Prospect Theory: Losses feel 2.25× stronger than gains — rejecting a 50/50 bet of ±$100 is rational under these preferences
With Kahneman & Tversky's original parameters (λ=2.25, α=β=0.88), a $100 loss feels 2.25× as painful as a $100 gain feels good. The certainty equivalent of a 50/50 ±$100 gamble is about -$13, meaning people need to be paid $13 just to accept a mathematically fair bet. This explains insurance buying, the endowment effect, and risk-seeking behavior when facing losses.
How We Really Decide
For centuries, economists assumed humans were perfectly rational maximizers of expected utility. Then in 1979, psychologists Daniel Kahneman and Amos Tversky published Prospect Theory, demonstrating that real human decisions systematically deviate from rational predictions. Their work earned Kahneman the 2002 Nobel Prize in Economics (Tversky had died in 1996) and spawned the field of behavioral economics.
The S-Shaped Value Function
The centerpiece of prospect theory is the value function — an S-shaped curve that replaces the smooth concave utility function of classical economics. For gains, the curve is concave: the jump from $0 to $100 feels much bigger than from $1,000 to $1,100. For losses, the curve is convex: losing the first $100 hurts terribly, but the incremental pain of further losses diminishes. Critically, the loss side is steeper — losses loom larger than gains.
Loss Aversion in Daily Life
Loss aversion (λ ≈ 2.25) explains a remarkable range of behaviors. People reject a 50/50 bet to win $110 or lose $100, even though the expected value is positive. Investors hold losing stocks too long (hoping to break even) while selling winners too quickly. Homeowners refuse to sell below their purchase price. Workers resist pay cuts even when inflation has already reduced their real wages. The reference point — what we consider 'normal' — shapes all of these decisions.
Beyond Individual Choice
Prospect theory has transformed fields far beyond psychology. In finance, it explains the equity premium puzzle and the disposition effect. In marketing, it explains why framing a discount as 'avoiding a surcharge' is more effective than 'getting a discount.' In policy, it shows why opt-out defaults are more powerful than opt-in. Adjust the parameters in this simulation to see how different levels of loss aversion and diminishing sensitivity reshape the value function and decision-making.
FAQ
What is prospect theory?
Prospect theory, developed by Daniel Kahneman and Amos Tversky in 1979, describes how people actually make decisions under risk, as opposed to how they should (expected utility theory). It identifies three key biases: reference dependence (outcomes are evaluated as gains or losses relative to a reference point), loss aversion (losses hurt more than equivalent gains), and diminishing sensitivity (the marginal impact of gains/losses decreases with size).
What is loss aversion?
Loss aversion means that the psychological pain of losing $100 is greater than the pleasure of gaining $100. Kahneman and Tversky estimated the loss aversion coefficient λ ≈ 2.25, meaning losses are felt about 2.25 times as strongly as gains. This explains why people reject favorable gambles, hold losing investments too long, and overvalue what they already own (endowment effect).
Why is the value function S-shaped?
The value function is concave for gains (risk aversion — a sure $50 feels better than a 50/50 chance of $100) and convex for losses (risk seeking — people prefer a 50/50 chance of losing $100 over a sure loss of $50, hoping to avoid the loss). The steeper slope for losses compared to gains reflects loss aversion.
How does prospect theory differ from expected utility theory?
Expected utility theory assumes people evaluate total wealth levels with a fixed concave utility function. Prospect theory instead says people evaluate changes from a reference point, are loss averse, have diminishing sensitivity in both directions, and overweight small probabilities. These differences explain many real-world anomalies like the Allais paradox, equity premium puzzle, and disposition effect.