Scalar Expectancy Theory and Choice Between Delayed Rewards

In this article scalar expectancy theory is applied to variable and fixed delays to reward. It is assumed that all delays are represented in memory with scalar variance and that subjects choose between alternatives by sampling from the memory distributions associated with each and choosing the smaller delay. This simple scheme is shown to entail four common findings in the choice literature: (a) approximate matching of choice ratios to reward ratios (the matching law) when both alternatives are associated with variable delays scheduled with constant probability; (b) undermatching, in which choice is closer to indifference than matching, when both alternatives are variable but scheduled with uniform distributions; (c) overmatching, in which choice is more extreme than matching, when both alternatives are fixed delays; and (d) preference for variable delays scheduled with a constant probability over fixed delays. Overmatching and Weber's law are illustrated in experiments using the time-left procedure ( Gibbon & Church, 1981 ). The preference for variable delay is demonstrated in this procedure, followed by study of a unique variable schedule of delays for which the theoretical account predicts, and the data confirm, the elimination of the preference for variability.