Edited by: Björn Brembs, Freie Universität Berlin, Germany
Reviewed by: Bruno B. Averbeck, National Insitute of Mental Health, USA; Anna Van Duijvenvoorde, University of Amsterdam, Netherlands; Simon Dymond, Swansea University, UK
*Correspondence: Annette Horstmann, Department of Neurology, Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstraße 1A, D-04103 Leipzig, Germany. e-mail:
This article was submitted to Frontiers in Decision Neuroscience, a specialty of Frontiers in Neuroscience.
This is an open-access article distributed under the terms of the
The Iowa Gambling Task (IGT) has been widely used to assess differences in decision-making under uncertainty. Recently, several studies have shown that healthy subjects do not meet the basic predictions of the task (i.e., prefer options with positive long-term outcome), hence questioning its basic assumptions. Since choice options are characterized by gain and net loss frequency in addition to long-term outcome, we hypothesized that a combination of features rather than a single feature would influence participants’ choices. Offering an alternative way of modeling IGT data, we propose to use a system of linear equations to estimate weights that quantify the influence of each individual feature on decision-making in the IGT. With our proposed model it is possible to disentangle and quantify the impact of each of these features. Results from 119 healthy young subjects suggest that choice behavior is predominantly influenced by gain and loss frequency. Subjects preferred choices associated with high-frequency gains to those with low-frequency gains, regardless of long-term outcome. However, among options with low-frequency gains, subjects learned to distinguish between choices that led to advantageous and disadvantageous long-term consequences. This is reflected in the relationship between the weights for gain frequency (highest), loss frequency (intermediate), and long-term outcome (lowest). Further, cluster analysis of estimated feature weights revealed sub-groups of participants with distinct weight patterns and associated advantageous decision behavior. However, subjects in general do not learn to solely base their preference for particular decks on expected long-term outcome. Consequently, long-term outcome alone is not able to drive choice behavior on the IGT. In sum, our model facilitates a more focused conclusion about the factors guiding decision-making in the IGT. In addition, differences between clinical groups can be assessed for each factor individually.
The Iowa Gambling Task (IGT, Bechara et al.,
Substantial critique has been raised regarding the general assumptions on IGT performance (Dunn et al.,
Possible reasons for the observed discrepancy between predicted and actual decisions on the IGT may be found in the particular payoff scheme of the task: in the original IGT, the four card decks are associated with the gain/loss structure presented in Table
Deck A | Deck B | Deck C | Deck D | |
---|---|---|---|---|
Gain | $100 | $100 | $50 | $50 |
Loss | $150–$350 | $1250 | $50 | $250 |
Gain/loss frequency (10 trials) | 5:5 | 9:1 | 5:5 | 9:1 |
Number of net losses (10 trials) | 5 | 1 | 0 | 1 |
Long-term outcome (10 trials) | −$250 | −$250 | $250 | $250 |
The four decks differ not only in long-term outcome, but also in two additional features: the relative number of gains vs. losses (subsequently termed “gain frequency”; high for decks B and D, low for decks A and C), and the relative number of
We hypothesized that participants’ choices in the IGT can only be explained by a
Iowa Gambling Task performance has previously been analyzed by way of different computational models such as the expectancy valence (EV) model (Busemeyer and Stout,
We applied our model to data from 119 healthy young subjects who performed 100 trials of the IGT, and assessed sensitivity of subjects’ choice behavior to expected long-term outcome, gain frequency and loss frequency. In order to examine the development of subjects’ model parameters over the course of learning, we applied the model independently to each of the five consecutive blocks á 20 trials. For a more detailed analysis, obtained model parameters were further subjected to clustering in order to investigate the homogeneity of subjects’ feature weightings and related response patterns.
The IGT requires participants to make a series of selections from four alternative card decks. The four decks (A, B, C, D) are associated with different financial rewards. For each selection from decks A and B participants win $100. For each selection from decks C and D participants win $50. In addition, each card deck is associated with occasional losses of different amounts and frequencies. For deck A and C, 5 in 10 choices are associated with an additional loss of $250 on average and $50, respectively. Note that deck C never conveys net losses while for deck A loss trials always lead to a net loss. For decks B and D, 1 in 10 choices is accompanied by a loss of $1250 and $250, respectively. Comparable to deck A, every loss trial for decks B and D leads to a net loss. This payoff scheme (see Table
One hundred nineteen healthy, non-smoking, right-handed subjects [66 female (mean age 25.2 years, SD 4.9 years) and 53 male (mean age 24.7 years, SD 3.1 years)] with comparable educational background (university-entrance diploma, German Abitur, or higher) performed a computerized version of the IGT comprising 100 trials. Deck position was fully randomized between participants and information that the task will last for 100 trials was provided in the instruction. Deck position was kept stable during the task for each participant to minimize non-task-related working memory load (see Pecchinenda et al.,
Task performance in the IGT can be modeled by a set of linear equations
Deck | Long-term outcome | Gain frequency | Loss frequency |
---|---|---|---|
A | 0.5 (−0.86) | 0.5 (−0.86) | 0.5 (−1.47) |
B | 0.5 (−0.86) | 0.9 (0.86) | 0.9 (0.34) |
C | 1 (0.86) | 0.5 (−0.86) | 1 (0.79) |
D | 1 (0.86) | 0.9 (0.86) | 0.9 (0.34) |
We did not incorporate a feature for immediate reward in our model. As already suggested by Dunn et al. (
Initial feature values were scaled to the effect that their sum across decks was equal for each feature. In addition, values were normalized by subtraction of the mean within each feature and division by the SD, resulting in unit variance. This ensures comparability of weights across features and decks. Hence, for each subject a linear relationship of three parameter values to four observations of choice behavior is described by
In order to investigate the homogeneity of subjects’ feature weighting at the beginning and end of the task, we applied hierarchical Two-Step clustering (Zhang et al.,
According to Bechara et al. (
A separate analysis of subjects’ choice behavior for all four decks revealed a clear preference for decks with frequent gains (decks B and D) over decks with infrequent gains (decks A and C) throughout the task (see Table
Deck | Block |
||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | |
A | 3.88 | 2.87 | 2.75 | 2.34 | 2.08 |
B | 6.76 | 7.45 | 6.68 | 6.18 | 6.52 |
C | 3.55 | 3.63 | 4.54 | 5.04 | 4.95 |
D | 5.82 | 6.05 | 6.03 | 6.44 | 6.45 |
To analyze which combination of the task’s features elicited this particular choice pattern, we applied the linear equation model to the number of cards drawn from each deck for each subject individually in blocks of 20 choices. The least-squares solution yields subjects’ individual weights for each feature (i.e., long-term outcome, gain frequency, and net loss frequency) of the IGT’s payoff scheme. Table
Deck | Long-term outcome ( |
Gain frequency ( |
Loss frequency ( |
Choices (%) |
---|---|---|---|---|
A | −0.86 | −0.86 | −1.47 | 0.15 |
B | −0.86 | 0.86 | 0.34 | 0.50 |
C | 0.86 | −0.86 | 0.79 | 0.10 |
D | 0.86 | 0.86 | 0.34 | 0.25 |
Table
Feature | Block |
||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | |
Long-term outcome | −0.029 (0.23) | 0.000 (0.23) | −0.029 (0.17) | 0.029 (0.23) | 0.000 (0.20) |
Gain frequency | 0.069 (0.13) | 0.087 (0.17) | 0.064 (0.17) | 0.075 (0.20) | 0.087 (0.18) |
Loss frequency | 0.000 (0.18) | 0.044 (0.18) | 0.044 (0.18) | 0.044 (0.22) | 0.044 (0.27) |
For gain frequency median weights are significantly above zero in all blocks (Wilcoxon signed rank, all
In relation to each other, weight for gain frequency has clearly the highest values at the beginning of the task and does not change significantly thereafter (see Figure
Taken together, this confirms our hypothesis that subjects do neither primarily nor exclusively focus on long-term outcome. Instead, subjects predominantly consider a combination of gain and loss frequency features. Note that we did not find an influence of participants’ gender or age on any of the dependent measures.
As evident from Table
The clustering procedure identified two clusters at the beginning (block one) and three clusters at the end (block five) of the experiment. The average silhouette measure of cohesion and separation was 0.6 for both.
In the first block of the task, the predictor importance was 1 for outcome, 0.93 for loss frequency, and 0.61 for gain frequency. About 78.2% of subjects belonged to cluster 1 (median weight for outcome −0.09, loss frequency 0.04, and gain frequency 0.04) and the remaining 21.8% belonged to cluster 2 (median weight for outcome 0.20, loss frequency −0.18, and gain frequency 0.20). The distribution of weights for both clusters and each feature can be seen in Figure
In the last block of the task, the predictor importance for cluster separation was 1 for gain frequency, 0.75 for loss frequency, and 0.53 for outcome. About 11.8% of subjects belonged to cluster 1 (median weight for outcome 0, loss frequency 0.44, and gain frequency −0.46), 75.6% of subjects belonged to cluster 2 (median weight for outcome 0.09, loss frequency 0.04, and gain frequency −0.06), and the remaining 12.6% to cluster 3 (median weight for outcome 0.38, loss frequency −0.31, and gain frequency 0.36). The distribution of weights for all clusters and each feature can be seen in Figure
Finally, we related cluster membership in the final block back to subjects’ choice behavior and the initially proposed difference score to measure task performance. In Figure
In the current study, healthy young adults were subjected to a learning task that requires the integration of frequency and magnitude information on both gains and losses, and the assessment of the long-term consequences of decisions (IGT). Offering an alternative way of modeling IGT data, we used a system of linear equations to estimate weights that quantify the influence of the following three features on decision-making in the IGT: (1) expected long-term outcome (i.e., the overall profitability of each deck; negative for decks A and B, positive for decks C and D), (2) gain frequency (i.e., how often is a card associated with a gain only; high for decks B and D, low for decks A and C), and (3)
Our results suggest that for normal subjects gain and loss frequency are the primary factors driving their decisions. We observed that subjects weighted both factors higher than long-term outcome. This clearly contrasts with the initial assumptions made by Bechara et al. (
The general preference for decks with low loss- and high gain frequency rather than for positive overall outcome is in disagreement with the task performance that was intended and observed by Bechara et al. (
Within the decks with high-frequency gains, we observed after an initial exploration phase a comparable choice pattern for decks B and D, but within the low-frequency gain decks a clear preference for deck C over deck A. This corroborates findings by Lin et al. (
The potential influence of features other than long-term outcome on task performance might remain undetected, if only difference scores between advantageous and disadvantageous decks are considered in the analysis of choice behavior. In the current study, we observed a slightly positive difference score when considering the entire group of subjects. MacPherson et al. (
Multi-dimensional clustering of parameter estimates from the linear equation model revealed sub-groups of participants with substantially different parameter patterns. Clustering revealed two groups at the beginning and three groups at the end of the experiment. In both cases the majority of subjects belonged to a cluster with no particular preference for one of the three features long-term outcome, gain frequency, or loss frequency. Only a minority of subjects developed relatively large weights for one or more of the features. However, contrary to Bechara’s initial assumptions, no group of subjects developed a high weight for long-term outcome exclusively.
Most interestingly, the profoundly different weight patterns in two groups of subjects were both associated with a high positive difference score: for subjects belonging to cluster 1 (high weight for loss frequency, low weight for gain frequency and a weight close to zero for outcome) and for subjects in cluster 3 (low weight for loss frequency, high weight for gain frequency and high weight for outcome). This is additional evidence for a more complex learning pattern involved in successful performance on the IGT than initially assumed. Interestingly, subjects in clusters with a high difference score did not learn to pick an equal amount of cards from deck C and D but preferred either deck C (cluster 1) or deck D (cluster 3). This indicates that gain and loss frequency, which determine the difference between decks C and D, are more salient features than long-term outcome. In addition, the majority of participants (members of cluster 3) seem not to pick up successful weighting of the three task features, i.e., a set of weights supporting a choice behavior that avoids disadvantageous decks A and B. One explanation for this behavior may be that for most subjects, the three features of the task are combined in a way that prohibits the evolution of a clear preference for one of them, i.e., if subjects start to prefer options associated with one feature they would have to decide actively against options associated with another feature they prefer. Another explanation would be that for most subjects, behavior is guided by something different than the extracted task features.
In sum, our results show that only a minority of subjects learned to restrict their choices to the advantageous decks C and D, whereby they generally developed a preference for only one of the two decks.
Note that Huizenga et al. (
Out of previously applied computational models, the EV model (Busemeyer and Stout,
The model assumes that subjects, after choosing a particular card, integrate the experienced gain or loss of that card into the so-called valence, modulated by a parameter reflecting the subject’s attention to gains and losses. Further, subjects learn expectancies about the valences by continuously sampling from the various decks and updating their expectancy according to the observed outcome with their individual learning rate. Finally, learned expectancies determine the subject’s choices, which are again modified by a parameter reflecting the subject’s response consistency or amount of exploration.
Although the EV model was shown to successfully map decision deficits in clinical populations to alterations in one or more of the assumed underlying psychological processes (Yechiam et al.,
Christakou et al. (
With our proposed model we provide a new tool to quantitatively analyze IGT performance. Unlike the EV and related models, we do not attempt to model specific cognitive processes underlying decision-making in the IGT. Rather with our model we are able to determine the behavioral relevance of different factors of the IGT payoff scheme influencing subjects’ decision-making. The model can be used and adapted to re-evaluate previously obtained behavioral data on the IGT. Thus, it might help to relate behavioral differences between clinical groups to differences in sensitivity to one or more of the features of the IGT.
The results of our study support the observation that, in contrast to the basic assumptions for the IGT, subjects in general do not learn to solely base their preference for particular card decks on the decks’ expected long-term outcome. Rather, choice options in the IGT are predominantly characterized by gain and loss frequency, and subjects’ choice behavior is influenced by a combination of these factors. If subjects regard long-term outcome as an important task feature, they additionally take into account gain and loss frequency. Consequently, long-term outcome alone is not able to drive choice behavior on the IGT. With our proposed linear equation model it is possible to disentangle and quantify the impact of each feature. Our modeling results point at gain and loss frequency as the primary factors guiding choice behavior in healthy young subjects. From our model, more focused conclusions about the factors guiding decision-making under uncertainty can be drawn. In addition, differences between clinical groups can be assessed for each factor individually.
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.
We thank Andreas Below, Karolin Gohlke, Jonas Klinkenberg, Katja Macher, and Ramona Menger for their invaluable help during data acquisition. We thank Christian Kalberlah and Stefan Kiebel for fruitful discussions on our model. We are also grateful to E.-J. Wagenmakers and Helen Steingröver for valuable discussions on the IGT and EV model. This work was supported by BMBF [Neurocircuits in obesity to Annette Horstmann, Arno Villringer; IFB Adiposity Diseases (FKZ: 01EO1001) to Annette Horstmann, Jane Neumann, Arno Villringer], the DFG (Mind and Brain), and the Einstein-Stiftung (Mind and Brain Institute).