Temporal discounting and preference reversals in choice between delayed outcomes

Subjects chose between pairs of hypothetical amounts of money available after different delays. When smaller, more immediate amounts were selected over larger, more delayed amounts, the addition of a constant delay to both outcomes resulted in reversals of preference, contrary to the standard discounted utility model of economics. The delays at which preference reversed were determined for three pairs of amounts ($20 vs. $50, $100 vs. $250, and $500 vs. $1,250). The relation between the delay to the larger amount and the delay to the smaller amount at preference reversal was well fit by both linear and quadratic functions. Intercepts increased with amount, strongly suggesting that rate of discounting decreases with amount. The presence of significant negative curvature in the data from the majority of individual subjects poses problems for exponential and hyperbolic models of temporal discounting in self-control, both of which predict a linear relation between the delays to the larger and smaller amounts.