Intermediatebehavioral
Prospect Theory: How We Really Choose Under Risk
Overview
Kahneman and Tversky's prospect theory (1979) is the most cited paper in economics. It replaces expected utility with a psychologically realistic account: we evaluate outcomes as gains and losses relative to a reference point, feel losses ~2x more than gains, and distort probabilities — overweighting small chances, underweighting near-certainties. This lesson walks through the value function, the weighting function, the classic experiments, applications, and the theory's limits.
Learning objectives
- Describe the value function: reference-dependence, diminishing sensitivity, loss aversion
- Explain the probability weighting function
- Reproduce the classic experiments (Asian disease, etc.)
- Apply prospect theory: disposition effect, insurance puzzles
- Evaluate critiques and cumulative prospect theory
The value function
Three properties define it. Reference-dependence: we code outcomes as gains or losses versus a reference point (status quo, expectations, goals) — not as final wealth states. A 200. Diminishing sensitivity: the difference between 200 feels bigger than between 1,200 — the function is concave for gains, convex for losses. Loss aversion: the function is steeper for losses — losing 100 pleases. The famous S-shape: concave above zero, convex below, kinked at zero.
Loss aversion's geometric signature: the value function's slope roughly doubles crossing from gains to losses. Small losses loom disproportionately — the engine of status-quo bias, the endowment effect, and much more.
The weighting function
We don't use objective probabilities — we weight them. Small probabilities get overweighted: the 1% lottery chance feels like 5% (why lotteries and terrorism fears thrive). Moderate-to-high probabilities get underweighted: 95% feels like 85% (why we underinsure against likely-ish risks... or rather, why certainty matters so much). And the endpoints are special: moving from 0% to 5% (possibility) and from 95% to 100% (certainty) have outsized impact — the 'certainty effect.' This explains gambling (overweight small win chances) and the simultaneous demand for insurance (overweight small disaster chances) — the puzzle that motivated the theory.
The weighting function is steepest near 0 and 1: gaining a small chance of something, or eliminating the last bit of risk, moves behavior most. Marketers and policymakers exploit both edges.
The classic experiments
The Asian disease problem: '200 saved' vs. '1/3 chance 600 saved' — 72% choose certainty; reframed as '400 die' vs. '2/3 chance 600 die' — 78% gamble. Identical outcomes, reversed choices: framing plus the reflection effect (risk-averse for gains, risk-seeking for losses). The loss-aversion gamble: most reject a 50/50 win-100 bet — expected value positive, yet refused, implying losses weigh ~2x. These aren't confused undergraduates — the patterns replicate across cultures, stakes, and expertise. Expected utility cannot accommodate them without absurd contortions (Rabin's calibration theorem).
To explain small-stakes risk aversion with standard concave utility, you'd need absurd large-stakes implications (rejecting 50/50 lose-$1000/gain-anything). Small-stakes risk aversion essentially proves loss aversion.
Applications: finance and beyond
The disposition effect: investors sell winners too early (lock in gains) and hold losers too long (avoid realizing losses) — costing real returns, documented in brokerage data worldwide. Myopic loss aversion: evaluating portfolios frequently makes stocks' short-run losses salient, explaining the equity premium puzzle (Benartzi-Thaler) — check less often, hold more equity. Insurance puzzles: we overinsure small risks (extended warranties — overweighting small probabilities) while underinsuring catastrophic ones. Marketing: 'limited-time,' reference prices, and free-trial endowments all exploit the value function. Prospect theory is applied psychology's workhorse.
Selling winners, riding losers — the direct portfolio footprint of prospect theory. Tax-aware investors do the opposite (harvest losses); most humans do the reverse.
Limits and cumulative prospect theory
The 1979 version had flaws: it could predict dominated choices (violating stochastic dominance) and handled only simple gambles. Cumulative prospect theory (1992) fixed this with rank-dependent weighting — the version economists use. Deeper critiques: reference points are underspecified (what sets them? expectations? goals? — Kőszegi-Rabin endogenized them); loss aversion's magnitude varies; and some 'violations' reflect narrow framing that might be rational given cognitive costs. Still, prospect theory remains the best descriptive account of choice under risk ever developed — the rare theory that is both psychologically rich and formally precise.
Key points
- Prospect theory: reference-dependent value (S-shaped, kinked at zero) plus distorted probability weighting.
- Loss aversion (~2:1) and diminishing sensitivity drive the value function; overweighting of small probabilities drives the weighting function.
- Classic proof: framing reversals (Asian disease), rejected positive-EV gambles, the disposition effect in investor data.
- Applications span finance (equity premium, disposition), insurance, and marketing.
- Cumulative (1992) prospect theory is the working version; reference-point specification remains the open question.
Common misconceptions
✓ Truth: It's subtler: risk-averse for gains, risk-seeking for losses (the reflection effect), plus loss aversion and probability distortion. Fourfold pattern, not blanket caution.
✓ Truth: It means losses weigh ~2x gains. People take plenty of risks — especially to avoid sure losses (gambling to 'get back to even' is loss-driven risk-seeking).
✓ Truth: They attenuate but persist — doctors, investors, and judges show framing effects. Expertise changes the reference point; it doesn't install expected utility.
Practice questions
Q1. The prospect-theory value function is characterized by:
- Linearity in wealth
- Reference-dependence, diminishing sensitivity, and loss aversion (steeper for losses)
- Risk neutrality
- Constant absolute risk aversion
The S-shape: concave for gains, convex for losses, kinked at the reference point with losses weighing ~2x — encoding how humans actually feel outcomes.
Q2. In the Asian disease experiment, most people choose the certain option when outcomes are framed as 'lives saved' but gamble when framed as 'lives lost' because:
- They can't do math
- Framing shifts the reference point, triggering risk aversion for gains and risk-seeking for losses
- They prefer gambling
- The probabilities differ
Identical outcomes, reversed choices — the reflection effect. Gains-frame → lock in the sure gain; losses-frame → gamble to avoid the sure loss.
Q3. The disposition effect (selling winners early, holding losers) follows from prospect theory because:
- Investors are geniuses
- Realizing gains feels good and realizing losses hurts (loss aversion); investors also gamble to get back to even
- Brokers advise it
- Taxes require it
Loss aversion makes realizing losses painful (so investors defer), while diminishing sensitivity makes locking in gains attractive. Tax logic says do the opposite.
Click a question to reveal the answer and explanation.
Frequently asked questions
What is the reflection effect?
Risk attitudes flip around zero: risk-averse for gains (take the sure $500 over 50% of $1000), risk-seeking for losses (gamble 50% of -$1000 over sure -$500). The value function's concave/convex split.
What is the 'fourfold pattern'?
Risk-averse for high-probability gains and low-probability losses; risk-seeking for low-probability gains (lotteries) and high-probability losses (desperate gambles) — prospect theory's signature prediction.
How is cumulative prospect theory different?
The 1992 version applies weighting to cumulative probabilities (rank-dependent), eliminating the original's dominated-choice predictions. It's the technically sound, widely used formulation.
What sets the reference point?
The active research question: status quo, expectations (Kőszegi-Rabin), goals, social comparisons all matter. Context-dependent reference points are the theory's main underspecification.