Path Dependency in the Discounting of Delayed and Probabilistic Gains and Losses

www.nature.com/scientificreports OPEN Received: 19 November 2018 Accepted: 5 June 2019 Published: xx xx xxxx Path Dependency in the Discounting of Delayed and Probabilistic Gains and Losses Wojciech Białaszek & Przemysław Marcowski Human decision making often involves outcomes that are both risky and delayed. In such delayed lottery scenarios, the question of how such prospects are evaluated arises. An individual can arrive at their choice by following three different subjective value elicitation paths: (1) a direct path by considering the delay and risk of an outcome simultaneously; (2) a delay-probability path by first considering the delay and then the risk of an outcome; and (3) a probability-delay path by first considering the probability and then the delay of an outcome. Using a discounting framework, we conducted an experiment to investigate whether individual choices are path dependent, i.e., if the three paths elicit different subjective values of risky and delayed gains or losses. The experiment included an arbitrary selection of delays and individual probability estimates corresponding to each delay, obtained in an additional delay-probability trade-off task. Such approach ensured the equal individual decision factor strength of each outcome delay and probability. Our findings demonstrate that the human choice of risky and delayed gains or losses is indeed path dependent, which contrasts with the normative view. Furthermore, we present evidence that human choice more closely follows the delay-probability elicitation path than the probability-delay path in the domain of gains. Time and risk are some of the most widely studied factors in decision-making. The majority of research (with some notable exceptions) focuses on the impact of one isolated factor on choice behavior. However, often decisions in real life are not made solely based on the delay or probability of their consequences, but their combination1,2. Here we report the findings from an experiment that focuses on choice scenarios that we refer to as delayed lotteries. In such scenarios, the occurrence of a rewarding or aversive outcome is linked to both the delay and probability of its receipt. In choices involving delayed lotteries, when outcome A is both delayed and probabilistic, individuals may evaluate the outcome in three different ways or paths3,4 (Fig. 1). The first is a direct evaluation, which corresponds to estimating the immediate certainty equivalent of the delayed lottery. We refer to this scenario as a direct (dir) path, where svdir(A) (subjective value of outcome A) is elicited by a direct evaluation of outcome A with a given delay and given probability. The second path of eliciting an immediate certainty equivalent of a delayed lottery would require a two-stage process. The first stage would be an estimation of the certainty equivalent of a delayed lottery (as though it was only risky), followed by a further estimation of the immediacy equivalent, ultimately yielding a subjective value of the complete delayed lottery. In this path, the outcome is first discounted by the probability and then by the delay, yielding svθd(A), which we refer to as the probability-delay (θd) path. The third path would first elicit a delay-discounted value, yielding an immediacy equivalent, which is then further discounted by the risk component of a delayed lottery, resulting in svdθ(A). We refer to this path as the delay-probability (dθ) path. We refer to probability as the odds against outcome receipt, i.e., θ = (1 − p)/p, where p refers to the outcome probability5. Normatively, from the perspective of expected utility theory6, the three subjective value elicitation paths outlined above should yield equal values, i.e., svdir(A) ≡ svθd(A) ≡ svdθ(A). However, previous studies suggest that delaying the risk reduces the aversion toward it, thus providing indirect support for path dependency. For example, Stevenson7 observed a seemingly counterintuitive result that equivalent monetary amounts were discounted more as a function of delay when outcome receipt was riskless compared to a choice scenario with the prospects being both delayed and risky. Stevenson hypothesized that delay might be less aversive in delayed lotteries than in Institute of Cognitive and Behavioral Neuroscience, SWPS University of Social Sciences and Humanities, Warsaw, 03-815, Poland. Correspondence and requests for materials should be addressed to W.B. (email: wbialaszek@swps. edu.pl) Scientific Reports | (2019) 9:8738 | https://doi.org/10.1038/s41598-019-45376-9 1 www.nature.com/scientificreports/ www.nature.com/scientificreports Figure 1. Theoretical model for delayed and risky outcome subjective value elicitation paths. Diagram representing each outcome value elicitation path that was translated into the experimental design. The initial undiscounted value of an outcome (A) can be first discounted by its delay and then by the probability of its receipt (expressed as odds against), yielding svdθ(A). This delay-probability elicitation path is depicted in green. In the probability-delay path (red), outcome A is first discounted by the probability of its receipt and then by its delay. In the direct path (black), the subjective value of an outcome A is discounted simultaneously by the delay and probability and yields svdir(A). standalone delayed, but certain payoffs, and that an addition of a lottery component distracts individuals from the delay in the outcome receipt. It is possible, that when delayed, not only the outcome but also risk is discounted8. Correspondingly, the findings that risk tolerance increases with the delay in the resolution of that risk seem quite robust, and manifest themselves in different response collection strategies, such as rating scales9 or commonly used risk assessment tasks10,11. The abovementioned studies suggest that svdir(A) should be greater than the subjective values obtained in the two indirect paths. To the best of our knowledge, only two previous studies have directly investigated path dependency in human decision making. The first study investigated whether the probability-delay path and a direct method of evaluating delayed lotteries yield equal results3. Using a matching task (in which participants directly provide a subjective value), the authors reported that the subjective values in the direct evaluation of delayed lotteries were higher than those obtained in the indirect probability-delay path. The effect generally held in both domains, but was more pronounced in the loss condition. In other words, the individuals in the matching procedure treated outcome probabilities as though they were larger than in scenarios in which the probabilities were resolved immediately. The second study was performed by Öncüler & Onay4, who employed a matching procedure to investigate path dependency in the domain of hypothetical monetary gains. They found that the subjective values were higher in the (...truncated)