Abstract Humans demonstrate an inherent bias towards making maladaptive decisions, as shown by a phenomenon known as the gambler’s fallacy (GF). The GF has been traditionally considered as a heuristic bias supported by the fast and automatic intuition system, which can be overcome by the reasoning system. The present study examined an intriguing hypothesis, based on emerging evidence from neuroscience research, that the GF might be attributed to a weak affective but strong cognitive decision making mechanism. With data from a large sample of college students, we found that individuals’ use of the GF strategy was positively correlated with their general intelligence and executive function, such as working memory and conflict resolution, but negatively correlated with their affective decision making capacities, as measured by the Iowa Gambling Task. Our result provides a novel insight into the mechanisms underlying the GF, which highlights the significant role of affective mechanisms in adaptive decision-making.

Citation: Xue G, He Q, Lei X, Chen C, Liu Y, Chen C, et al. (2012) The Gambler’s Fallacy Is Associated with Weak Affective Decision Making but Strong Cognitive Ability. PLoS ONE 7(10): e47019. https://doi.org/10.1371/journal.pone.0047019 Editor: Thomas Boraud, Centre national de la recherche scientifique, France Received: April 19, 2012; Accepted: September 7, 2012; Published: October 5, 2012 Copyright: © Xue et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This research was supported by the following grants from the National Science Foundation of China (31130025), the 1000 Young Talents Program, the Advancing Scholarship in the Humanities and Social Sciences, the 111 project (B07008) and NIMH (PO1 NS19632). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist.

Introduction Humans often make non-optimal decisions involving random events. One such example is the gambler’s fallacy (GF), which is the belief that the occurrence of a certain random event is less likely after a series of the same event. The GF has been found to bias individuals’ judgments and decisions in many situations, such as gambling [1], lottery play [2], stock investment [3], and many laboratory tasks [4]. One typical pattern of the decisions guided by the GF is that people are more likely to predict the break of a streak when the streak gets longer. The GF has been traditionally considered as a heuristic bias characterized by the law of small numbers [5], [6], that is, a segment of a random sequence should reflect the overall distribution. Although the heuristic bias hypothesis suggests that the GF is supported by a fast, emotional and intuitive system, and that it can be overcome by deliberative reasoning [7], [8], emerging evidence, mainly from neuroscience studies, implicates that the GF might result from imbalanced cognitive and emotional decision making mechanisms [4], [9]. In particular, we have formulated the hypothesis that the GF is associated with (1) weak function in the affective decision making system, and (2) strong function in the cognitive system supported by the lateral prefrontal cortex (LPFC) [10]. Abundant evidence from animal research, lesion patient studies and functional imaging studies have emphasized the role of the LPFC in general intelligence and top-down executive controls [11], [12], [13], [14], [15], [16]. In terms of decision making, the LPFC plays an important role in detecting and constructing patterns [17] and updating decision-making strategy according to context [18], which are two component processes required to implement the GF strategy. The GF-like decision (e.g., more risk-taking behavior after losses than after wins) was correlated with left prefrontal cortex activity [10]. A recent study used a combination of functional magnetic resonance imaging (fMRI) and transcranial direct current stimulation (tDCS) technologies in an attempt to establish a causal relationship between activities in the prefrontal cortex and the use of the GF strategy [4]. The results suggest that brain responses in the left lateral prefrontal cortex (LPFC) to the current outcome preceded the use of the GF strategy that followed 10 seconds later. Furthermore, anodal tDCS over the left LPFC, which enhanced the LPFC function, increased the use of the GF strategy. On the other hand, the GF could be further increased by a weak affective decision making mechanism. Patients with impaired affective decision making due to lesions in the mesial OFC/ventromedial prefrontal cortex and the amygdala exhibited behavioral patterns that assemble the GF [9], [19]. For example, in the Iowa gambling task (IGT) that simulates daily-life decision-making [9], healthy participants gradually shift to advantageous decks by (implicitly) developing predictive somatic responses to disadvantageous decks, whereas patients with focal brain damages in the ventromedial PFC keep choosing the disadvantageous decks after severe losses [9], [20]. The patients showed normal switching to other decks after receiving a large loss, but just returned to bad deck (e.g., Deck B) more quickly than the healthy controls. When the patients were confronted with the question: ‘‘Why are you selecting the decks that you have just told me were bad decks?’’ the most frequent answer has been ‘‘I thought that my luck is going to change’’ (unpublished clinical observations). Similarly, in an investment game [19], the VMPFC and amygdala patients with impaired affective decision making (as measured by the IGT) continued to invest after several losses, providing preliminary evidence for the association between VMPFC function, affective decision making and the GF. For healthy subjects, the VMPFC also showed reduced activity to gains than to losses under long streaks [4], which presumably also facilitated the implementation of the GF strategy under long streaks. With behavioral data from a large sample of 438 college students, the present study aimed at examining both hypotheses on the same subject population using an individual differences approach. We predicted that subjects with strong cognitive ability, as reflected by higher general intelligence and executive function, such as working memory and conflict resolution, would show more GF. In contrast, subjects with stronger affective decision-making capacity, as measured by the IGT, would show less GF.

Results Table 1 showed descriptive statistics (N, mean, SD and Range) for the main measures. Note that due to technical errors, not all subjects had data for all the tasks. Focusing on the GF task, we found that, under short streaks (i.e., 1–3), subjects mainly used the WSLS strategy, but they shifted to the GF strategy starting with a streak length of 4 (Figure 1A), consistent with many previous observations [3], [4], [28]. We thus calculated the GF strategy rate only under the long streaks (> = 4) and use it as a measure of individuals’ GF strategy tendency. The averaged GF rate under long streaks for our highly educated and intelligent (average IQ, 124±9 as measured by both RAMP and WAIS) college students is 58.40%, which is significantly higher than 50% (p<.001). More importantly, we found that the range of GF rate varied from 0% to 100%, suggesting significant individual differences (Figure 1B). As shown in Table 2, the different measures of cognitive ability were correlated with each other, but not with the measures of affective decision making. Exploratory factor analysis was then performed on these measures. Kaiser-Meyer-Olkin (KMO) test measure of sampling adequacy (KMO = .54) and Bartlett’s test of sphericity (χ2(21) = 212.76, p<.001) suggested our data was suitable for factor analysis. Principle component analysis (PCA) extracted two components with factor eigenvalue greater than 1, which in total explained 45.54% of the variance. Varimax with Kaiser Normalization was used to rotate the loading matrix. As shown in Table 3, the RAPM, WAIS-RC, WMT and Stroop tests primarily loaded on the first factor, which was named the cognitive ability; in contrast, the two IGT scores primarily loaded on the second factor, which was named the affective decision making ability. Next we examined the core hypothesis of this study by correlating individuals’ GF strategy use with their cognitive and affective decision making capacities. Consistent with our hypothesis, we found that subjects’ GF strategy use was positively correlated with the cognitive ability (r = .170, p<.001), suggesting that higher intelligence and higher executive function was associated more GF strategy use. In contrast, we found that the use of GF strategy was negatively correlated with affective decision making ability (r = −.109, p<.033), suggesting that subjects with higher affective decision-making ability showed lower GF rate in the task. PPT PowerPoint slide

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larger image TIFF original image Download: Figure 2. A proposed three-component model for model-based decision making, including an abstract world-model, the LPFC cognitive system and the MPFC affective system. Depending on the situations and the subjective world model, the LPFC and the MPFC could both play constructive and/or destructive roles. https://doi.org/10.1371/journal.pone.0047019.g002

Discussion Many early behavioral studies have suggested that the gambler’s fallacy (GF) is determined by the wrong beliefs (or world models) that are probably formed through years of evolution in response to the real world. In addition to the law of small numbers [5], other beliefs regarding the randomness of underlying generating mechanism [28], [29], the “gestalt” of the events [30], the replenishment of natural reinforcers [31], could all affect the GF strategy. Computational models show that a rational mind guided by a false “world model” (i.e., outcome dependency) could well generate this type of suboptimal decisions, which can be changed by alternations of the “world model” [32]. Although many previous studies suggest higher cognitive skills are usually associated with more rational choices in accordance with economic decision theories, such as less temporal discounting [33], [34], [35], less loss aversion [33], [34], less framing effect and conjunction fallacy [36], and better performance in a sequential Prisoner’s Dilemma game [34], the present study suggested that people with higher cognitive abilities (intelligence and executive function) are more likely to engage the GF strategy. It should be emphasized that our subjects were chosen from a top-tier university in China, and they had an averaged intelligence of 124±9, as measured by both RAPM and WAIS. Yet they on average showed significant GF. More important, correlational analysis further suggested that the higher the cognitive ability they have, the more likely they engage the GF. There are two potential reasons for why this may occur. First, it is possible that the neural mechanisms of affective decision-making are weaker to begin with in those individuals. Another potential reason is that people with higher cognitive ability tend to exert stronger control over their affective/emotional systems thus rendering them inefficient in executing their functions. Unlike the other biases where heuristic response was associated with strong emotional responses, the implementation of the GF strategy requires great cognitive control [4]. In contrast to the win-stay-loss-shift strategy that is likely to be guided by a model-free reinforcement learning mechanism, the GF strategy represents a case in which subjects showed a win-shift-loss-stay pattern, as guided by a false “world model”. To implement this counterintuitive decision strategy thus requires subjects to hold the prepotent WSLS response and switch to the opposite response. Consistently, the GF is associated with strong LPFC activation [4], [10]. Also in accordance with this view, it has been found that subjects engaged more GF when the inter-trial interval was increased, thus allowing more time and cognitive resources to implement the strategy [37]. On the other hand, a strong affective decision making mechanism could help create an affective label to a disadvantageous choice, e.g., the recently unrewarded color, and thus counteract this fallacy. This signal is particularly important to alarm the negative future consequences of a particular choice, and thus prevent subjects from further gambling after a series of losses. The importance of this alarm signal has been studied under the somatic marker framework, and patients who lose the capacity to trigger this signal (somatic marker) from prior reward/punishment begin to make maladaptive choices, despite maintaining a high level of intellect [38]. Consistent with many previous studies, the present large-sample study suggested that the IGT captures performance that is separated from the cognitive abilities, such as general intelligence, executive control and response inhibition. Our factorial analysis results are in line with a recent meta-analysis of 43 studies aimed at examining the relationship between IGT performance and cognitive ability, which concluded that the majority of the existing studies found non-significant correlations, and the minority of studies that reported statistically significant effects only revealed small to modest effect sizes [39]. Lesion study further showed that patients with lesions in the VMPFC were impaired on the IGT, but not on the working memory tasks. In contrast, patients with DLPFC lesions were impaired on the working memory tasks but not on the IGT [40]. Using cognitive and decision making tasks that tap into the functions of the lateral and medial PFC, our results suggest a differential role of the lateral and medial PFC in maladaptive decision making such as the GF. Future studies should examine whether the personality variables may also contribute to the GF, such as the rationality measured by the framing biases, the self-control, and the risk-taking attitude, which have been also associated with functions in the medial and lateral PFC. For example, the framing effect has been associated with activation in the VMPFC [41], the risk-taking is associated with activation in both the ventral and dorsal MPFC [42], and the self-control has been related to functions in the lateral prefrontal cortex [43]. Moreover, future studies should examine the relationship between the GF, and the anatomical, functional and genetic variances across individuals, which would provide further evidence for the genetic and neural mechanisms of the GF. Taken together, emerging evidence has converged to suggest that the GF is contributed by three factors: (1) a false world model, (2) strong cognitive mechanisms, and (3) poor affective decision making mechanisms. The same three-component model can be applied to other types of belief-based or model-based decision-making (Figure 2). For example, when guided by a real world model that “vegetable is good for health”, a strong cognitive mechanism implemented by the lateral prefrontal cortex can exert self-control to modulate the affective decision mechanism and help to overcome the tendency for fat and sweet food [43]. The same lateral prefrontal cortex system, when being ‘hijacked’ by a false world model, like the GF, can also contribute to maladaptive decisions, whereas the affective decision making mechanism that help to differentiate good from bad choices. These results provide a novel insight into the mechanisms underlying adaptive and maladaptive decisions.

Author Contributions Conceived and designed the experiments: GX Chuansheng Chen QD. Performed the experiments: QH XL Chunhui Chen YL. Analyzed the data: GX QH. Wrote the paper: GX Chuansheng Chen ZL AB.