The value function is the central component of Prospect Theory, replacing the utility function of expected utility theory. Three key properties distinguish it: reference dependence (outcomes are evaluated as changes from a reference point, not as final states), diminishing sensitivity (marginal value decreases with distance from the reference point), and loss aversion (losses loom larger than gains of equal magnitude).
Functional Form
v(x) = −λ(−x)ᵝ for x < 0
α = β ≈ 0.88 (diminishing sensitivity)
λ ≈ 2.25 (loss aversion coefficient)
The exponents α and β (both less than 1) produce concavity for gains and convexity for losses — reflecting diminishing sensitivity in both domains. A gain of $100 feels less than twice as good as $50, and a loss of $100 feels less than twice as bad as $50. The loss aversion parameter λ ≈ 2.25 means that losses are weighted about 2.25 times more heavily than gains of equal size.
Empirical Evidence
The value function's properties have been confirmed across many cultures, stimulus types (money, goods, time), and elicitation methods. Loss aversion explains the endowment effect (people demand more to sell an object than they would pay to buy it), the status quo bias, and the equity premium puzzle in finance. The exact value of λ varies across studies (1.5 to 2.5) but the qualitative pattern of loss aversion is remarkably robust.