# Prospect Theory: How Losses Loom Larger Than Gains

Cite as: Gorak, R. (2026). Prospect Theory: How Losses Loom Larger Than Gains. Tradicted. https://www.tradicted.com/research/kahneman-prospect-1979/
Paper: Daniel Kahneman and Amos Tversky — *Prospect Theory: An Analysis of Decision under Risk*
Published in: Econometrica (1979)
Original: https://web.mit.edu/curhan/www/docs/Articles/15341_Readings/Behavioral_Decision_Theory/Kahneman_Tversky_1979_Prospect_theory.pdf

Key finding: 82% of subjects preferred a certain 2,400 over a three-outcome gamble (2,500 at .33, 2,400 at .66, 0 at .01) in Problem 1, while 83% reversed that preference in the structurally equivalent Problem 2 — a direct violation of expected utility theory.

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Prospect theory describes how people evaluate gains and losses relative to a reference point rather than as final wealth states. Kahneman and Tversky (1979) presented hypothetical choice problems to 66–141 students and faculty per problem across Israeli, Swedish, and U.S. universities. In Problem 1, 82% of subjects (N=72) chose a certain 2,400 over a three-outcome gamble: 2,500 with probability .33, 2,400 with probability .66, and 0 with probability .01. In Problem 2, 83% reversed that preference — a direct violation of expected utility theory. The value function is concave for gains, convex for losses, and steeper for losses than for gains.

## What the Study Found

80% of subjects (N=95) chose a certain gain of 3,000 over a gamble of 4,000 at probability .80. In the mirrored loss version, 92% chose the risky loss of 4,000 at probability .80 over a certain loss of 3,000. 78% of subjects (N=141) chose differently across standard vs. sequential formulations of identical prospects (isolation effect). 80% of subjects (N=95) rejected probabilistic insurance offering half the premium with a 50% chance of coverage. 72% of subjects (N=72) preferred a lottery of 5,000 at probability .001 over a certain 5. 83% preferred a certain payment of 5 over a loss gamble of 5,000 at probability .001. In 30 business decision makers studied by Fishburn and Kochenberger, utility functions were considerably steeper for losses than for gains in all but one case.

## Methodology

The study used hypothetical choice questionnaire experiments. Subjects were students and faculty at universities in Israel, Sweden (University of Stockholm), and the United States (University of Michigan, Stanford University). Sample sizes ranged from 66 to 141 respondents per problem. Problems were presented in booklets of up to 12 problems each, with multiple forms varying problem order. Left-right positioning of prospects was reversed across versions and responses were anonymous.

## Key Statistics

| Metric | Finding | Context |
|---|---|---|
| Certainty effect (Problem 1) | 82% chose certain 2,400 over (2,500, .33; 2,400, .66) | N=72; significant at .01 level |
| Reflection effect (Problem 3 vs. 3-prime) | 80% risk-averse for gains; 92% risk-seeking for equivalent losses | N=95 each |
| Isolation effect (Problem 4 vs. 10) | 78% chose (3,000) in sequential form vs. 35% in standard form | N=141 vs. N=95; same underlying prospect |
| Probabilistic insurance rejection | 80% rejected probabilistic insurance | N=95 Stanford students |
| Low-probability overweighting (Problem 14) | 72% preferred (5,000, .001) over certain 5 | N=72 |
| Risk seeking, small probabilities (Problem 8) | 73% chose (6,000, .001) over (3,000, .002) | N=66 |
| Risk aversion, large probabilities (Problem 7) | 86% chose (3,000, .90) over (6,000, .45) | N=66 |
| Value function — regular prospects | V(x, p; y, q) = π(p)v(x) + π(q)v(y) | Equation (1); π = decision weight, v = subjective value |
| Value function — strictly positive/negative | V(x, p; y, q) = v(y) + π(p)[v(x) − v(y)] | Equation (2); separates riskless and risky components |
| Loss aversion condition | v(x) < −v(−x) | Losses loom larger than equivalent gains |
| Subcertainty | π(p) + π(1 − p) < 1 for all 0 < p < 1 | Decision weights for complementary events sum to less than 1 |

## Why This Matters

Prospect theory provides the formal basis for explaining why investors hold losing positions longer than rational models predict and sell winning positions prematurely. The asymmetric steepness of the value function for losses versus gains underpins the disposition effect documented in retail brokerage data. Loss aversion alters the attractiveness of insurance, options strategies, and stop-loss rules in ways that expected utility models cannot account for. The isolation effect shows that identical investment choices can produce opposite decisions depending only on framing. Loss aversion is hard to observe in yourself in the moment and straightforward to observe afterward. A [trading journal](/trading-journal/) that records your reasoning before the outcome gives you that record.

## FAQ

### What is the certainty effect in prospect theory?

82% of subjects (N=72) chose a certain 2,400 over a three-outcome gamble (2,500 at .33, 2,400 at .66, 0 at .01) in Kahneman and Tversky (1979). In the structurally equivalent Problem 2, where both options were probabilistic, 83% reversed and chose the higher-value gamble. People overweight certain outcomes relative to probable ones, producing inconsistent preferences across equivalent choices.

### How does loss aversion manifest in experimental choice problems?

92% of subjects (N=95) chose a risky loss at probability .80 over a smaller certain loss, reversing the risk aversion seen for identical positive prospects. Kahneman and Tversky (1979) show the value function is steeper for losses than gains. Fishburn and Kochenberger confirmed this in all but one of 30 business decision makers across five independent studies.

### What is the isolation effect and what does it show about framing?

78% of subjects (N=141) chose a certain 3,000 in a sequential game equivalent to a standard choice where only 35% chose it. Kahneman and Tversky (1979) show that people discard shared components of prospects, making preference contingent on framing rather than final-state probabilities and outcomes.

### How does prospect theory explain simultaneous gambling and insurance purchasing?

72% of subjects (N=72) preferred a lottery of 5,000 at probability .001 over a certain 5. 83% preferred a certain small payment of 5 over a .001 probability of losing 5,000. Overweighting of small probabilities makes both lottery tickets and insurance policies attractive — each exploits the same nonlinearity in the decision weighting function π.

## Source

Kahneman, D., & Tversky, A. (1979). Prospect Theory: An Analysis of Decision under Risk. *Econometrica*, 47(2), 263–291.

[Read the full paper →](https://web.mit.edu/curhan/www/docs/Articles/15341_Readings/Behavioral_Decision_Theory/Kahneman_Tversky_1979_Prospect_theory.pdf)