Properties of the value and weighting functionsMore on Value FunctionsThe emphasis on changes as the carriers of value does not mean that the value of a particular change is independent of the initial position. Value functions are likely to become more linear with increases in assets. A change from $100 to $200 is likely to have a much higher value than a change from $1100 to $1200. The value function is then concave above the reference point (v"(x) < 0 for x > 0), and convex below it (v"(x) > 0 for x < 0). Meaning, it is concave for gains and convex for losses. More on the weighting functionThe weighting function π, which relates decision weights to stated probabilities, is an increasing function of p, with π(0) = 0 and π(1) = 1. However, people tend to overweight very small probabilities, like 0.001, so that π(p) > p for very small p.  
