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This article was submitted to Quantitative Psychology and Measurement, a section of the journal Frontiers in Psychology.

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Impulsivity has been defined as choosing the smaller more immediate reward over a larger more delayed reward. The purpose of this research was to gain a deeper understanding of the mental processes involved in the decision making. We examined participants’ rates of delay discounting and probability discounting to determine their correlation with time-probability trade-offs. To establish the time-probability trade-off rate, participants adjusted a risky, immediate payoff to a delayed, certain payoff. In effect, this yielded a probability equivalent of waiting time. We found a strong, positive correlation between delay discount rates and the time-probability trade-offs. This means that impulsive people have a compulsion for immediate gratification, independent of whether the immediate reward is certain or uncertain. Thus, they seem not to be concerned with risk but rather with time.

Perhaps the two most fundamental principles in financial decision making are the time value of money and the trade-off between risk and return. It is not so surprising, then, that in the laboratory, numerous experiments have attempted to measure how people make the trade-offs between reward now and reward later and trade-offs between reward that will definitely be received and reward that might or might not happen (for a review see:

When offered a choice between two payoffs, people usually prefer a larger payoff to a smaller one, an earlier payoff to a later one, and a certain payoff to an uncertain one. In combination, those who prefer a smaller, earlier payoff to a larger, later one are said to be more impulsive (

Is impulsivity independent of individual’s risk aversion, that is, is it purely a consequence of her desire for immediate gratification? Or is impulsivity at least somewhat correlating with risk aversion. Thus far, empirical tests have not been conclusive, with researchers finding no correlation or weakly positive correlation between impulsivity and risk aversion (

Do people choose smaller, immediate reward because they are just reluctant to wait, compelled to get a reward instantly (even in a form of a lottery)? In other words: what is the nature of impulsivity. Very little research has examined the mental trade-off between the delay of a certain payoff and the probability of an uncertain, immediate one.

We examined the correlations between the time-probability trade-off [

Two hundred and seventeen participants (91 males and 126 females), ranging in age from 19 to 23 years and enrolled in obligatory lectures, were recruited for the study. They were all students of the Warsaw University of Life Sciences. All participants signed informed consent forms, and the procedures were approved by the local ethics committee (Kozminski University).

Of 217 individuals who participated, data for 12 were not considered due to non-systematic discounting. Discounting data were considered systematic and used if: (a) the participant had a higher initial indifference point (example 95% chance of obtaining PLN 200 or obtaining PLN 200 in 6 months) than the final indifference point (a 5% probability or a 5 years delay). (This criterion assumes delay decreases the value of a reward); (b) the participant’s indifference points did not increase across consecutive delays (or probabilities) by more than 20% of the larger later or larger more probable reward. (Substantial increases in the value of a reward across delays or probabilities suggests that the value of a reward is enhanced with increased delay or risk); (c) in both conditions—the probability and delay discounting components of the procedure—the data met criterion (a) and (b). These criteria are based on the expectation of a monotonically decreasing discounting function and are similar to the algorithm used by

As the measures of the rates of delay and probability discounting and the measure of the time-probability trade-off, we used simple arithmetic means computed from all indifference points in each condition. These measures are very similar to those of the area under the curve (AUC,

There were four analogous, independent between-group conditions in this study. Each participant was randomly assigned to one of the four of them, either a gain or a loss of PLN 200 (respectively,

Participants made choices between two alternatives presented to them on their computer screens by clicking on their preferences. Each participant went through three parts of the experimental procedure addressing: (1) the time-probability trade-off

For every condition, the algorithm of the procedure was based on the same adjusting gain or loss algorithm, adapted from the procedure by

For example, to measure

With the two other conditions,

We conducted analyses in two steps. In the first step, we analyzed correlations among the time-probability trade-off, delay discounting, and probability discounting. In the second step, we used two factor ANOVA analysis to investigate whether factors (amount and sign) affected the height of indifference points. All pairwise, multiple comparisons used Sidak’s correction.

The results of the correlation analyses showed that there is a strong relationship between

PLN 200 | PLN 5000 | ||||
---|---|---|---|---|---|

Gains | 0.578* | 0.077 | 0.694* | 0.146 | |

1 | 0.464* | 1 | 0.241 | ||

Losses | 0.544* | 0.199 | 0.681* | 0.146 | |

1 | 0.435** | 1 | 0.168 |

Figure

One factor was amount (PLN 200 and PLN 5000) and the other was sign (gain or loss). In the ^{2} = 0.096] and of sign [^{2} = 0.027]. The interaction effect was also significant [^{2} = 0.054]. For interaction there were significant differences between the two amounts for gains, but not for losses (respectively,

For delay discounting, there was a significant main effect of sign [^{2} = 0.026] and of amount [^{2} = 0.078]. The interaction effect was also significant [^{2} = 0.053]. Delay discount rates displayed he same relations as for

Probability discount rates showed significant effects for sign [^{2} = 0.033] but not for amount [^{2} = 0.016]. There was no significant interaction between the two factors [^{2} = 0.019]. For probability discount rates, losses were discounted less steeply than gains. Although neither the main effect, nor interaction reach the statistical significance criterion, the result can be classified as statistical tendency. The descriptive statistics for f(p) conditions are presented on Figure

The above analyses show a magnitude effect for

The primary goal of the research was to examine the nature of impulsivity. If one considers the familiar connotations of the label, one might expect impulsive individuals to not only be unable to postpone reward, but also to be risk takers. This would imply a negative correlation between probability and delay discounting, i.e., participants would choose smaller sooner reward instead of larger delayed one and riskier, larger option instead of smaller, but certain. However, prior research (

The experimental design enabled us to study delay discounting and the time-probability trade-off, taking into accounting both the amount effect and the sign effect. For all amounts and signs, the time-probability trade-off rate was significantly positively correlated with the delay discounting rate. Therefore, when confronted with an uncertain outcome now and a certain outcome in the future, people tend to assess the situation as if they were simply confronting a small amount now versus a larger amount in the future, regardless of amounts and signs. Impulsive people prefer smaller, immediate reward over larger, delayed ones because they have a need for immediate, even uncertain, gratification. A revealed time-probability trade-off rate shows how much risk an individual is willing to bear in order to receive a reward immediately rather than waiting. Here, the main result of our research is a confirmation of the research hypothesis, finding a strong positive correlation between the delay discounting rate and the time-probability trade-off. This means that impulsive people choose smaller, immediate reward over larger, delayed ones because they are motivated by a desire for instant gratification, even if that means bearing the uncertainty of a lottery. The risk inherent in delay may not be a factor in their decisions. People with self-control having the ability to wait will choose larger, later reward. Moreover, the time-probability trade-off is uncorrelated with the probability discounting. This means that the question “How much is one able to risk in order not to wait?” has nothing common with the question “How much is one able to risk?” The classical risk attitude describes human preferences when all options are available in the present without the component of delay. It seems that when one of the outcomes is immediate, an individual tends to act not according to her risk attitude but according to her time-probability trade-off rate. The time-probability tradeoff measures the conversion of delay into risk, since one of the outcomes is certain and delayed and the other is immediate and uncertain.

There are other findings which go beyond previous research. For the time-probability trade-off, our results showed a sign effect for small amounts (losses have larger subjective value than gains) and an amount effect for gains (bigger payoffs have larger subjective values than smaller ones).

There are other findings which confirm previous research. These include: (1) The sign effect for delay discounting for small amounts (

The present research was done on hypothetical, not real reward. It has been shown that the discounting process is comparable across real and hypothetical payments (

Overall, the results suggest that when one of the outcomes is immediate, an individual tends to act not according to her risk attitude, which matters for instant outcomes but according to her time-probability trade-off rate. A strong positive correlation between the time-probability trade-off and the delay discounting rate indicates that impulsive people choose smaller, immediate reward over larger, delayed ones because they may be mainly motivated by a desire for instant gratification, even if that means bearing the uncertainty of a lottery.

All authors contributed to the presented work. Each of the authors took part in drafting or revising it critically for important intellectual content and approved the final version to be published. Also all authors ensured that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. Especially: WB, PZ: substantial contribution to the conception and design of the work, acquisition, analysis, interpretation of data for the work; MG: acquisition of the data; EMG: interpretation of data.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

This research is supported by: the Polish National Science Centre research grant DEC-2012/04/A/HS6/00614; subsidies from University of Social Sciences and Humanities and grant WP/2014/B/42.