Using the factorial structure of the task, we tested the impact of volatility on performance with a two-factor repeated measures ANOVA, where the two factors were information source (card versus advice) and phase (stable versus volatile). Across all behavioral metrics, we observed an effect of phase, indicating a reduction in performance in volatile compared to stable phases, and a phase × information interaction, indicating that the effect was larger for the social than the individual source of information. First, for the accuracy with which participants predicted lottery outcome, we found a main effect of phase (df = (1,36), F = 187.94, p = 7.7e-16) and an information source-by-phase interaction (df = (1,36), F = 11.13, p = 0.0020) (see Figure 1—figure supplement 1a). Thus, in-keeping with the rationale that arbitration relates to relative information quality, the degree to which participants relied on each information source was a function of precision as manipulated using the volatility structure of the task. Participants performed significantly better in stable compared to volatile periods of the task. These effects were not modulated by fatigue, as we found no significant differences between early and late phases of the task.

Second, advice-taking behavior differed as a function of volatility and information source: For the percentage of trials in which participants followed a given source of information, we detected a main effect of phase (df = (1,36), F = 56.26, p=7.3073e-09) and an information source-by-phase interaction (df = (1,36), F = 25.86, p=1.1561e-05) (Figure 1—figure supplement 1b). Thus, participants took advice less often particularly when it was volatile rather than stable.

Third, the amount of points wagered also depended on the task volatility and the information source. We observed a main effect of phase (df = (1,36), F = 28.78, p = 4.54e-06) and an information source-by-phase interaction (df = (1,36), F = 16.75, p = 2.21e-04; Figure 1—figure supplement 1c). Participants wagered fewer points particularly when advice was volatile. Moreover, the number of points wagered correlated significantly with the total score in stable phases (r = 0.37, $p$ = 0.02), but not in volatile phases (r = 0.30, $p$ = 0.06). Simulations using a two-level HGF (with low and fixed volatility) suggested that tracking volatility is beneficial for task performance: a hypothetical person who did not take the volatility of the task phases into account gained on average 21.6 points less than an agent tracking volatility. In line with previous evidence (Behrens et al., 2008), these results emphasize the impact of volatility on the willingness to invest and investment success as measured here by total score.

Participants were asked to rate the advisor (i.e. helpful, misleading, or neutral with regard to suggesting the correct outcome) in a multiple-choice question presented five times during the experiment. The time points were associated with different social and individual information (initial/prior: 1st trial; stable advice, stable card phase = (14th trial); stable advice, volatile card phase (49th trial); volatile advice, volatile card phase (73rd trial); volatile advice, stable card phase = 115th trial). On average, participants rated the advice as 75.0 ± 4.6% (mean ± standard deviation) helpful in the stable advice phase. The corresponding values were 50 ± 3.4% in the volatile advice phase, 63.8 ± 4.4% in the stable card phase, and 61.2 ± 3.8% in the volatile card phase.

We examined the extent to which participants’ ratings changed as a function of the task phases, and found a significant main effect of phase (df = (1,36), F = 15.67, p = 3.3e-04) and a significant information source × phase interaction (df = (1,36), F = 8.42, p = 0.0062). This suggests that advice ratings decreased during volatile compared to stable phases, and this effect was more strongly related to the advice compared to the card information.

After completing the task, participants filled out a task-specific debriefing questionnaire, assessing their perception of the advisor and how they integrated the social information during the task. The questions were originally presented to participants in their native German, and are translated here into English.

First, participants were asked to describe the strategy the advisor used in the game (debriefing question 3: ‘Did the advisor intentionally use a strategy during the task? If yes, describe what strategy that was’). Thirty out of 38 participants answered ‘Yes’ to this question, and described (in their own words) the advisor’s strategy. We repeated our analyses including only these 30 participants and found that all conclusions remained statistically the same. Second, participants were asked to rate the advice on a 6-point Likert scale ranging from unhelpful to very helpful (debriefing question 4: ‘How helpful did you perceive the advice you received?”). In general, participants rated the advisors’ recommendations as helpful (mean ratings 4.2 ± 1.0, ranging from 2 to 6). Finally, we also asked participants to rate, in terms of percentages, how often they followed the advice (debriefing question 5: ‘How often did you follow the recommendations of the advisor?”). On average, participants reported that they followed the advice 60% of the time (mean ratings 60 ± 12), which significantly differed from chance (t(37) = 5.02, p=1.29e-05). Thus, participants experienced advisors as intentional and helpful, which are core characteristics of social agents.

We used computational modeling with hierarchical Gaussian Filters (HGF; Figure 2) to explain participants’ responses on every trial. To contrast competing mechanisms underlying learning and arbitration, our model space included a total of nine models (Figure 3a). Non-normative perceptual models varied in complexity of volatility processing (three-level full HGF vs. two-level no-volatility HGF), normative perceptual models assumed optimal Bayesian inference (normative HGF), and response models varied in the extent of arbitration (arbitration; no arbitration: advice only; no arbitration: card information only). Bayesian model selection (Stephan et al., 2009) served to compare models (see Materials and methods and Figure 2 for details). For model comparison, we used the log model evidence (LME), which represents a trade-off between model complexity and model fit.

Figure 3

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The winning model was the three-level HGF with arbitration (${\varphi }_p$ = 0.999; Bayes Omnibus Risk = 4.26e-11; Figure 3b; Table 1a). This model formalised arbitration as a ratio of precisions: the precision of the prediction about advice accuracy and color probability, divided by total precision. Moreover, the model included a social bias parameter reflecting the degree to which participants followed the advisor irrespective of task information. The model family that included volatility of both information sources outperformed models without volatility, in-keeping with the model-independent finding that perceived volatility of both information sources affected behavior.

The winning three-level full HGF model includes multiple parameters that need to be estimated. A general question is whether these parameters are ‘practically identifiable’, that is whether their values can be recovered accurately given the actual experimental design. To examine this question, we simulated responses based on all participants’ maximum-a-posteriori estimates of the parameters, and then fitted the model to those simulated responses in order to test whether we could recover the same parameter estimates.

To assess and compare degrees of parameter recovery, we categorized it in terms of effect sizes, that is, whether the relationship between the original and the recovered values indicates small, medium, or large effect sizes as quantified by Cohen’s $f$. For a multiple regression analysis, a Cohen’s $f$ above 0.4 is conventionally regarded as a large effect size. Based on this criterion, we could recover all parameters well, as all Cohen’s $f$ values equaled or exceeded 0.4 (see Figure 2—figure supplement 1).

Three parameters modulated the arbitration signal of the winning model. These included: (i) $\kappa$ or the coupling between the two hierarchical levels that determined the impact of volatility on the inferred predictions of each information source (Equation 6), (ii) $\vartheta$, determining the variance of the volatility (Equation 12), and (iii) $\zeta$, the social bias which reflected the reliance on the advice independent of its reliability (Equation 19). Both coupling $\kappa$ and volatility parameter $\vartheta$ did not differ significantly between learning from individual and social information (t(36) = 0.28, p=0.77 for $\kappa$ and t(36) = -1.59, p=0.12 for $\vartheta$; Figure 4a-b). In fact, they were highly correlated: r₁=0.55, p₁=0.003 for $\kappa$ and r₂=0.64, p₂=0.001 for $\vartheta$. This result suggests that participants learned similarly from individual (volatile card probabilities) and social (advisor fidelity) information.

Figure 4

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The reliability-independent social bias parameter ζ differed significantly from zero (t(36) = 5.09, p=1.07e-05). Importantly, since the social bias parameter ζ is coded in log-space, the prior value of zero refers to a uniform weighting of the two cues in linear parameter space. Thus, on average, participants relied more on the advisor’s recommendations compared to their own sampling of the card outcomes (Figure 4c).

Decisions of how many points participants were willing to wager on a given trial (a measure of confidence) were related to several model-based quantities, including (irreducible) uncertainty of the agent’s beliefs about the decision, arbitration, and the estimated volatility of the advisor’s intentions (belief uncertainty: t(37) = -10.37, $p_{bonf}$ = 1.0e-11; arbitration: t(37)=5.16, $p_{bonf}$ = 5e-05; and estimated advisor volatility: t(37)=-7.41 $p_{bonf}$ = 4.75e-08) (Figure 5). The stronger the bias to arbitrate in favor of social information, the more points participants wagered. Conversely, estimated advisor volatility was negatively associated with the amount wagered: the higher the estimated advisor volatility, the fewer points participants were willing to wager on a given trial (see Table 2 for the priors over the parameters, Table 1b for all parameter estimates, and Figure 5 for the trial-wise influence of the average computational quantities on wager amount).

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We aimed to examine at the behavioral level whether the model predictions were consistent with participants’ perceptions of the advice accuracy during the experiment. Participants judged advice accuracy (i.e. helpful, misleading, or neutral with regard to predicting actual card color) in a multiple-choice question presented 5fivetimes during the experiment (initial/prior: 1st trial; stable advice, stable card phase = (14th trial); stable advice, volatile card phase (49th trial); volatile advice, volatile card phase (73rd trial); volatile advice, stable card phase = 115th trial). We first tested whether the responses to these questions positively related to estimates of advice accuracy (${\widehat{\mu }}_{1,a}^{\left(k\right)})$ that were extracted from the winning model. A linear regression analysis demonstrated that the inferred advice accuracy or ${\widehat{\mu }}_{1,a}^{\left(k\right)}$ measured at the time of the multiple-choice question, predicted participants’ selections. Specifically, the estimated beta parameter estimate across all task phases was significantly different from zero (t(36) = 4.71, p=3e-05). These findings suggest that the model predicted independently (and discretely) measured perception of advice accuracy, in-keeping with the internal validity of the model.

Next, we tested whether the wager amounts predicted by the model correlated with participants’ actual wagers. In all four conditions of the task, the predicted wager significantly correlated with the number of points participants actually wagered: (i) advice stable phase r₁ = 0.62, $p_1$ = 3e-05; (ii) advice volatile phase r₂ = 0.63, $p_2$ = 2e-05; (iii) card stable phase r₃ = 0.81, $p_4$ = 9e-10; and (iv) card volatile phase r₄ = 0.80, $p_4$ = 1e-09 (Figure 5—figure supplement 1). These findings suggest that the winning model explained variation in (the continuously measured) actual wager amount.

We used classical multiple regression and post-hoc tests to examine whether the model parameter estimates extracted from the winning model (M₁) explained participants’ advisor ratings, as measured by debriefing questions after the main experiment outside the scanner. Participants who reported that the advisor intentionally tried to help or mislead at different phases of the task showed a trend towards a larger estimate of the social weighting parameter $\zeta$ (df = (1,36), F = 3.49, p = 0.06). Moreover, advice helpfulness ratings were explained by model parameter estimates (R² = 32.2%, F = 2.46, p=0.04). This effect was primarily driven by parameter ${\kappa }_a$ (r(37)=0.47, p=0.0026), indicating that participants who rated the advice as being helpful showed stronger coupling between two levels of the hierarchical model. More specifically, participants who rated the advice as more helpful displayed higher ${\kappa }_a$ values, that is, increased sensitivity to the changing phases of advice validity, adjusting their wagering behavior more strongly to the advisor’s strategy. Thus, not only did the participants perceive the advice in our task as intentional and helpful, our model also explained some of these impressions.

Using behaviorally fitted computational trajectories to generate participant-specific GLMs for model-based fMRI analysis, we examined how the brain arbitrates between social and individual learning systems. We conceptualized the learning and arbitration process as hierarchical Bayesian inference, and fitted the participant-specific trajectories that reflect arbitration (Equation 20) to fMRI data.

Hierarchical precision-weighted PE signals were replicated in the same dopaminergic and frontoparietal regions as in previous studies using other sensory and social learning domains (see Iglesias et al., 2013; Diaconescu et al., 2017), indicating that the modifications in the experimental paradigm did not affect basic learning processes (see Figure 6—figure supplements 1–2).

Undirected tests for arbitration activity identified ventral prefrontal regions, such as the left ventromedial PFC (peak at [-2, 46,–10]) and the right orbitofrontal cortex (OFC) [26, 34, -10]. Interestingly, frontal activations also included the right frontopolar cortex [4, 54, 30] and ventrolateral prefrontal cortex (VLPFC) [50, 36, 0], regions previously associated with arbitration between model-based and model-free forms of individual learning (Lee et al., 2014; Figure 6). The right VLPFC showing arbitration-related effects at [48, 35, -2] significantly overlapped with the arbitration-related reliability activations detected by Lee and colleagues, supporting the notion that arbitration is to some extent domain-independent.

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In addition, we found that a wide network of cortical and subcortical regions contributes to arbitration that included occipital areas, the anterior insula, left thalamus, left putamen, bilateral middle cingulate sulcus, supplementary motor area (SMA) [−2, -8, 52], left dorsal middle cingulate gyrus [−10,–26, 44], the right amygdala [18, -10, -16] and the left midbrain [−6,–18, −12] (Table 3, Figure 6). Thus, a network of cortical and subcortical regions contributed to arbitration.

Directed tests for arbitration in favor of individual over social information identified activity increases in the right dorsolateral PFC [36, 46, 30], left SMA/anterior cingulate sulcus [−2,–8, 52] and the midbrain [−6,–18,−12] (Figure 7a). The BOLD signal change in these regions peaked during the time window of the wager decision. In summary, primarily dorsal regions of PFC were modulated by arbitration in favor of individually estimated card probability.

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Conversely, activity in the right amygdala, VLPFC, orbitofrontal and ventromedial PFC was modulated by arbitration in favor of the advisor’s suggestions (Figure 7b). Outside PFC, the right anterior TPJ [56, -52, 24], right superior temporal gyrus [52, -18, -8], and right precuneus [6, -51, 32] showed similar effects (Tables 4 and 5 for the entire list of brain regions). Thus, primarily ventral regions of PFC together with temporal and parietal regions were more active during arbitration in favor of social information.

To examine effects of arbitration in dopaminergic, cholinergic, and noradrenergic regions, we also performed region-of-interest (ROI) analyses using a combined anatomical mask of dopaminergic, cholinergic, and noradrenergic nuclei. A single cluster in the right substantia nigra survived small-volume correction (p<0.05 FWE voxel-level corrected for the entire ROI; peak at [−6,–18, −12]; Figure 8). Activity in this region increased with arbitration in favor of individual estimates of card probabilities rather than advice.

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It is important to note that these regions showed significantly larger effects of arbitration than of the amount of points wagered. Responses reflecting arbitration dominated over responses reflecting wager amount in cerebellar, midbrain, occipital, parietal, medial prefrontal, and temporal regions including the amygdala. Activity in precuneus and ventromedial prefrontal cortex in turn correlated with wager amount (Figure 9). As wager amount can be taken as a proxy for decision value or confidence (Lebreton et al., 2015), these data suggest that arbitration signals arise on top of decision value and confidence. Moreover, we captured arbitration as a model-derived, continuous, and time-resolved variable. Thus, our findings elucidate the process rather than the result of arbitration.

Figure 9

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To examine arbitration from a different angle, we also conducted a factorial analysis. This was possible because we employed a 2 × 2 factorial design – that is, two sources of information (individual versus social) in two different states (stable versus volatile) (Figure 10a). Specifically, we contrasted volatile with stable phases across both information modalities. Volatility is closely tied to arbitration because it potentiates the perceived uncertainty associated with a given information source, and thereby the need to arbitrate. We assumed that arbitration increased when one of the two information sources was perceived as being more stable than the other. In all comparisons, we controlled for decision value and confidence by using the trial-wise wager amount as a parametric modulator in the analysis of brain data. We found two significant results (Figure 10b): (i) a main effect of task phase (i.e. stability/volatility), and (ii) a significant interaction of task phase with source of information.

Figure 10

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By contrasting stable against volatile phases, irrespective of information source, we found that the right supramarginal gyrus, bilateral inferior occipital gyri, postcentral/precentral gyri, and the right anterior insula were more active for stable compared to volatile periods. Furthermore, an interaction between task phase and information source showed preferential activity for stable card information in the midbrain [−4,–22, −8]. Additional activations were detected in the right OFC, VLPFC, dorsomedial cingulate gyrus, and anterior cingulate sulcus/SMA (Figure 10; Table 6 and Table 7). These regions processed stability (vs. volatility) more strongly for card than advice information.

Importantly, the regions processing stability (vs. volatility) more strongly for advice than card information also overlapped with the arbitration signal, and included the amygdala, the superior temporal sulcus, and the ventromedial PFC (Figure 11). Thus, model-dependent and model-independent analyses agree in localizing arbitration to frontoparietal regions in the individual domain and to ventromedial prefrontal and amygdala regions in the social domain.

Figure 11

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To address the question of distinct representation of social compared to non-social signatures of learning, we investigated precision-weighted predictions of social and non-social outcomes. The precision-weighted predictions consist of the two factors that enter the computation of integrated beliefs (Equation 21) about the outcome. The first reflects the individual card color estimates weighted by arbitration in favor of the individually sampled card probabilities (non-social weighting), whereas the second reflects the predictions of advice accuracy weighted by arbitration in favor of the advisor (social weighting). Increased effects of non-social compared to social weighting were detected in bilateral cerebellum, occipital cortices (lingual gyrus, superior occipital cortex), left anterior cingulate sulcus, right supramarginal gyrus, and left postcentral gyrus. Conversely, we found increased representations of social compared to non-social weighting in the left subgenual ACC with a maximum at [−7, 36,–11] (Figure 7—figure supplement 1).

To test whether the task used in this study replicates previous findings on the representation of hierarchical precision-weighted PEs (Diaconescu et al., 2017; Iglesias et al., 2013), we performed the same model-based analysis using Bayesian surprise (equivalent to an unsigned precision-weighted outcome PE; the absolute value of Equation 14). Replicating the previous study (Iglesias et al., 2013), we found that the outcome-related BOLD activity of the substantia nigra positively correlated with the unsigned precision-weighted outcome PE, as did the bilateral inferior/middle occipital gyri, anterior insula, (ventro)lateral PFC, and the intraparietal sulcus (Figure 6—figure supplement 1a and Supplementary file 1A). In the previous study, participants predicted a visual outcome using an auditory cue (Iglesias et al., 2013). Thus, the PE coding of these regions seems to be sensory modality-independent.

With respect to the signed precision-weighted advice PE (Equation 8), we also replicated results from another recent study (Diaconescu et al., 2017) that employed a different advice-taking paradigm, where participants learned about advice and integrated it along with unambiguous individual information to predict the outcome of a binary lottery. Effects of signed precision-weighted advice PE were detected in right VTA/substantia nigra, the right insula, left middle temporal cortex, right dorsolateral, left dorsomedial and middle frontal cortex (Figure 6—figure supplement 1b and Supplementary file 1B).

Please note that we used the unsigned (absolute) precision-weighted PEs for the card outcomes, but the signed precision-weighted PEs for the advice. In the case of the card, the sign of this PE depends on an arbitrarily chosen coding of the color and the sign is meaningless (see Iglesias et al., 2013). In contrast, for the advice, the sign refers to the valence and instances of surprise where the advisor was more helpful than predicted, and may have a different meaning than instances of surprise where the advisor was more misleading than predicted (see Diaconescu et al., 2017). For completeness, we also investigated the neural correlates of the signed reward precision-weighted PE and noted a similar network of posterior parietal and dorsolateral prefrontal regions.

Effects of precision-weighted volatility PEs for card outcomes were represented in the right superior temporal gyrus, supramarginal gyrus, and posterior insula (Figure 6—figure supplement 2a) while the effects of precision-weighted volatility PEs for the adviser fidelity were encoded in the right anterior supplementary motor area (SMA) and anterior insula.

Finally, we also replicated the finding that higher-level, volatility PEs (Equations 13 and 15) were represented in cholinergic regions. This time, however, we observed effects of advice volatility precision-weighted PEs in the cholinergic nuclei in the tegmentum of the brainstem, that is, the pedunculopontine tegmental (PPT) and laterodorsal tegmental (LDT) nuclei (p<0.05 FWE voxel-level within an anatomical mask including all cholinergic nuclei) (Figure 6—figure supplement 2b).

Using both model-based and model-independent (factorial) fMRI analysis, we found that the arbitration signal correlated with activity in dorsolateral and ventrolateral PFC, frontopolar, and orbitofrontal cortex (Figures 6 and 11). These findings corroborate previous insights on arbitration between different forms of individual information also pointing to lateral prefrontal cortex (Lee et al., 2014), in line with domain generality for arbitrating. Note though that arbitration activity in the prefrontal cortex followed a self-versus-other axis: dorsal prefrontal activity increased the more strongly participants weighed their own predictions of reward probabilities over the perceived reliability of the advisor. Conversely, activity in the ventromedial PFC and orbitofrontal cortex showed the opposite pattern and increased in activity as participants relied more heavily on their own reward probability estimates relative to the advice (Figure 7). Together, arbitration appears to be sensitive to the source of information entering the arbitration process, contrary to an entirely domain-general process.

The results of both model-based and factorial analyses suggest a key role of the midbrain in arbitrating for individual estimates about card color over advice (Figure 8). Primate studies found that sustained dopamine neuron activity signaled expected uncertainty (Fiorillo et al., 2003; Schultz, 2010; Schultz et al., 2008). This was further supported by human pharmacological studies (Burke et al., 2018; Ojala et al., 2018) as well as fMRI research showing possible involvement of dopamine in risk taking and of dopaminoceptive regions, such as the caudate, anterior insula, ACC and the medial PFC in uncertainty coding (e.g. Dreher et al., 2006; Preuschoff et al., 2008; Tobler et al., 2009) and social advice predictions under uncertainty (Henco et al., 2020). In particular, studies employing hierarchical Bayesian models have identified ventral tegmental area/substantia nigra activation correlated to precision of predictions about desired outcomes (Friston et al., 2014; Schwartenbeck et al., 2015).

These findings may also underscore the role of dopamine in modulating participants’ ability to optimize learning to suit ongoing estimates of environmental volatility. Potential neurobiological mechanisms include meta-learning models, which propose an important role of phasic dopamine signals in training prefrontal system dynamics, to infer on the statistical structure of the environment (Collins and Frank, 2016; Wang et al., 2018). Such models imply that improved learning of the structure of the environment, for example current levels of volatility, results in more appropriate arbitration adjustment.

The amygdala processed perceived reliability of social information, reflected in activity increasing the more participants discounted their own estimates of rewarded card color probabilities in favour of the advisor's recommendations. The amygdala has been implicated in processing facial expressions related to affective ToM (Schmitgen et al., 2016) and more generally, processing affective value and motivational significance of various stimuli, including other people (Güroğlu et al., 2008; Zink et al., 2008; Zerubavel et al., 2015). Together these findings suggest that the amygdala may represent the uncertainty of socially-relevant stimuli, inferred from processing the intentions of others.

Similar to the amygdala, the orbitofrontal cortex showed a significant interaction between task phase and information source, indicative of arbitrating in favor of social information. This finding is consistent with the hypothesis that the orbitofrontal cortex and other areas of the social brain evolved to enable primates and particularly humans to successfully navigate complex social situations (Dunbar, 2009). This notion received support from strong positive correlations between orbitofrontal cortex grey matter volume and social network size (Powell et al., 2012), as well as sociocognitive abilities (Powell et al., 2010; Scheuerecker et al., 2010). Furthermore, in-keeping with a role of orbitofrontal cortex in mental state attribution for ambiguous social stimuli (Deuse et al., 2016), our findings suggest that this region reduces the uncertainty of social cues that signal changes in intentionality.

With respect to social learning signatures, we observed that the sulcus of the ACC represents predictions related to one’s own estimates of the card color outcomes, whereas the subgenual ACC represents predictions about the advisor’s fidelity. This is consistent with previous findings that the sulcus of ACC dorsal to the gyrus plays a domain-general role in motivation (Rushworth et al., 2007; Rushworth and Behrens, 2008; Apps et al., 2016), whereas the gyrus of the ACC signals information related to other people (Behrens et al., 2008; Apps et al., 2013; Apps et al., 2016; Lockwood, 2016).

An intriguing extension of the current study concerns the question of whether arbitration occurs differently in patients with psychiatric and neurodevelopmental disorders involving ToM processes. If so, how do these processing differences affect behavior? For example, individuals with autism spectrum disorder may preferentially rely on their own experiences rather than on the recommendations of others. Indeed, they appear to represent social prediction errors less strongly than individuals without autism (Balsters et al., 2017). Accordingly, they may be able to better infer the volatility of the card color probability compared to the advice in our task. In contrast, patients with schizophrenia may be overly confident about their ability to judge advice validity due to fixed beliefs about the advisor’s intentions (Freeman and Garety, 2014) or show an over-reliance on social information in line with accounts of over-mentalization in this disorder (Montag et al., 2011; Andreou et al., 2015). Future work may test these intriguing possibilities.

One limitation of our study is that it did not include reciprocal social interactions, but rather used pre-recorded videos of human partners. ToM processes may be more prominent in interactive paradigms (Diaconescu et al., 2014) or interactions that involve higher levels of recursive thinking (Devaine et al., 2014a; Devaine et al., 2014b). By extension, our study may have limited generalizability to real-world social interactions. However, assessing arbitration between social and individual information necessitated the standardization of the advice given to each participant. To make the task as close as possible to a realistic social exchange, the videos of the advisor were extracted from trials when they truly intended to help or truly intended to mislead. More importantly, to adequately compare learning from social and individual information in stable and volatile phases, we needed to ensure that the two information types were orthogonal to each other and balanced in terms of volatility.

Second, we did not include a non-social control task. Thus, it is unclear how ‘social’ the presently investigated form of learning about the advisor’s fidelity and volatility actually is. The differences in activated regions at least suggest that our participants processed the two sources of information differently. However, whether the process we identified is specifically social in nature or rather reflects learning from an indirect information source needs to be examined in future studies by including an additional control condition.

In order to distinguish general inference processes under volatility from inference specific to intentionality, we previously included a control task (Diaconescu et al., 2014), in which the advisor was blindfolded and provided advice with cards from predefined decks that were probabilistically congruent to the actual card color. This control task closely resembled the main task, with the exception of the role of intentionality. Model selection results suggested that participants in the control task did not incorporate time-varying estimates of volatility about the advisor into their decisions. In the current study, we tested this by including models without volatility, but found that they performed substantially worse than models with volatility (see Figure 2 and Table 2a for details). Thus, our participants appeared to process advisor intentionality.

Our study indicates that arbitrating between social and individual sources of information corresponds to weighing the relative reliability of each source. This process appears to engage different brain regions for social and individual information, in-keeping with domain specificity. However, the lateral prefrontal cortex appears to adjudicate between several different types of learning, in-keeping with domain generality. These findings contribute to our understanding of arbitration in neurotypical individuals, which may provide a knowledge basis for future insight into disorders with impaired arbitration.

We recruited 48 volunteers (mean age 23.6 ± 1.4, 32 females) who were non-smokers, right-handed, and had normal or corrected-to-normal vision. Participants had no history of neurological or psychiatric illness, or of drug abuse. Psychology students were excluded from participation because of previous exposure to similar advice-taking paradigms in their courses. Participants were asked to abstain from alcohol 24 hr prior to the study and from medication, including aspirin, 3 days prior to the study. We did not analyse the data of 10 participants: two pilot participants; one participant who stopped the experiment midway due to head pain; one participant who fell asleep; and six participants where stimulus presentation malfunctioned during the experiment. Altogether, 38 participants (mean age 24.2 ± 1.3; 26 females) entered the final analysis.

We modified the deception-free binary lottery game of Diaconescu et al., 2014. In each trial, the participant had to predict the color of a card draw – blue or green. Participants could base their predictions on social information and/or on individually experienced recent outcome history (see below). They received social information from the ‘advisor’, who held up a card in one of the two colors before every draw, recommending to the participant which option to choose. The advisor based his or her suggestion on information that was true with a probability of 80%, although the participants were not informed of this fact. Furthermore, the advisor received monetary incentives to change his or her strategy and thus provide either helpful or misleading advice at different stages of the game (Figure 1b) with the average probability of advice being correct in 56% of trials. To compare participants in terms of their learning and decision-making parameters, we needed to standardize the advice. This means that each participant received the same input sequence,that is order and type of videos.

To display social information in a standardized fashion and gender-match advisors and participants, we created videos from two male and two female advisors, who changed their advice as a function of the incentives in a previously recorded face-to-face session (see Diaconescu et al., 2014). Their advice on each trial was recorded for an entire experimental session and the full-length videos were edited into 2 s segments, focusing on the advice period. We received informed consent from all advisors in the initial (face-to-face) behavioral study to record and use the advice-giving videos in subsequent studies. All video clips were matched in terms of their luminance, contrast, and color balance using Adobe Photoshop Premiere CS6.

To standardize the advice, avoid implicit cues of deception, and make the task as close as possible to a social exchange in real time, the videos of the advisor were extracted from trials when they truly intended to help or truly intended to mislead. Although each participant received the same advice sequence throughout the task, the advisors displayed in the videos varied between participants, in order to ensure that physical appearance and gender did not impact on their decisions to take advice into account. Advisor-to-participant assignment was randomized (within the gender-matching constraint) and balanced. We found no differences in performance and degree of reliance on advice between the four advisors: F(1,36) = 1.82, p=0.16.

In contrast to previous studies (Diaconescu et al., 2014; Diaconescu et al., 2017), participants had to infer card color probabilities (blue versus green) from individually experienced outcomes of previous trials rather than being provided with (changing) pie charts explicitly stating the probabilities. In each trial, they had to arbitrate between following either social information (previous advice, inferring on intention) or individual information (previous cards, inferring on probability). Moreover, also in contrast to previous studies, for each lottery prediction, participants wagered between one and ten points to indicate how confident they were about their predictions. The tick mark on the wager bar was randomly positioned in each trial to avoid providing a reference point (a regression analysis confirmed that the starting position of the wager indeed failed to explain each participant’s trial-wise wager selection, t(37) = −0.89, p=0.31). Depending on the correctness of the prediction, the wager was added to or subtracted from the cumulative score and thereby affected the participant's payment at the end of the experiment (see below).

Each trial (Figure 1a) began with a video of the advisor holding up a card, followed by a decision screen in which participants selected the blue or green card. At the next screen, they were asked to provide the wager. The subsequent outcome screen revealed the drawn card. Finally, the updated cumulative score appeared. The color-to-button assignment used to convey the lottery prediction (blue or green) and the orientation of the wager bar were randomized between participants to prevent confounding with visuomotor processes.

Across trials, the color-reward probabilities and the advisor intentions varied independently of each other. In other words, the probability distributions of the two information sources – card color and advice – were designed to be statistically independent. This allowed for a 2 × 2 factorial design structure, where trials could be divided into four conditions: (i) stable card and stable advisor, (ii) stable card and volatile advisor, (iii) volatile card and stable advisor, and (iv) volatile card and volatile advisor in a total of 160 trials (Figure 1b). Based on this factorial structure, we predicted that arbitration signals would vary as a function of the stability of each information source.

We explained the deception-free task to participants and ensured their comprehension with a written questionnaire, which required them to describe the instructions in their own words. The task instructions, which were originally presented to participants in their native German, were translated into English for the purpose of this paper. Pronouns were adapted to the advisor’s gender: "The advisor has generally more information than you about the outcome on each trial. The objective of the advisor is to use this information to guide your choices and reach his/her own goals. Note that the advisor does not have 100% accurate information about which color ‘wins’ and he/she might be incorrect. Nevertheless, he/she will on average have better information than you and his/her advice may be valuable to you." The actual experiment was divided into two sessions, with a 2-min break in the middle when participants could close their eyes and rest. The first session included 70 trials and the second session 90 trials.

To test the construct validity of our computational model and verify whether participants inferred on the advisor’s fidelity, we asked them to rate the usefulness of the advisor’s card recommendation based on a multiple choice question (including, ‘helpful,’ ‘misleading,’ or ‘neutral’). This question was presented six times throughout the task and responses allowed us to assess whether at any point in time, the model could significantly predict participants’ responses.

Participants could earn a bonus of 10 Swiss Francs for a cumulative score of at least 380 points, and a bonus of 20 Swiss Francs for winning more than 600 points. Importantly, participants were not given any information about the bonus thresholds in order to prevent induction of local risk-seeking or risk-averse wagering behavior (reference point effects) when participants were close to a threshold. Participants on average reached the first reward bonus and were paid 82.3 ± 8.4 Swiss Francs (including the performance-dependent bonus) at the end of the study. After the task, participants completed a debriefing questionnaire, and we revealed to them the general trajectory of the advisor’s intentions.

We acquired functional magnetic resonance images (fMRI) from a Philips Achieva 3T whole-body scanner with an 8-channel SENSE head coil (Philips Medical Systems, Best, The Netherlands) at the Laboratory for Social Neural Systems Research at the University Hospital Zurich. The task was presented on a display at the back of the scanner, which participants viewed using a mirror placed on top of the head coil. The first five volumes of each session were discarded to allow for magnetic saturation.

During the task, we acquired gradient echo T2*-weighted echo-planar imaging (EPI) data with blood-oxygen-level dependent (BOLD) contrast (slices/volume = 33; TR = 2665 ms; voxel volume = 2×2 x 3 mm³; interslice gap = 0.6 mm; field of view (FOV) = 192×192 x 120 mm; echo time (TE) = 35 ms; flip angle = 90°). The images were oblique, slices with −20° right-left angulation from a transverse orientation. The entire experiment comprised 1300 volumes, with 600 volumes in the first session and 700 in the second. Heart rate and breathing of the participants were recorded for physiological noise correction purposes using ECG and a pneumatic belt, respectively.

We also measured the homogeneity of the magnetic field with a T1-weighted 3-dimensional (3-D) fast gradient echo sequence (FOV = 192×192 x 135 mm³; voxel volume = 2×2 x 3 mm³; flip angle = 6°; TR = 8.3 ms; TE1 = 2 ms; TE2 = 4.3 ms). After the experiment, we acquired T1-weighted structural scans from each participant using an inversion-recovery sagittal 3-D fast gradient echo sequence (FOV = 256×256 x 181 mm³; voxel volume = 1×1 x 1 mm³; TR = 8.3 ms; TE = 3.9 ms; flip angle = 8°).

The software package SPM12 version 6470 (Wellcome Trust Centre for Neuroimaging, London, UK; http://www.fil.ion.ucl.ac.uk/spm) was used to analyse the fMRI data. Temporal and spatial preprocessing included slice-timing correction, realignment to the mean image, and co-registration to the participant’s own structural scan. The structural image underwent a unified segmentation procedure combining segmentation, bias correction, and spatial normalization (Ashburner and Friston, 2005); the same normalization parameters were then applied to the EPI images. As a final step, EPI images were smoothed with an isotropic Gaussian kernel of 6 mm full-width half-maximum.

BOLD signal fluctuations due to physiological noise were modeled with the PhysIO toolbox (http://www.translationalneuromodeling.org/tapas) (Kasper et al., 2017) using Fourier expansions of different order for the estimated phases of cardiac pulsation (3rd order), respiration (4th order) and cardio-respiratory interactions (1st order; Glover et al., 2000). The 18 modeled physiological regressors entering the subject-level GLM along with the six rigid-body realignment parameters and regressors of interest were used to account for BOLD signal fluctuations induced by cardiac pulsation, respiration, and the interaction between the two.

We formalized arbitration in terms of hierarchical Bayesian inference as the relative perceived reliability of each information source. In other words, arbitration was defined as a ratio of precisions: the precision of the prediction about advice accuracy and color probability, divided by the total precision. The precisions of the predictions afforded by each learning system are obtained by applying a two-branch hierarchical Gaussian filter (Mathys et al., 2011; Mathys et al., 2014) along with a response model (see below) to participants’ trial--wise behavior (i.e. choices and wagers).

The HGF is a model of hierarchical Bayesian inference widely used for computational analyses of behavior (e.g. [Iglesias et al., 2013; Vossel et al., 2014; Hauser et al., 2014; de Berker et al., 2016; Marshall et al., 2016]). To apply it to our task, we assumed that the rewarded card color (individual learning) and the advice accuracy (social learning) varied as a function of hierarchically coupled hidden states: $x_1^{\left(k\right)},x_2^{\left(k\right)},\dots ,x_n^{\left(k\right)}$. They evolved in time by performing Gaussian random walks. At every level, the step size was controlled by the state of the next-higher level (Figure 2a).

Starting from the bottom of the hierarchy, states $x_{1,a}$ and $x_{1,c}$ represented binary variables, namely the advice accuracy (1 for accurate, 0 for inaccurate) and the rewarded card color (1 for blue, 0 for green). All states higher than $x_1$ were continuous. They denoted (i) the advisor fidelity and tendency for a given card color to be rewarded, and (ii) the rate of change of the advisor’s intentions and card color contingencies, respectively. Four learning parameters, namely, ${\kappa }_a$, ${\kappa }_c$,${\vartheta }_a$ and ${\vartheta }_c$ determined how quickly the hidden states evolved in time. Parameter $\kappa$ represented the degree of coupling between the second and the third levels in the hierarchy, whereas $\vartheta$ determined the variability of the volatility over time (meta-volatility). This constitutes the generative model of the process producing the outcomes observed by participants. The overall model and the formal equations describing these relations in a social learning context are detailed in Diaconescu et al., 2014.

In accordance with Bayes’ rule, we assumed that participants who make inferences on advice and card colors form posterior beliefs over the hidden states (i.e. congruency of advice with actual card color; rewarded card color) based on the outcomes they observe. Model inversion is the application of Bayes’ rule to a generative model such as the one described above. This leads to a recognition or perceptual model, which describes participants’ beliefs about hidden states. Assuming Gaussian distributions, these agent-specific beliefs are denoted by their summary statistics, that is µ (mean) and $\sigma$ (variance/uncertainty) or the inverse of the variance $\pi =1/\sigma$ (precision/certainty).

Using variational Bayes under the mean-field approximation, simple analytical trial-by-trial update equations can be derived. The posterior means ${\mu }_i^{\left(k\right)}$ or predictions on each trial $k$ at each level of the hierarchy i change as a function of precision-weighted prediction errors (PEs):

Throughout, predictions or prior beliefs about the hidden states (before observing the outcome) are denoted with a hat symbol. States ${\displaystyle {\hat{\pi }}_{i-1}^{\left(k\right)}}$ and ${\pi }_i^{\left(k\right)}$ represent the estimated precisions about (i) the input from the level below (i.e. precision of the data – advice congruency or rewarded card color) and (ii) the belief at the current level, respectively.

The updates about the advisor’s fidelity are:

where

Variable $u^{\left(k\right)}$ is the sensory input at trial k, where given advice is either accurate ${\displaystyle \left(u^{(k)}=1\right)}$ or inaccurate ${(u}^{\left(k\right)}=0)$. Furthermore, ${\displaystyle {\hat{\mu }}_{1,a}^{\left(k\right)}}$ corresponds to the logistic sigmoid of the current expectation of the advisor fidelity:

The current belief precision is equivalent to:

with the predicted (i) belief precision ${\displaystyle {\hat{\pi }}_{2,a}^{(k)}}$ and (ii) the sensory, lower-level precision about the advice ${\displaystyle {\hat{\pi }}_{1,a}^{(k)}}$ computed as:

Thus, the advice belief precision depends on (i) the predicted sensory precision of the input ${\displaystyle {\hat{\pi }}_1^{(k)}}$ , and (ii) the predicted volatility, ${\mu }_{3,a}^{(k-1)}$ from the level above via Equation 6.

The precision-weighted PE about the advice, which is used to update the belief about fidelity is equivalent to:

Going up the hierarchy, the updates of advice volatility are proportional to precision-weighted PEs:

They depend on the higher-level volatility PE ${\displaystyle {\delta }_{2,a}}$:

and the higher level volatility precision ${\displaystyle {\pi }_3}$:

with the precision of the prediction about volatility given by

The third level, the precision-weighted volatility PE is equivalent to:

The same form of update equations (and precision-weighted PEs) can be derived for the individual information source, updating beliefs about the rewarded card color, i.e.:

and

The prediction errors exhibit a similar form as for the advice, with

for the outcome PE and

for the card volatility PE. The individually estimated card color probability is equivalent to the logistic sigmoid of the current expectation of the rewarding card color:

In this context, Bayes-optimality is individualized with respect to the values of the learning parameters, which were allowed to differ across participants.

To map beliefs to decisions, we assumed that the prediction of card color on a given trial k is a function of arbitration and of the predictions afforded by each source (see Equation 21). The response model predicts two components of the behavioral response: (i) the participant’s decision to accept or reject the advice and (ii) the number of points wagered on every trial. Responses were coded as $y=1$ when participants took the advice and chose the card color indicated by the advisor, and $y=0$ when participants decided against following the advice and chose the opposite card color. The expected outcome probability is thus a precision-weighted sum of the two information sources, the estimates of advice accuracy and rewarding color probability.

where ${\xi }_{i,a}^{\left(k\right)}$ and ${\xi }_{1,c}^{\left(k\right)}$ are the arbitration for each information source; ${\displaystyle {\hat{\mu }}_{1,a}^{\left(k\right)}}$ is the expected advice accuracy (Equation 4) and ${\widehat{\mu }}_{1,c}^{\left(k\right)}$ is the transformed expected card color probability from the perspective of the advice (i.e. the estimated card color probability indicated by the advisor).

It follows from Equation 21, that social weighting is represented by the first term of this integrated sum – that is ${\displaystyle {\xi }_{i,a}^{\left(k\right)}\cdot {\hat{\mu }}_{1,a}^{\left(k\right)}}$ whereas card color weighting is represented by the second term or ${\displaystyle {\xi }_{1,c}^{\left(k\right)}\cdot {\hat{\mu }}_{1,c}^{\left(k\right)}}$.

The probability that participants chose a particular card color according to their expectations about the outcome (Equation 21) was modeled by a softmax function:

where ${\beta }_{choice}>0$ is the participant-specific inverse decision temperature parameter. A low decision temperature (high ${\beta }_{choice}$) means always choosing the highest probability color, whereas a high decision temperature (low ${\beta }_{choice}$) means sampling randomly from a uniform distribution.

The number of points wagered provided us with a behavioral readout of decision confidence. We aimed to formally explain trial-wise wager responses as a linear function of various sources of uncertainty and precision associated with the lottery outcome prediction: (i) irreducible decision uncertainty or ${\displaystyle {\hat{\sigma }}_b^{\left(k\right)}}$ about the outcome, (ii) arbitration, (iii) informational uncertainty about the card color or the advice, and (iv) environmental uncertainty/volatility about the card color or the advice. We transformed these computational quantities down to the first level in the hierarchy using the sigmoid transformation and used them to predict the trial-by-trial wager (Figure 5 for the group average of each of these quantities):

with

Parameter ζ captures the social bias in arbitration (equation 19) and $I_{2,\text{a}}^{\left(\text{k}\right)}$ is the informational uncertainty about the advisor fidelity

where ${\displaystyle {\hat{\sigma }}_{2,a}^{\left(k\right)}}$ is the inverse of ${\displaystyle {\hat{\pi }}_{2,a}^{\left(k\right)}}$ and represents the informational uncertainty of the prediction about the advisor’s fidelity (Equation 6).

The environmental volatility is defined as:

Equivalent equations can be derived for the individual information source.

The trial-wise wager amount predicted by the model is then defined as:

where ${\beta }_{wager}$ is a stochasticity parameter associated with the wager amount. For the priors of all $\beta$ parameters estimated here, please refer to Table 2.

To contrast competing mechanisms underlying learning and arbitration, our model space consisted of a total of 9 models (Figure 3). On the one hand, we included non-normative perceptual models varying in the degree of volatility processing (three-level full HGF vs. two-level no-volatility HGF) and normative perceptual models assuming optimal Bayesian inference (normative HGF). On the other hand, we included response models varying in the level of arbitration (arbitration; no arbitration: advice only; no arbitration: card information only).

We considered three families of perceptual models. The first family included the full, three-level version of the HGF (as described above). By contrast, the second family lacked the third level, and assumed that agents do not estimate the volatility of the card probabilities or the advice. Thus, comparing families with and without volatility tested whether volatility mattered for arbitrated behavior. Finally, the third family assumed a Bayes-optimal, normative process of learning from the advice and card outcomes.

In terms of response models, we also considered three families, capturing different ways in which participants may arbitrate between social and individual sources of information to make decisions. These included: (i) an ‘Arbitrated’ model, which assumed that participants combine and arbitrate between the two information sources, possibly unequally, (ii) an ‘Advice only’ model, assuming arbitration-free reliance on social information only, and (iv) a ‘Card only’ model, representing arbitration-free reliance on the inferred card color probabilities only (Figure 3a).

All models were compared formally using Bayesian model selection (BMS Stephan et al., 2009). Random effects BMS results in a posterior probability for each model given the participants’ data. The relative goodness of models is denoted by the ‘protected exceedance probability’ reflecting how likely it is that a given model has a higher posterior probability than any other model in the set of models considered (Stephan et al., 2009; Rigoux et al., 2014).

We adopted a similar set of priors over the perceptual model parameters as in our previous studies (Diaconescu et al., 2014) (see Table 2). Maximum-a-posteriori (MAP) estimates of model parameters were obtained using the HGF toolbox version 3.0, freely available as part of the open source software package TAPAS at http://www.translationalneuromodeling.org/tapas.

Contrast images from the 38 participants entered a random effects group analysis (Penny and Holmes, 2007). We used F-tests to identify undirected arbitration signals. Moreover, one-sample t-tests to investigate directed social or individual arbitration signals and positive or negative BOLD responses for each of the computational trajectories of interest described above.

Participant gender and age were included as covariates of no interest at the group level (the findings remained the same without these covariates). To investigate individual variability in the representation of social arbitration as a function of reliance on advice, we used parameter $\zeta$ to perform a median split of the group of participants.

For all analyses, we report results that survived whole-brain family-wise error (FWE) correction at the cluster level at p<0.05, under a cluster-defining threshold of p<0.001 at the voxel level using Gaussian random field theory (Worsley et al., 1996). Given recent debate regarding the vulnerabilities of cluster-level FWE procedures (Eklund et al., 2016), it is worth emphasising that this cluster-defining threshold ensures adequate control of cluster-level FWE rates in SPM (Flandin and Friston, 2016). The coordinates of all brain regions were expressed in Montreal Neurological Institute (MNI) space.

Based on recent results that precisions at different levels of a computational hierarchy may be encoded by distinct neuromodulatory systems (Payzan-LeNestour et al., 2013; Schwartenbeck et al., 2015), we also performed ROI analyses based on anatomical masks. We included (i) the dopaminergic midbrain nuclei substantia nigra (SN) and ventral tegmental area (VTA) using an anatomical atlas based on magnetization transfer weighted structural MR images (Bunzeck and Düzel, 2006), (ii) the cholinergic nuclei in the basal forebrain and the tegmentum of the brainstem using the anatomical toolbox in SPM12 with anatomical landmarks from the literature (Naidich and Duvernoy, 2009) and (iii) the noradrenergic locus coeruleus based on a probabilistic map (Keren et al., 2009) (see Figure 8—figure supplement 1 for this neuromodulatory ROI).

The routines for all analyses are available as Matlab code: https://github.com/andreeadiaconescu/arbitration (Kasper and Diaconescu, 2020; copy archived at https://github.com/elifesciences-publications/arbitration). The instructions for running the code in order to reproduce the results can be found in the ReadMe file.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

We are grateful for support by the Swiss National Science Foundation (Ambizione grant PZ00P3_167952 to AOD; PP00P1_150739, 100014_165884, and 100019_176016 to PNT) and the Krembil Foundation to AOD. We are also grateful to Klaas Enno Stephan for providing guidance and funding for the study.

Human subjects: Informed consent, and consent to publish, was obtained from all participants. The study was approved by the Ethics Committee of the Canton of Zürich (KEK-ZH 2010-0327). All participants gave written informed consent before taking part in the study.

© 2020, Diaconescu et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.