Abstract: The Effect of Temporal Delay on the Interpretation of Probability Amber N. Bloomfield (a-bloomfield@northwestern.edu) Department of Psychology, 2029 Sheridan Road Evanston, IL 60208 USA produce a solid preference when their probabilities are multiplied by a common probability. A person might be indifferent between a 5% chance of $10 and 2% chance of $15, but prefer the $15 option if both probabilities are multiplied by 50%. Immediacy and certainty effects involve the overweighting of immediate outcomes in intertemporal choice and the overweighting of certain outcomes in risky choice. Magnitude effects occur when large amounts are discounted to a lesser (temporal discounting) or greater (discounting for risk) degree than are small amounts. Sign effects involve a tendency towards risk-aversion for gains and risk-seeking for losses in risky choice, and a steeper discounting of gains than losses in intertemporal choice. Given these parallels, it is not surprising that some researchers have suggested that discounting for risk and discounting for delay arise from the same source. For instance, Benzion, Rapoport and Yagil (1989) argue that, in addition to the time value of money (characterized as the accepted interest rate) delay introduces a risk premium, which arises from the implicit risk associated with delay. By this interpretation, the temporal discounting stems from implicit risk combined with the rational time value of money. Alternatively, Rachlin and Raineri (1992) argue that probability can be expressed as waiting time, by estimating the number of trials until a win (60% chance ≈ 6 out of 10 trials are wins), and adding together the amount of time between each trial preceding the first win to calculate overall waiting time. These two ideas both argue for a fundamental source of uncertainty (either risk or delay) that leads to both types of discounting. It is likely that because of the focus on equating probability and delay little attention has been paid to how they affect each other, both in determining the value of outcomes and directly. Only a few studies have actually presented participants with outcomes that are both delayed and probabilistic. Keren and Roelofsma (1995) argue for two different types of uncertainty present in intertemporal choice: internal (involving doubts about one’s ability to predict future tastes/needs) and external (concerning doubts about whether promised future payments will be honored). Internal uncertainty is the type of uncertainty typically associated with intertemporal choice. External uncertainty is probabilistic uncertainty, which they argue is also a component of any temporal delay. They found that the immediacy effect could be derailed by making the options probabilistic (the immediate option was no longer over- weighted), and that adding a delay to a certain option weakened the certainty effect (the certain option was no longer as over-weighted, and more people preferred a risky Abstract The studies reported here investigate the interaction between probability and delay. In the first study, the fits of a range of high and low probability words were calculated for numerical probabilities presented with either a short or long delay. Results show that participants in the long delay condition felt that high probability words fit small numerical probabilities better and that low probability words fit large numerical probabilities better than did participants in the short delay condition. In a second study, participants were presented with money offers that were both delayed and risky. Findings indicate that delay is given less weight at low probabilities, and probability is given less weight at large delays when probabilities are mid-range. Combined, these data suggest that a trade-off occurs between giving attention to delay and giving attention to probability in judgments. One component of this arises from long time delays “dampening down” the influence of probability level, but the complete nature of the interaction between probability and delay remains to be explored. Introduction In everyday decision making, individuals must determine the value that various outcomes have for them. Often, even if people have a clear idea of the value that an outcome has for them in general (such as a week in Paris), they must assess its value in terms of different types of uncertainty associated with the outcome. One type of uncertainty arises from the outcome having a less than 100% likelihood of occurring (i.e., it is probabilistic). This type of uncertainty is normatively applied by translating an outcome into its expected value (EV): multiplying the value of the outcome by its probability of occurring. Another type of uncertainty associated with outcomes is temporal delay. Adjustment of an outcome due to temporal delay is referred to as temporal discounting. Choice involving risk (i.e., probabilistic outcomes) and intertemporal choice have several parallel anomalies (Prelec & Loewenstein, 1991). These anomalies include common difference and ratio effects, immediacy and certainty effects, magnitude effects and sign effects. Common difference effect occurs when a pair of delayed outcomes which an individual is indifferent between produce a decisive preference for him or her when a common delay is added to both. For instance, a person might be indifferent between $25 now and $40 is one week, but may express a preference for the $40 if a one-week delay is added to both options. Similarly, common ratio effect occurs when two probabilistic options which a person is indifferent between