Kahneman & Tversky's prospect theory replaces expected utility with a subjective value function that is concave for gains, convex for losses, and steeper for losses than gains relative to a reference point R (the anchor). The purple curve on the plot is this function; the amber dot marks your current outcome x. The scatter band below simulates a crowd independently estimating a true value V — as anchoring strength rises their estimates get pulled from V toward the arbitrary anchor R.
v(x) = (x-R)^α if x ≥ R (gain)
v(x) = -λ·(R-x)^α if x < R (loss)
crowd estimate_i = R + (1-a)·(V-R) + noise_i
R = anchor, V = true value, a = anchoring strength
- α — curvature of diminishing sensitivity to gains/losses
- λ — loss aversion coefficient (how much steeper losses feel than equivalent gains)
- R (anchor) — the reference point that reframes what counts as a gain or loss
- Anchoring strength — how strongly the crowd's estimates cling to R instead of the true value
- Outcome x — moves the marker along the value curve to read off v(x)
This is why a "50% off" sale (anchored at the original price) feels like a gain even if the discounted price is still high, and why the pain of losing £100 outweighs the pleasure of gaining £100.