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 <i>x</i> with a probability <i>p</i> at time <i>t</i>. 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. <i>This paper was accepted by Peter Wakker, decision analysis.</i>