gains) than assets that have decreased in value (realizing losses)
  • This behavior is consistent with the idea that people are risk-averse for gains and risk-seeking for losses
• Prospect theory can also shed light on the equity premium puzzle, the observation that the average return on stocks is much higher than the average return on bonds, even after accounting for the higher risk of stocks
  • Loss aversion and probability weighting can make the potential losses from investing in stocks feel more salient and likely than the potential gains, leading to a higher required return for holding stocks
• In insurance markets, prospect theory can explain why people are willing to pay more for insurance than the expected value of the potential losses
  • The overweighting of small probabilities makes the possibility of a large loss feel more significant, increasing the perceived value of insurance
• Prospect theory has also been applied to public policy, such as in the design of tax systems and the framing of public health messages
  • For example, presenting a tax as a "bonus" for a desirable behavior (positive frame) may be more effective than presenting it as a "penalty" for an undesirable behavior (negative frame), even if the financial outcomes are equivalent

Critiques and Limitations

• Some researchers argue that prospect theory is too complex and has too many free parameters, making it difficult to falsify or apply in practice
  • The specific shapes of the value and weighting functions can vary across individuals and contexts, limiting the theory's predictive power
• Prospect theory focuses primarily on individual decision-making and may not fully account for the influence of social factors, such as norms, expectations, and emotions
  • For example, the theory does not directly address how people's decisions are affected by the presence or actions of others
• The editing phase of prospect theory is not well-specified, and there is debate about the exact nature and sequence of the operations involved
  • Different assumptions about the editing process can lead to different predictions, making it difficult to test the theory empirically
• Prospect theory is a descriptive model of decision-making under risk and uncertainty, not a normative model of how people should make decisions
  • While the theory can help explain observed behavior, it does not necessarily provide guidance on how to make optimal decisions
• Some studies have found that the predictions of prospect theory do not always hold in all contexts or for all individuals
  • For example, experienced traders in financial markets may exhibit less loss aversion and probability weighting than the general population
• Prospect theory does not fully address the role of learning and experience in shaping decision-making over time
  • As people gain more information and feedback about the outcomes of their decisions, their preferences and strategies may change in ways not captured by the theory

Real-World Examples and Case Studies

• The framing of public health messages during the COVID-19 pandemic
  • Messages emphasizing the potential lives saved by wearing masks and social distancing (positive frame) may be more effective than messages emphasizing the potential lives lost by not taking these precautions (negative frame)
• The design of retirement savings plans
  • Automatically enrolling employees in a 401(k) plan with a default contribution rate (positive frame) can lead to higher participation and savings rates than requiring employees to opt-in to the plan (negative frame)
• The pricing of insurance policies
  • Offering a policy with a low deductible and a high premium (emphasizing the potential gains of coverage) may be more appealing than offering a policy with a high deductible and a low premium (emphasizing the potential losses of out-of-pocket expenses)
• The behavior of investors during market bubbles and crashes
  • The overweighting of small probabilities can lead investors to chase highly speculative investments (e.g., cryptocurrency) during market bubbles, while loss aversion can lead to panic selling during market crashes
• The negotiation of international trade agreements
  • Framing a proposed agreement as a "win-win" opportunity for both parties (positive frame) may be more effective than framing it as a "concession" or "compromise" (negative frame)
• The design of warning labels on cigarette packages
  • Graphic images depicting the health consequences of smoking (negative frame) may be more effective at discouraging smoking than text-only warnings (neutral frame)
• The structuring of performance bonuses for employees
  • Offering a bonus for exceeding a sales target (positive frame) may be more motivating than imposing a penalty for falling short of the target (negative frame), even if the financial outcomes are equivalent