Effects of delay and probability combinations on discounting in humans

Abstract

To determine discount rates, researchers typically adjust the amount of an immediate or certain option relative to a delayed or uncertain option. Because this adjusting amount method can be relatively time consuming, researchers have developed more efficient procedures. One such procedure is a 5-trial adjusting delay procedure, which measures the delay at which an amount of money loses half of its value (e.g., $1000 is valued at $500 with a 10-year delay to its receipt). Experiment 1 (n=212) used 5-trial adjusting delay or probability tasks to measure delay discounting of losses, probabilistic gains, and probabilistic losses. Experiment 2 (n=98) assessed combined probabilistic and delayed alternatives. In both experiments, we compared results from 5-trial adjusting delay or probability tasks to traditional adjusting amount procedures. Results suggest both procedures produced similar rates of probability and delay discounting in six out of seven comparisons. A magnitude effect consistent with previous research was observed for probabilistic gains and losses, but not for delayed losses. Results also suggest that delay and probability interact to determine the value of money. Five-trial methods may allow researchers to assess discounting more efficiently as well as study more complex choice scenarios.

Keywords: Complex choice; Delay discounting; Probability discounting.

Fig. 1

Example adjustments of choice alternatives in the 5-trail adjusting delay loss (left) and 5-trial adjusting probability loss (right) tasks. The trial number represents the order of choice presentation. The index number corresponds to the index listing in Table 1 (delay discounting) or in Table 2 (probability discounting). Circled alternatives represent the choice made by a hypothetical participant leading to the presented choice index in the following trial. The final parameter represents the rate at which the value of $1000 reduces as a function of increasing delay (k) or increasing odds against (h).

Fig. 2

Median indifference points and best fitting curves from Eq. (3) (left panels) and Eq. (4) (right panels) for Experiment 2. The upper panels are delayed and probabilistic gains. The lower panels are delayed and probabilistic losses.

Fig. 3

Median indifference points and best fitting curves from Eq. (6) (left panels) and Eq. (5) (right panels) for Experiment 2. The upper panels are delayed and probabilistic gains. The lower panels are delayed and probabilistic losses.