Value function
Also known as: S-shaped value function
The S-shaped curve that maps gains and losses onto felt value, kinked at the reference point.
What it means
The value function is the prospect-theory analog of the utility function, but defined over changes from a reference point rather than final wealth. It has three signature properties: it is concave for gains (risk aversion), convex for losses (risk seeking), and steeper for losses than for gains (loss aversion), producing a kink at the origin. Its concavity-then-convexity encodes diminishing sensitivity, while the steeper loss limb encodes the roughly 2:1 pain-to-pleasure ratio. Because the curve is anchored to a movable reference point, the same final state can be coded as a gain or a loss, which is what makes framing so powerful. The function is the engine that, combined with decision weights, generates prospect theory's predictions.
Examples
Winning $100 then losing $80 nets +$20 in money but can feel like a loss, because the $80 drop is read on the steep loss limb.
A bonus £500 smaller than last year's stings more than an extra £500 would please. The identical pay packet reads as a punishment or a reward depending on which year you compare it against.
Losing your umbrella ruins the morning. Losing your umbrella on the day you also crash the car barely registers — the second loss lands on a limb that has already flattened out.
First described in Kahneman & Tversky (1979).