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.     

General cognitive slowing in the nonlexical domain: an experimental validation.

Older and younger adults were tested on 4 nonlexical tasks: choice reaction time, letter classification, mental rotation, and abstract matching. A positively accelerated relation was observed between older and younger adults' latencies. Consistent with general slowing, the relation observed with the same subjects in each condition was more than 3 times as precise as in a comparable meta-analysis. Further analyses compared the ability of various models to describe the present data and also to predict the data on the basis of parameters estimated from a previous meta-analysis. Compared with linear models, the information-loss and overhead models provided more accurate accounts of general cognitive slowing in the nonlexical domain.     

Interference with spatial working memory: An eye movement is more than a shift of attention

In the present experiments, we examined whether shifts of attention selectively interfere with the maintenance of both verbal and spatial information in working memory and whether the interference produced by eye movements is due to the attention shifts that accompany them. In Experiment 1, subjects performed either a spatial or a verbal working memory task, along with a secondary task requiring fixation or a secondary task requiring shifts of attention. The results indicated that attention shifts interfered with spatial, butnot with verbal, working memory, suggesting that the interference is specific to processes within the visuospatial sketchpad. In Experiment 2, subjects performed a primary spatial working memory task, along with a secondary task requiring fixation, an eye movement, or an attention shift executed in the absence of an eye movement. The results indicated that both eye movements and attention shifts interfered with spatial working memory. Eye movements interfered to a much greater extent than shifts of attention, however, suggesting that eye movements may contribute a unique source of interference, over and above the interference produced by the attention shifts that accompany them.     

Amount of reward has opposite effects on the discounting of delayed and probabilistic outcomes

Previous research has shown that the value of large future rewards is discounted less steeply than is the value of small future rewards. These experiments extended this line of research to probabilistic rewards. Two experiments replicated the standard findings for delayed rewards but demonstrated that amount has an opposite effect on the discounting of probabilistic rewards. That is, large probabilistic amounts were discounted at the same or higher rates than small amounts. Although amount had opposite effects on the discounting of delayed and probabilistic rewards, nevertheless, the same form of mathematical function accurately described discounting of both types of reward. The findings suggest that fundamentally similar, but not identical, processes are involved in decision making regarding delayed and probabilistic rewards. The implications of these findings for impulsivity and self-control are discussed.     

Modeling the effect of reward amount on probability discounting

The present study with college students examined the effect of amount on the discounting of probabilistic monetary rewards. A hyperboloid function accurately described the discounting of hypothetical rewards ranging in amount from $20 to $10,000,000. The degree of discounting increased continuously with amount of probabilistic reward. This effect of amount was not due to changes in the rate parameter of the discounting function, but rather was due to increases in the exponent. These results stand in contrast to those observed with the discounting of delayed monetary rewards, in which the degree of discounting decreases with reward amount due to amount-dependent decreases in the rate parameter. Taken together, this pattern of results suggests that delay and probability discounting reflect different underlying mechanisms. That is, the fact that the exponent in the delay discounting function is independent of amount is consistent with a psychophysical scaling interpretation, whereas the finding that the exponent of the probability-discounting function is amount-dependent is inconsistent with such an interpretation. Instead, the present results are consistent with the idea that the probability-discounting function is itself the product of a value function and a weighting function. This idea was first suggested by Kahneman and Tversky (1979), although their prospect theory does not predict amount effects like those observed. The effect of amount on probability discounting was parsimoniously incorporated into our hyperboloid discounting function by assuming that the exponent was proportional to the amount raised to a power. The amount-dependent exponent of the probability-discounting function may be viewed as reflecting the effect of amount on the weighting of the probability with which the reward will be received.     

The effects of environmental support and secondary tasks on visuospatial working memory

In the present experiments, we examined the effects of environmental support on participants’ ability to rehearse locations and the role of such support in the effects of secondary tasks on memory span. In Experiment 1, the duration of interitem intervals and the presence of environmental support for visuospatial rehearsal (i.e., the array of possible memory locations) during the interitem intervals were both manipulated across four tasks. When support was provided, memory spans increased as the interitem interval durations increased, consistent with the hypothesis that environmental support facilitates rehearsal. In contrast, when environmental support was not provided, spans decreased as the duration of the interitem intervals increased, consistent with the hypothesis that visuospatial memory representations decay when rehearsal is impeded. In Experiment 2, the ratio of interitem interval duration to intertrial interval duration was kept the same on all four tasks, in order to hold temporal distinctiveness constant, yet forgetting was still observed in the absence of environmental support, consistent with the decay hypothesis. In Experiment 3, the effects of impeding rehearsal were compared to the effects of verbal and visuospatial secondary processing tasks. Forgetting of locations was greater when presentation of to-be-remembered locations alternated with the performance of a secondary task than when rehearsal was impeded by the absence of environmental support. The greatest forgetting occurred when a secondary task required the processing visuospatial information, suggesting that in addition to decay, both domain-specific and domain-general effects contribute to forgetting on visuospatial working memory tasks.