Probability and Time Trade-Off

Probability and time are integral dimensions of virtually any decision. To treat them together, we consider the prospect of receiving outcome x with a probability p at time t. We define risk and time distance, and show that if these two distances are traded off linearly, then preferences are characterized by three functions: a value function, a probability discount rate function, and a psychological distance function. The concavity of the psychological distance function explains the common ratio and common difference effects. A decreasing probability discount rate accounts for the magnitude effect. The discount rate and the risk premium depend on the shape of these three functions. This paper was accepted by Peter Wakker, decision analysis.