Prospect Theory & Loss Aversion

About Prospect Theory

Prospect Theory, developed by Daniel Kahneman and Amos Tversky (1979), revolutionized our understanding of decision-making under risk. It describes how people actually make choices involving probability and value, rather than how they "should" according to expected utility theory. The theory won Kahneman the Nobel Prize in Economics in 2002.

The Value Function

Unlike expected utility theory's assumption of constant risk attitudes, Prospect Theory proposes an S-shaped value function with three key properties:

• Reference dependence: Outcomes are evaluated as gains or losses relative to a reference point (often the status quo), not as final wealth states
• Loss aversion: Losses loom larger than equivalent gains—the pain of losing $100 is greater than the pleasure of gaining $100. Typically λ ≈ 2.25, meaning losses hurt about twice as much as gains feel good
• Diminishing sensitivity: The function is concave for gains (risk averse) and convex for losses (risk seeking). The difference between $0 and $100 feels larger than between $1000 and $1100

The value function is: v(x) = x^α for gains (x ≥ 0), and v(x) = -λ|x|^α for losses (x < 0)

Probability Weighting

People don't weight probabilities linearly. Instead, they use a probability weighting function w(p) with these features:

• Overweighting small probabilities: Events with 1% probability are treated as more likely than they are—explaining lottery purchases and fear of rare disasters
• Underweighting moderate-to-high probabilities: Events with 90% probability are treated as less certain than they are
• Subcertainty: w(p) + w(1-p) < 1 except at extremes
• Subproportionality: The ratio w(pq)/w(p) decreases as p increases

The weighting function is: w(p) = p^γ / (p^γ + (1-p)^γ)^1/γ

Classic Phenomena Explained

• Certainty Effect: People prefer a sure $3,000 over 80% chance of $4,000 (risk averse for gains), but prefer 25% chance of $3,000 over 20% chance of $4,000 (violating expected utility)
• Reflection Effect: Risk preferences reverse for losses—people are risk seeking to avoid certain losses but risk averse for gains
• Endowment Effect: Loss aversion explains why people demand more to give up something than they'd pay to acquire it
• Status Quo Bias: Changes from the reference point feel like losses, creating inertia
• Framing Effects: Describing outcomes as gains vs. losses changes choices, even when objective outcomes are identical

The Fourfold Pattern of Risk Attitudes

Combining loss aversion with probability weighting produces four distinct patterns:

This explains why people buy both insurance (risk averse for low-probability large losses) and lottery tickets (risk seeking for low-probability large gains).

Philosophical and Practical Implications

• Descriptive vs. Normative: Prospect Theory describes how people actually decide, but debate continues about whether these patterns reflect bounded rationality or genuine preference
• Policy and Nudges: Understanding these biases enables "choice architecture" that helps people make better decisions (e.g., opt-out vs. opt-in for retirement savings)
• Market Anomalies: Loss aversion and probability weighting help explain financial market phenomena like the equity premium puzzle
• Rationality Debate: Are these "biases" or adaptive heuristics? Evolution may have favored these patterns in ancestral environments
• Manipulation Concerns: Framing effects raise ethical questions about persuasion, marketing, and informed consent

Extensions and Critiques

Cumulative Prospect Theory (1992): Tversky and Kahneman refined the theory to handle multiple outcomes by applying probability weighting to cumulative rather than individual probabilities, resolving stochastic dominance violations.

Context Dependence: The reference point is malleable and context-dependent, making predictions difficult without knowing how people frame decisions.

Preference Reversals: Some empirical patterns remain unexplained, and alternative theories (e.g., regret theory, rank-dependent utility) compete in various domains.