Discounting of delayed and probabilistic losses over a wide range of amounts.

The present study examined delay and probability discounting of hypothetical monetary losses over a wide range of amounts (from $20 to $500,000) in order to determine how amount affects the parameters of the hyperboloid discounting function. In separate conditions, college students chose between immediate payments and larger, delayed payments and between certain payments and larger, probabilistic payments. The hyperboloid function accurately described both types of discounting, and amount of loss had little or no systematic effect on the degree of discounting. Importantly, the amount of loss also had little systematic effect on either the rate parameter or the exponent of the delay and probability discounting functions. The finding that the parameters of the hyperboloid function remain relatively constant across a wide range of amounts of delayed and probabilistic loss stands in contrast to the robust amount effects observed with delayed and probabilistic rewards. At the individual level, the degree to which delayed losses were discounted was uncorrelated with the degree to which probabilistic losses were discounted, and delay and probability loaded on two separate factors, similar to what is observed with delayed and probabilistic rewards. Taken together, these findings argue that although delay and probability discounting involve fundamentally different decision-making mechanisms, nevertheless the discounting of delayed and probabilistic losses share an insensitivity to amount that distinguishes it from the discounting of delayed and probabilistic gains.