Psychol Rec (2014) 64:433–440 DOI 10.1007/s40732-014-0052-9
ORIGINAL ARTICLE
Magnitude Effects in Delay and Probability Discounting When Monetary and Medical Treatment Outcomes Are Discounted Jeffrey N. Weatherly & Heather K. Terrell
Published online: 8 May 2014 # Association of Behavior Analysis International 2014
Abstract Delay and probability discounting occur when the subjective value of an outcome decreases because it is delayed or uncertain, respectively. Research using monetary outcomes has shown that both types of discounting are influenced by the magnitude of the outcome, but in the opposite direction. In Experiment 1, university participants completed a delaydiscounting task involving hypothetical monetary ($100 or $100,000) or medical treatment (acne or brain cancer) outcomes. In Experiment 2, university participants completed a probability-discounting task involving those same outcomes. Results from Experiment 1 replicated previous research in that participants discounted the “smaller” outcomes ($100 & acne treatment) more than the “larger” ones ($100,000 & braincancer treatment). Results from Experiment 2 demonstrated that this magnitude effect reversed for probability discounting of the monetary outcomes, with $100,000 discounted more than $100. However, acne treatment was discounted more than brain-cancer treatment. This study represents the novel finding that the magnitude effect for medical outcomes may not reverse between delay and probability discounting as it does for monetary outcomes. The results suggest that delay and probability discounting are at least partially independent. Keywords Delay discounting . Probability discounting . Money . Medical treatment . University students Discounting is the process whereby the subjective value of an outcome is reduced because the receipt of the outcome is either delayed or uncertain (see Madden and Bickel 2010). In the former case, the process is labeled delay discounting. In
J. N. Weatherly (*) : H. K. Terrell University of North Dakota, Corwin-Larimore Hall 319 Harvard St., PO Box 8380, Grand Forks, ND, USA e-mail:
[email protected]
the latter case, it is labeled probability discounting. For instance, a person who is owed $1,000 but must wait 3 years to obtain it might be willing to take a lesser amount to obtain the money immediately. Likewise, someone given the chance to win $1,000 at the probability of 0.5 might be willing to accept a lesser amount of money to guard against the chance of receiving nothing. How quickly the subjective value of the outcome decreases as it becomes increasingly delayed or uncertain determines that person’s “rate” of discounting. Researchers have been interested in rates of discounting for a number of reasons. Rates of discounting are informative about a number a choices people face (e.g., consumer behavior; e.g., Foxall et al. 2011). They have also been associated with a several behavioral disorders (e.g., pathological gambling; Dixon et al. 2003; Petry and Madden 2010), either as helping produce the disorders or maintaining them (e.g., Weatherly and Dixon 2007). These rates also represent behavioral measures of certain personal characteristics. Rates of delay discounting, for example, have been used as a behavioral measure of self-control (preferring a larger-later outcome over a smaller-sooner one) versus impulsivity (preferring a smaller-sooner outcome over a larger-later one). Rates of probability discounting, on the other hand, have been used as a behavioral measure of risk aversion (preferring a smallermore certain outcome over a larger-less certain one) versus risk seeking (preferring a larger-less certain outcome over a smaller-more certain one; see Madden and Bickel 2010, for a review of discounting). Despite being referred to by different labels, there has been some debate as to whether delay and probability discounting might be one in the same, or at least similar to one another. For instance, if an outcome is delayed, it might be devalued because the likelihood of actually receiving it decreases (e.g., one could perish before the end of the delay; see Green and Myerson 1996). Then again, the value of an uncertain outcome might be devalued because one may have to try
434
multiple times to obtain it, which would incur a delay (see Rachlin et al. 1986). Consistent with these ideas, there are a number of similarities between delay and probability discounting. One example is that the data from the two types of discounting can be described by the same mathematical model (see Madden and Bickel 2010). Another example is that researchers have reported being able to determine the point at which a probabilistic outcome is equivalent to a delayed outcome (or vice versa; Rachlin et al. 1991). However, there are also differences between delay and probability discounting. Researchers have suggested that they invoke different neural substrates (e.g., Mobini et al. 2000). Others have suggested that the different types of discounting may be differentially associated with certain behavioral disorders (e.g., Andrade and Petry 2012). Research has also indicated that uncertainty alters rates of delay discounting but delays do not alter, or have less influence, on rates of probability discounting (Weatherly et al. 2014). Lastly, research has shown that manipulating the same variables produces different changes in the two types of discounting (e.g., Estle et al. 2006). One of these differences is the manipulation of the magnitude of the outcome being discounted. Such a manipulation produces what is known as the magnitude effect, which is one of the more robust findings in the study of discounting (e.g., Chapman 1996; Thaler 1981). As the magnitude of the outcome increases in a delay-discounting paradigm, rates of discounting decrease. For instance, someone owed $1,000 who has to wait 3 years to obtain it might be willing to take $750 today rather than waiting. The same person, however, would be less likely to accept $75,000 rather than waiting 3 years to obtain $100,000. Conversely, as the magnitude of the outcome increases in a probability-discounting paradigm, rates of discounting typically increase. For instance, someone with a 50 % chance to win $1,000 may be reluctant to take less than $500, preferring the chance of winning the larger amount. On the other hand, the same person may be willing to accept less than $50,000 rather than taking a 50 % chance on winning $100,000, losing, and ending up with nothing. Although magnitude effects appear to manifest differently in delay and probability discounting, one could argue that their different manifestations occur because of a theoretical similarity. As the magnitude of the outcome increases, individuals tend to display more self-control (i.e., the propensity to wait for the larger-later outcome). Also, as the magnitude of the outcome increases, individuals tend to display more risk aversion (i.e., the propensity to choose the smaller-more certain outcome). In both cases, one might describe both decisions in terms of becoming more conservative. It is not clear, however, that this explanation is consistent with existing empirical data. Weatherly et al. (2011) had participants discount the delayed hypothetical outcomes of
Psychol Rec (2014) 64:433–440
receiving $1,000 or $100,000. As one would expect, participants tended to discount $1,000 to a greater extent than they did $100,000. Participants also discounted the delayed hypothetical outcome of receiving medical treatment for a serious medical condition. Participants discounted this outcome less than either monetary amount. In terms of the above explanation, this result might suggest that people are more conservative when making decisions about their own health than they are when making decisions about money. Weatherly and Derenne (2013a, b) also had participants discount the hypothetical outcomes of receiving $1,000 or $100,000, but this time using a probability-discounting procedure. As one would expect, participants tended to discount $100,000 more than $1,000. Participants also discounted the probabilistic hypothetical outcome of receiving medical treatment for a serious medical condition. If individuals’ decisions become more conservative as the magnitude of the outcome increases, and medical treatment is of greater magnitude than money, then one would expect more probability discounting of the medical treatment than either of the monetary outcomes. However, participants discounted medical treatment less, not more, than both monetary outcomes. Thus, across the two studies, participants showed the tendency to wait to receive medical treatment relative to monetary outcomes, but also tended to be more risk-seeking about receiving medical treatment relative to monetary outcomes. This latter finding would appear inconsistent with the idea that decision making becomes more conservative as the magnitude of the outcome increases. One potential explanation for these results is that, for some outcomes such as money, magnitude effects are reversed for delay and probability discounting, but for other outcomes such as receiving medical treatment, they are not. This possibility cannot be fully interpreted from the results of Weatherly et al. (2011) and Weatherly and Derenne (2013a, b) because both studies investigated only one level of medical outcome (i.e., they did not manipulate the magnitude of the medical problem). Previous research on delay discounting (Chapman 1996; Chapman and Elstein 1995) has demonstrated that magnitude effects can be observed for health-related outcomes and the direction of those effects are similar to that of monetary outcomes, but it is not yet known whether magnitude effects for medical treatment would reverse as they do for monetary outcomes when tested in a probability-discounting procedure. Making this determination is important for several reasons. For one, it would help to elucidate further the relationship between delay and probability discounting. Secondly, it would be informative to know how decision making occurs as a function of specific types of outcome (e.g., money vs. medical treatment). The present study was designed with three goals in mind. The first goal was to replicate prior research and demonstrate that magnitude effects could be observed when participants
Psychol Rec (2014) 64:433–440
discounted treatments for different medical conditions in a delay-discounting procedure. The second goal was to determine whether magnitude effects would be observed for medical treatments in a probability-discounting procedure. If the second goal was met, the third goal was to determine whether that magnitude effect would reverse between delay and probability discounting as is typically observed for monetary outcomes.
Experiment 1 Participants were recruited to complete a delay-discounting task involving four different hypothetical outcomes. Two of the outcomes were monetary amounts ($100 or $100,000). The remaining two outcomes were receiving treatment for two medical ailments (acne or brain cancer). Given previous research (Chapman 1996; Chapman and Elstein 1995; Estle et al. 2006), we predicted that participants would discount $100 more than $100,000 and acne treatment more than treatment for brain cancer.
Method Participants The original sample of participants consisted of 166 students enrolled in an undergraduate psychology class at the University of North Dakota. After employing an exclusionary criterion (explained below), the final sample consisted of 82 (56 women; 26 men) participants. The mean age of the participants was 20.0 years (SD =2.9 years) and their selfreported grade point average was 3.3 out of 4.0 (SD=0.5). The vast majority of the participants were Caucasian (78; 95.1 %). Thirty-three participants (40.2 %) reported that they had been treated for acne. One participant (1.2 %) reported that s/he had been treated for cancer. Participants received (extra) course credit in their psychology class as compensation for their participation.
435
The second item shown to all participants was a brief demographic questionnaire. The questionnaire asked about the information presented in the participant’s section. The final item shown to all participants was a delaydiscounting task that involved four separate outcomes. Two of the outcomes were monetary (i.e., $100 or $100,000). The question about the monetary outcomes was: If you won $100 ($100,000) and were not going to get the money for Y time, what is the smallest amount of money you would accept today rather than having to wait Y time? The remaining two outcomes pertained to receiving treatment for a medical condition (i.e., acne or brain cancer). The question about the medical treatment outcomes was: Suppose you were suffering from acne (brain cancer). Your physician informs you that you will need to wait Y time before obtaining a treatment that is 100 % effective. However, you could immediately begin a treatment that has a lesser chance of success. What percent chance of success would you be willing to accept for the different treatment in order to choose it rather than waiting Y time? Each discounting question was asked a total of five times, with the delay to receiving the full outcome varying across questions. The delays were 6 months, 1 year, 3 years, 5 years, and 10 years. Participants answered each question using a variation of the multiple-choice method (Beck and Triplett 2009). That is, participants chose the answer to each question from a series of 51 possible response options that ranged from 0 – 100 % of the full outcome in 2 % increments (e.g., $2 or $2,000). This method of collecting delay-discounting data has been shown to produce interpretable results (Weatherly and Derenne 2011) that are temporally reliable (Beck and Triplett 2009). Thus, participants answered 20 discounting questions (i.e., four outcomes X five delays). Participants answered all five questions about one particular outcome before answering questions about the next outcome. The order of outcomes varied randomly across participants. Likewise, the order of the delays varied randomly across outcomes and participants.
Materials and Procedure Data Analysis Participants completed the experiment online via a datamanagement system (SONA Systems, Ltd; Version 2.72; Tallinn, Estonia) and all materials were completed electronically. This system tracked participation on an individual basis, ensuring that no individual could participate more than once. The first item shown to all participants was the description of the study as approved by the Institutional Review Board at the University of North Dakota. The participant’s continued participation beyond this information was considered the granting of informed consent.
The discounting data were first screened to ensure that only data from participants who displayed systematic discounting were included in the analysis. The exclusionary criterion was a simplified version of that proposed by Johnson and Bickel (2008). Specifically, participants’ data were excluded if the indifference point (i.e., the subjective value of the delayed outcome) at the longest delay (i.e., 10 years) was greater than it was at the shortest delay (i.e., 6 months) for any of the four outcomes tested. In other words, if the subjective value of the
436
Psychol Rec (2014) 64:433–440
i¼1
With Eq. 1, y represents the participant’s response at a particular delay and x is the delay to the full outcome (calculated in months). The AUC is then calculated by summing the areas of the successive trapezoids created across the different delays and then converting the result into a proportion. Large AUC values represent little to no discounting, whereas small AUC values represent steep discounting. Equation 1 was chosen over other potential analysis methods because it does not presuppose the form that the discounting data should take. This point is important because if one assumes a presupposed form (e.g., a hyperbola) and the data do not follow that form, then one’s dependent measure of discounting is not accurately representing the data.2 Next, it standardizes discounting rates across different outcomes because it is a proportion, and it typically generates parametric 1
The number of participants excluded for each outcome is not reported because that number would vary depending on the order that the different outcomes were analyzed. For example, a participant who did not systematically discount any outcome would have his/her data excluded when the criterion was applied the first time. Thus, which outcome that was responsible for excluding that participant’s data would depend on which of the four outcomes was analyzed first. 2 The data were also fit to a hyperbolic equation (Mazur 1987), but the resulting fit was typically not good (i.e., R2
