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

Wojciech Białaszek,Przemysław Marcowski,Paweł Ostaszewski

doi:10.1007/s12144-018-0092-4

Wojciech Białaszek, Przemysław Marcowski + Show 1 more

Open Access

https://doi.org/10.1007/s12144-018-0092-4

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Abstract

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.

Highlights

One common method to investigate the role of risk in intertemporal decision making is by stating it explicitly—directly—in the choice situation (Cox and Dallery 2016; Vanderveldt et al 2015).in most situations, the risk involved in choice is not stated in such a manner
In the final step of the analysis, we investigated the form of the delay discounting, probability discounting and the subjective probability of obtaining delayed rewards, which consisted of comparing the model fits described by Eqs. 1, 2 and 3 to the indifference points obtained from delay discounting, probability discounting, and Subjective Probability Questionnaire (SPQ)
We found a magnitude effect present in delay discounting (F(1, 137) = 7.625; p = .007; η2 = .053), which means that large rewards (M (SD) = 0.432(0.253); 95% CI [0.369, 0.475]) were discounted at a slower rate than small rewards (M (SD) = 0.310(0.269); 95% CI [0.248, 0.371]) and a reverse magnitude effect in probability discounting (F(1, 137) = 29.696; p < .001; η2 = .178), which means that large gains (M (SD) = 0.130(0.126); 95% CI [0.089, 0.172]) were discounted at a higher rate than small payoffs (M (SD) = 0.289(0.206); 95% CI [0.249, 0.330])

Summary

Introduction

One common method to investigate the role of risk in intertemporal decision making is by stating it explicitly—directly—in the choice situation (Cox and Dallery 2016; Vanderveldt et al 2015).in most situations, the risk involved in choice is not stated in such a manner. One common method to investigate the role of risk in intertemporal decision making is by stating it explicitly—directly—in the choice situation (Cox and Dallery 2016; Vanderveldt et al 2015). These authors found that people spontaneously incorporate risk into delays. This concept was extended by Takahashi et al (2007) who measured perceived risk of future gains, and found that this risk increased with the delay. Their findings were in line with the theory developed by Sozou (1998), who stated that

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