You Cannot be Partially Pregnant: A Comparison of Divisible and Nondivisible Outcomes in Delay and Probability Discounting Studies

Risk inherent in delay accounts for magnitude effects in intertemporal decision making

If the future is indeed uncertain, then is the subjective riskiness of future gains and losses amount-dependent? To address this question, we performed two experiments, one regarding hypothetical monetary gains and the other regarding hypothetical monetary losses. Our main objective was to determine whether the magnitude effect observed in delay discounting can be explained by the subjective probability of receiving a future outcome. We employed a well-grounded discounting paradigm with a fixed-sequence procedure and the Subjective Probability Questionnaire across different magnitudes of gains and losses. We replicated prior findings indicating that the magnitude effect (observed in delay discounting) or the reverse magnitude effect (observed in probability discounting) are present for monetary gains but not for monetary losses. We found that the subjective probability of receiving future outcomes is amount-dependent for gains but not for losses. We propose that the magnitude effect can be a by-product of the risk associated with future payoffs of different magnitudes, as shown by mediation analysis. Our secondary goal was to investigate the form of the subjective probability function over time to determine if the change in risk inherent in delay is best described by the hyperbolic or exponential equations. We demonstrate that delay and probability discounting, as well as the subjective probability function, are best described by a simple hyperbolic model.

Information Use Differences in Hot and Cold Risk Processing: When Does Information About Probability Count in the Columbia Card Task?

Objective: This paper aims to provide insight into information processing differences between hot and cold risk taking decision tasks within a single domain. Decision theory defines risky situations using at least three parameters: outcome one (often a gain) with its probability and outcome two (often a loss) with a complementary probability. Although a rational agent should consider all of the parameters, s/he could potentially narrow their focus to only some of them, particularly when explicit Type 2 processes do not have the resources to override implicit Type 1 processes. Here we investigate differences in risky situation parameters' influence on hot and cold decisions. Although previous studies show lower information use in hot than in cold processes, they do not provide decision weight changes and therefore do not explain whether this difference results from worse concentration on each parameter of a risky situation (probability, gain amount, and loss amount) or from ignoring some parameters.

Methods: Two studies were conducted, with participants performing the Columbia Card Task (CCT) in either its Cold or Hot version. In the first study, participants also performed the Cognitive Reflection Test (CRT) to monitor their ability to override Type 1 processing cues (implicit processes) with Type 2 explicit processes. Because hypothesis testing required comparison of the relative importance of risky situation decision weights (gain, loss, probability), we developed a novel way of measuring information use in the CCT by employing a conjoint analysis methodology.

Results: Across the two studies, results indicated that in the CCT Cold condition decision makers concentrate on each information type (gain, loss, probability), but in the CCT Hot condition they concentrate mostly on a single parameter: probability of gain/loss. We also show that an individual's CRT score correlates with information use propensity in cold but not hot tasks. Thus, the affective dimension of hot tasks inhibits correct information processing, probably because it is difficult to engage Type 2 processes in such circumstances. Individuals' Type 2 processing abilities (measured by the CRT) assist greater use of information in cold tasks but do not help in hot tasks.