We communicate our confidence to others to share our beliefs about uncertainty with them. However, numerous studies have shown that even the same verbal or numerical expression of confidence can have very different meanings for different people in terms of the underlying uncertainty (Ais et al., 2016; Navajas et al., 2017; Fleming et al., 2010). Similar inter-individual diversity has been found at the neural level (Fleming et al., 2010; Sinanaj et al., 2015; Baird et al., 2013). Still, people manage to cooperate successfully in decision making under uncertainty (Bahrami et al., 2010; Austen-Smith and Banks, 1996). What computational and neuronal mechanisms enable people to converge to a shared meaning of their confidence expressions in interactive decision making despite the extensively documented neural and cognitive diversity? This question drives at the heart of recent efforts to understand the neurobiology of how people adapt their communication to their beliefs about their interaction partner (Stolk et al., 2016). A number of studies have provided compelling empirical evidence of brain-to-brain coupling that could underlie adaptive communication of shared beliefs (Silbert et al., 2014; Honey et al., 2012; Hasson et al., 2004; Dikker et al., 2014; Konvalinka et al., 2010). These works remain, to date, mostly observational in nature. Plausible neuro-computational mechanism(s) accounting for how interpersonal alignment of beliefs may arise from the firing patterns of decision-related neural populations in the human brain are still lacking (Hasson and Frith, 2016; Wheatley et al., 2019). Using a multidisciplinary approach, we addressed this question at behavioral, computational, and neurobiological levels.

By sharing their confidence with others, joint decision makers can surpass their respective individual performance by reducing uncertainty through interaction (Bahrami et al., 2010; Sorkin et al., 2001). Recent works showed that during dyadic decision making, interacting partners adjust to one another by matching their own average confidence to that of their partner (Bang et al., 2017). Such confidence matching turns out to be a good strategy for maximizing joint accuracy under a range of naturalistic conditions, e.g., uncertainty about the partner’s reliability. However, at present there is no link connecting these socially observed emergent characteristics of confidence sharing with the elaborate frameworks that shape our understanding of confidence in decision making under uncertainty (Navajas et al., 2017; Fleming et al., 2010; Pouget et al., 2016; Adler and Ma, 2018; Aitchison et al., 2015).

Theoretical work has shown that sequential sampling can, in principle, provide an optimal strategy for making the best of whatever uncertain, noisy evidence is available to the agent (Heath, 1984). These models have had great success in explaining the relationship between decision reaction time (RT) and accuracy under a variety of conditions ranging from perceptual (Hanks and Summerfield, 2017; Gold and Shadlen, 2007) to value-based decisions (Ruff and Fehr, 2014) guiding the search for the neuronal mechanisms of evidence accumulation to boundary in rodent and primate brains (Schall, 2019). The relation between RT and accuracy, known as speed-accuracy trade-off, has been recently extended to a three-way relationship in which choice confidence is guided by both RT and probability (or frequency) of correct decision (Pouget et al., 2016; Kiani et al., 2014; Vickers, 1970). Critically, these studies have all focused on decision making in isolated individuals deciding privately (Wheatley et al., 2019). Little is known about how these computational principles and neuronal mechanisms can give rise to socially shared beliefs about uncertainty.

To bridge this gap, we examined confidence-speed-accuracy trade-off in social vs isolated context in humans. We combined a canonical paradigm (i.e. dynamic random dot motion [RDM]) extensively employed in psychophysical and neuroscientific studies of speed-accuracy-confidence trade-off (Hanks and Summerfield, 2017; Gold and Shadlen, 2007; Kelly and O’Connell, 2013) with interactive dyadic social decision making (Bahrami et al., 2010; Bang et al., 2017). We replicated the emergence of confidence matching and obtained pupillometry evidence for shared subjective beliefs in our social implementation of the random dot paradigm and we observed a novel pattern of confidence-speed-accuracy trade-off specifically under the social condition. We constructed a neural attractor model that captured this trade-off, reproduced confidence matching in virtual social simulations and made neural predictions about the coupling between neuronal evidence accumulation and social information exchange that were born out by the empirical data.

We used a discovery-and-replication design to investigate the computational and neurobiological substrates of confidence matching in two separate steps: 12 participants (4 female) were recruited in study 1 (discovery) and 15 (5 female, age: 28 (mean) ± Std (7)) in study 2 (replication, second study was pre-registered: https://osf.io/5zces). In each study, participants reported the direction of a random-dot motion stimulus and indicated their confidence (Figure 1a) while EEG and eye tracking data were recorded, simultaneously. After an extensive training procedure (see Materials and methods for the recruitment), participants reached a stable behavioral (accuracy and RT) performance level. Then, two experimental sessions were conducted: first a private session (200 trials) in which participants performed the task alone; then a social session (800 trials for study 1 and 400 for study 2) in which they performed the task interactively together with a partner (implied to be another participant in a neighboring lab room).

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In every trial (Figure 1a), after fixation for 300 ms was confirmed by closed-loop real-time eye tracking, two choice-target points appeared at 10° eccentricity corresponding to the two possible motion directions (left and right). After a short random delay (200–500 ms, truncated exponential distribution), a dynamic RDM (see Shadlen and Newsome, 2001) was centrally displayed for 500 ms in a virtual aperture (5° diameter). At the end of the motion sequence, the participant indicated the direction of motion and their confidence on a 6-point scale by a single mouse click. A horizontal line intersected at midpoint and marked by 12 rectangles (6 on each side) was displayed. Participants moved the mouse pointer – initially set at the midpoint – to indicate their decision (left vs right of midpoint) and confidence by clicking inside one of the rectangles. Further distance from the midpoint indicated more confidence. RT was calculated as the time between the onset of the motion stimulus sequence and the onset of deviation of the mouse pointer (see Materials and methods for more details) (Resulaj et al., 2009) at the end of stimulus presentation.

In the isolated trials, the participant was then given visual feedback for accuracy (correct or wrong). In the social trials (Figure 1a, bottom panel), after the response, participants proceeded to the social stage. Here, the participants’ own choice and confidence as well as that of their partner were displayed coded by different colors (white for participants; yellow for partners). Joint decision was automatically arbitrated in favor of the decision with higher confidence. Finally, three distinct color-coded feedback messages (participant, partner, and joint decision) were displayed.

Participants were instructed to try to maximize the joint accuracy of their social decisions. In order to achieve joint benefit, confidence should be expressed such that the decision with higher probability of correct outcome dominates (Bahrami et al., 2010). For this to happen, the participant needs to factor in the partner’s behavior and adjust her confidence accordingly. For example, if the participant believes that her decision is highly likely to be correct, her confidence should be expressed such that joint decision is dominated by the partner only if the probability that the partner’s decision is correct is even higher (and not, for example, if the partner expressed a high confidence habitually). This social modulation of one’s confidence in a perceptual decision comprises the core of our model of social communication of uncertainty.

Following from an earlier study (Bang et al., 2017), for each block the participants were led to believe that they were paired with a new, anonymous human partner. In reality, in separate blocks, they were paired with four computer generated partners (henceforward, CGPs; see Materials and methods) constructed and tuned to parameters obtained from the participant’s own behavior in the isolated session: (1) high accuracy and high confidence (HAHC; i.e. this CGP’s decisions were more likely to be more confident as well as more accurate); (2) high accuracy and low confidence (HALC); (3) low accuracy and high confidence (LAHC); and (4) low accuracy and low confidence (LALC) (see Materials and methods for details). For study 2, we used two CGPs (HCA and LCA) while the agent accuracy was similar to those of participants (Bang and Fleming, 2018) (Wilcoxon rank sum, p=0.37, df = 29, zval = 0.89). See Figure 1—figure supplement 1 for confidence and accuracy data of CGPs. Each participant completed 4 blocks of 200 trials cooperating with a different CGP in each block. Our questionnaire results also confirmed that our manipulation indeed worked (Figure 1—figure supplement 4) and more importantly none of the subject suspected their partners was an artificial one.

Having observed the confidence matching effect in both studies (Figure 1b), a permutation analysis confirmed that this effect did not arise trivially from mere pairing with any random partner (Bang et al., 2017; Figure 1—figure supplement 2). The difference between the participant’s confidence and that of their partner was smaller in the social (vs isolated) condition (Figure 1—figure supplement 2) consistent with the prediction that participants would match their average confidence to that of their partner in the social session (Bang et al., 2017).

Having established the socially emergent phenomenon of confidence matching in the dynamic RDM paradigm, we then proceeded to examine choice speed, accuracy, and confidence under social conditions (Figure 1c). We observed that when participants were paired with a high (vs low) confidence partner, there was no significant difference in accuracy between the social conditions (p=0.92, p=0.75 for study 1 and 2 respectively, generalized linear mixed model [GLMM], see Supplementary materials for details of the analysis [Table 1], Figure 1c top-left panel); confidence, however, was significantly higher (p<0.001 for both studies, Table 1, Figure 1c middle panel) and RTs were significantly faster (p<0.001 for both, Table 1, Figure 1c bottom panel) in the HCA vs LCA.

This pattern of dissociations of speed and confidence from accuracy is non-trivial because the expectations of the standard sequential sampling models would be that a change in confidence should be reflected in change in accuracy (Pouget et al., 2016; Sanders et al., 2016). Many alternative mechanistic explanations are, in principle, possible. The rich literature on sequential sampling models in the random-dot paradigm permit articulating the components of such intuitive explanations as distinct computational models and comparing them by formal model comparison (see further below).

In order to assess the impact of social context on the participants’ level of subjective uncertainty and rule out two important alternative explanations of confidence matching, we next examined the pupil data. Several studies have recently established a link between state of uncertainty and baseline (i.e. non-luminance mediated) variations in pupil size (Bang et al., 2017; Wei and Wang, 2015; Nassar et al., 2012; Eldar et al., 2013; Murphy et al., 2014; Urai et al., 2017). If the impact of social context on confidence were truly reflective of a similar change in the participant’s belief about uncertainty, then we would expect the smaller pupil size when paired with high (HCA) vs low confidence agent (LCA) indicating lower subjective uncertainty. Alternatively, if confidence matching were principally due to pure imitation (Rendell et al., 2011; Iacoboni, 2009) or due to some form of social obligation in agreeing with others (e.g. normative conformity [Stallen and Sanfey, 2015]) without any change in belief, we would expect the pupil size to remain unaffected by pairing condition under social context. We found that during the inter-trial interval (ITI), pupil size was larger in the blocks where participants were paired with LCA (vs HCA) (Figure 2, GLMM analysis, p<0.01 and p<0.001 for study 1 and 2 respectively, see Supplementary materials for details of the analysis; Table 2). We have added a time series analysis that demonstrates the temporal encoding of experimental conditions in the pupil signal during ITI (see Figure 2—figure supplement 2). It is important to bear in mind that pupil dilation has been linked to other factors such as mental effort (Lee and Daunizeau, 2021), level of surprise (Kloosterman et al., 2015), and arousal level (Murphy et al., 2014) as well. These caveats notwithstanding, the patterns of pupil dilation within the time period of ITI that are demonstrated and replicated here, are consistent with the hypothesis that participants’ subjective belief was shaped by interactions with differently confident partners. To support this conclusion further, we provide supplementary evidence linking the participant’s own confidence to pupil size (Figure 2—figure supplement 1).

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To arbitrate between alternative explanations and develop a neural hypothesis for the impact of social context on decision speed and confidence, we constructed a neural attractor model (Wong and Wang, 2006), a variant from the family of sequential sampling models of choice under uncertainty (Bogacz et al., 2006). Briefly, in this model, noisy sensory evidence was sequentially accumulated by two competing mechanisms (red and blue in Figure 3a left) that raced toward a common pre-defined decision boundary (Figure 3a right) while mutually inhibiting each other. Choice was made as soon as one mechanism hits the boundary. This model has accounted for numerous observations of perceptual and value-based decision-making behavior and their underlying neuronal substrates in human (Hunt et al., 2012) and non-human primate (Wei and Wang, 2015) brain. Following previous works (Wei and Wang, 2015; Balsdon et al., 2020; Rolls et al., 2010; Atiya et al., 2019) we defined model confidence as the time-averaged difference between the activity of the winning and losing accumulators (corresponding to the shaded gray area between the two accumulator traces in Figure 3a right, for the model simulation see Figure 3—figure supplement 2) during the period of stimulus presentation (from 0 to 500 ms). Importantly, this definition of confidence is consistent with recent findings that computations of confidence continue after a decision has been made as long as sensory evidence is available (Ruff and Fehr, 2014; Balsdon et al., 2020; van Kempen et al., 2019; Moran et al., 2015). We also demonstrate that our results do not depend on this specific formulation and also replicate with another alternative method (Vickers, 1979)(see Figure 3—figure supplement 3).

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Earlier works that demonstrated the relationship between decision uncertainty and pupil-related, global arousal state in the brain (Murphy et al., 2014; Urai et al., 2017) guided our modeling hypothesis. We modeled the social context as a global, top-down additive input (Figure 3a; W_x) in the attractor model. This input drove both accumulator mechanisms equally and positively. The impact of this global top-down input is illustrated in Figure 3a right: with a positive top-down drive (W_x>0), the winner (thick blue) and the loser (thick red) traces both rise faster compared to zero top-down drive (dotted lines). The model’s counterintuitive feature is that the surface area between the winning and losing accumulator is larger in the case of positive (dark gray shading) versus zero (light gray shading) top-down input. Model simulations show that when 0<W_x, this difference in surface area leads to faster RTs and higher confidence but does not change accuracy because it does not affect the decision boundary. These simulation results are consistent with our behavioral findings comparing HCA vs LCA conditions (Figure 1c).

We formally compared our model to three alternative, plausible models of how social context may affect the decision process. Without loss of generality, we used data from study 2 to fit the model. The first model hypothesized that partner’s confidence dynamically modulated the decision bound (Balsdon et al., 2020) (parameter B in Equation 21). In this model, the partner’s higher confidence reduced the threshold for what counted as adequate evidence, producing the faster RTs under HCA (Figure 1.c). The second model proposed that partner’s confidence changed non-decision time (NDT) (Stine et al., 2020; Equation 22). Here, pairing with high confidence partner would not have any impact on perceptual processing but instead, non-specifically decrease RTs across all coherence levels without affecting accuracy. Finally, in the third model, the stimulus-independent perceptual gain (Eldar et al., 2013; Li et al., 2018) parameter of input current (parameter μ₀ in Equation 23) was modulated by partner confidence. Here, higher partner confidence increased the perceptual gain (as if increasing the volume of the radio) leading to increased confidence and decreased RT (Figure 1c) and would be consistent with the pupillometry results. In each model, in the social condition, the parameter of interest was linearly modulated by the confidence of the partner in the previous trial. Importantly, in Figure 1—figure supplement 3, we show that empirically, such trial-by-trial dependence is observed in confidence and RTs data in both study 1 and 2. Formal model comparison showed that our top-down additive current model was superior to all three alternatives (see Figure 3—figure supplement 4).

Having shown that a common top-down drive can qualitatively reproduce the impact of social context on speed-accuracy-confidence and quantitatively excel other alternatives in fitting the observed behavior, we then used the winning model to simulate our interactive social experiment virtually (Figure 3c). We simulated one decision maker with high confidence (subject 1 in Figure 3d) and another one with low confidence (subject 2). To simulate subject 1, we slightly increased the excitatory and the inhibitory weights. The opposite was done to simulate subject 2 (see Materials and methods for details). We then paired the two simulated agents by feeding the confidence of each virtual agent (from trial t–1) (Bang et al., 2017) as top-down input to the other virtual agent (in trial t).

Using this virtual social experiment, we simulated the dyadic exchanges of confidence in the course of our experiment and drew a prediction that could be directly tested against the empirical behavioral data. Without any fine-tuning of parameters or any other intervention, confidence matching emerged spontaneously when two virtual agents with very different confidence levels in isolated condition (Figure 3d left) were paired with each other as a dyad (Figure 3d right). Importantly, the model could be adapted to show different speed of matching as well (see Figure 3—figure supplement 6). However, for simplicity we presented the simplest case in the main text.

To identify the neural correlates of interpersonal alignment of belief about uncertainty, we note that previous works using non-invasive electrophysiological recordings in humans engaged in motion discrimination (Twomey et al., 2016; Stolk et al., 2013) have identified the signature, accumulate-to-bound neural activity characteristic of evidence accumulation in the sequential sampling process. Specifically, these findings show a centropareital positivity (CPP) component in the event-related potential that rises with sensory evidence accumulation across time. The exact correspondence between the neural CPP and elements of the sequential sampling process are not yet clear (O’Connell et al., 2018). For example, CPP could have resulted from the spatial superposition of the electrical activity of both accumulators or be the neural activity corresponding to the difference in accumulated evidence. These caveats notwithstanding, consistent with the previous literature, we found that in the isolated condition, our data replicated those earlier findings: Figure 4a shows a clear CPP event-related potential whose slope of rise was strongly modulated by motion coherence (GLMM, p<0.001 and p=0.01 for study 1 and 2 receptively, see Supplementary file 1d and Figure 4—figure supplement 2 for more details). Importantly, we have added the response-locked analysis of the CPP signals (see Figure 4—figure supplement 4). We do see that the response-locked CPP waveforms converge to one another for high vs low coherence trials at the moment of the response.

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Our model hypothesized that under social condition, a top-down drive – determined by the partner’s communicated confidence in the previous trial – would modulate the rate of evidence accumulation (Figure 3a). We tested if the CPP slope were larger within every given coherence bin when the participant was paired with an HCA (vs LCA). Indeed, the data demonstrated a larger slope of CPP rise under HCA vs LCA (Figure 4c, study 1 for the social condition p=0.15 but for the second study p<0.01, see Tables 3 and 4 for more details). These findings demonstrate that interpersonal alignment of confidence is associated with a modulation of neural evidence accumulation – as quantified by CPP – by the social exchange of information (also see Figure 4—figure supplement 3). It is important to note a caveat here before moving forward. These data show that both CPP and confidence are different between the HCA and LCA conditions. However, due to the nature of our experimental design, it would be premature to conclude from them that CPP contributes causally to the alignment of subjectively held beliefs or behaviorally expressed confidence. Put together with the behavioral confidence matching (Figure 1b) and the pupil data (Figure 2) our findings suggest that some such neural-social coupling could be the underlying basis for the construction of a shared belief about uncertainty.

We brought together two so-far-unrelated research directions: confidence in decision making under uncertainty and interpersonal alignment in communication. Our approach offers solutions to important current problems in each.

For decision science, we provide a model-based, theoretically grounded neural mechanism for going from individual, idiosyncratic representations of uncertainty (Navajas et al., 2017; Fleming et al., 2010) to socially transmitted confidence expressions (Bahrami et al., 2010; Bang et al., 2017) that are seamlessly shared and allow for successful cooperation. The social-to-neuronal coupling mechanism that we borrowed from the communication literature (Hasson and Frith, 2016; Wheatley et al., 2019) is crucial in this new understanding of the neuronal basis of relationship between subjectively private and socially shared uncertainty.

For communication science, by examining perceptual decision making under uncertainty in social context, we created a laboratory model in which the goal of communication was to arrive at a shared belief about uncertainty (rather than creating a look-up table for the meaning of actions [Stolk et al., 2016; Silbert et al., 2014; Honey et al., 2012]). In this way, we could employ the extensive theoretical, behavioral, and neurobiological body of knowledge in decision science (Pouget et al., 2016; Adler and Ma, 2018; Aitchison et al., 2015; Hanks and Summerfield, 2017; Gold and Shadlen, 2007; Ruff and Fehr, 2014; Schall, 2019; Kiani et al., 2014; Kelly and O’Connell, 2013; Shadlen and Newsome, 2001; Resulaj et al., 2009; Sanders et al., 2016; Wei and Wang, 2015; Eldar et al., 2013; Urai et al., 2017; Yeung and Summerfield, 2012; Fleming and Daw, 2017; Kiani and Shadlen, 2009) to construct a mechanistic neural hypothesis for interpersonal alignment.

Over the past few years, the efforts to understand the ‘brain in interaction’ have picked up momentum (Wheatley et al., 2019; Frith and Frith, 1999). A consensus emerging from these works is that, at a conceptual level, successful interpersonal alignment entails the mutual construction of a shared cognitive space between brains (Stolk et al., 2015; Wheatley et al., 2019; Friston and Frith, 2015). This would allow interacting brains to adjust their internal dynamics to converge on shared beliefs and meanings (Hasson and Frith, 2016; Gallotti and Frith, 2013). To identify the neurobiological substrates of such shared cognitive space, brain-to-brain interactions need to be described in terms of information flow, i.e., the impact that interacting partners have on one another’s brain dynamics (Wheatley et al., 2019).

The evidence for such information flow has predominantly consisted of demonstrations of alignment of brain-to-brain activity (i.e. synchrony at macroscopic level, e.g. fMRI BOLD signal) when people process the same (simple or complex) sensory input (Honey et al., 2012; Hasson et al., 2004; Breveglieri et al., 2014; Mukamel et al., 2005; Hasson and Honey, 2012) or engage in complimentary communicative (Silbert et al., 2014) roles to achieve a common goal. More recently, dynamic coupling (rather than synchrony) has been suggested as a more general description of the nature of brain-to-brain interaction (Hasson and Frith, 2016). Going beyond the intuitive notions of synchrony and coupling, to our knowledge, no computational framework – grounded in the principles of neural computing – has been offered that could propose a plausible quantitative mechanism for these empirical observations of brain-to-brain coupling.

Combining four different methodologies, the work presented here undertook this task. Behaviorally, our participants engaged in social perceptual decision making under various levels of sensory and social uncertainty (Bahrami et al., 2010; Bang et al., 2017). Emergence of confidence matching (Figure 1b) showed that participants coordinated their decision confidence with their social partner. Pupil data (Figure 2) suggested that participant’s belief about uncertainty was indeed shaped by the social coordination. A dissociation (Figure 1c) of decision speed and confidence from accuracy was reported that depended on the social context. This trade-off, as well as the emergence of confidence matching, was successfully captured by a neural attractor model (Figure 3) in which two competing neural populations of evidence accumulators – each tuned to one choice alternative – were driven by a common top-down drive determined by social information. This model drew predictions for behavior (Figure 3d) and neuronal activity (Figure 4, Figure 4—figure supplements 1–5) that were born out by the data. Social exchange of information modulated the neural signature of evidence accumulation in the parietal cortex.

Although numerous previous works have employed sequential sampling models to explain choice confidence, the overwhelming majority (Pouget et al., 2016; Aitchison et al., 2015; Hanks and Summerfield, 2017; Gold and Shadlen, 2007; Ruff and Fehr, 2014; Schall, 2019; Kiani et al., 2014; Sanders et al., 2016; Kiani and Shadlen, 2009; Krajbich and Rangel, 2011) have opted for the drift diffusion family of models. Neural attractor models have so far been rarely used to understand confidence (Rolls et al., 2010; Atiya et al., 2019; Wang, 2002). Our attractor model is a reduced version (Wong and Wang, 2006) of the original biophysical neural circuit model for motion discrimination (Wang, 2002). The specific affordances of attractor models allowed us to implement social context as a sustained, tonic top-down feedback to both accumulator mechanisms. More importantly, we were able to simulate social interactive decision making by virtually pairing any given two instances of the model (one for each member of a dyad) with each other: the confidence produced by each in a given trial served as top-down drive for the other in the next trial. Remarkably, a shared cognitive space about uncertainty (i.e. confidence matching) emerged spontaneously from this simulated pairing without us having to tweak any model parameters.

At a conceptual level, deconstructing the social communication of confidence into a comprehension and a production process (Silbert et al., 2014) is helpful. Comprehension process refers to how socially communicated confidence is incorporated in the recipient brain and affects their decision making. Production process refers to how the recipient’s own decision confidence is constructed to be, in turn, socially expressed. It is tempting to attribute the CPP neural activity in the parietal cortex to the production process. Comprehension process, in turn, could be the top-down feedback from prefrontal brain areas previously implicated in confidence and metacognition (Fleming et al., 2010; Fleming and Daw, 2017; De Martino et al., 2017) to the parietal cortex. However, we believe that our neural attractor model in particular and the empirical findings do not lend themselves easily to this conceptual simplification. For example, the evidence accumulation process can be a part of the production (because confidence emerges from the integrated difference between accumulators) as well as the comprehension process (because the rate of accumulation is modulated by the received social information). As useful as it is, the comprehension/production dichotomy’s limited scope should be recognized. Instead, armed with the quantitative framework of neural attractor models (for each individual) and interactive virtual pairing (to simulate dyads), future studies can now go beyond the comprehension/production dichotomy and examine the neuronal basis of interpersonal alignment with a model that have a strong footing in biophysical realities of neural computation.

Several limitations apply to our study. We chose different sets of coherence levels for the discovery (experiment 1) and replication (experiment 2). This choice was made deliberately. In experiment 1 we included a very high coherence (51%) level to optimize the experimental design for demonstrating the CPP component in the EEG signal. In experiment 2, we employed peri-threshold coherence levels in order to focus on behavior around the perceptual threshold to strengthen the model fitting and model comparison. This trade-off created some marginal differences in the observed effect sizes in the neural data across the two studies. The general findings were in good agreement.

The main strength of our work was to put together many ingredients (behavioral data, pupil and EEG signals, computational analysis) to build a picture of how the confidence of a partner, in the context of joint decision making, would influence our own decision process and confidence evaluations. Many of the effects that we describe here are well described already in the literature but putting them all together in a coherent framework remains a challenge. For example, our study did not directly examine neural alignment between interaction partners. We measured the EEG signal one participant at a time. The participant interacted with an alleged (experimenter-controlled) partner in any given trial. Our experimental design, however, permitted strict experimental control and allowed us to examine the participants’ social behavior (i.e. choices and confidence), pupil response, and brain dynamics as they achieved interpersonal alignment with the partner. Moreover, while the hypotheses raised by our neural attractor model did examine the nature of brain dynamics involved in evidence accumulation under social context, testing these hypotheses did not require hyper-scanning of two participants at the same time. We look forward to future studies that use the behavioral and computational paradigm described here to examine brain-to-brain neural alignment using hyper-scanning.

We have interpreted our findings to indicate that social information, i.e., partner’s confidence, impacts the participants’ beliefs about uncertainty. It is important to underscore here that, similar to real life, there are other sources of uncertainty in our experimental setup that could affect the participants’ belief. For example, under joint conditions, the group choice is determined through the comparison of the choices and confidences of the partners. As a result, the participant has a more complex task of matching their response not only with their perceptual experience but also coordinating it with the partner to achieve the best possible outcome. For the same reason, there is greater outcome uncertainty under joint vs individual conditions. Of course, these other sources of uncertainty are conceptually related to communicated confidence, but our experimental design aimed to remove them, as much as possible, by comparing the impact of social information under high vs low confidence of the partner.

Our study brings together questions from two distinct fields of neuroscience: perceptual decision making and social neuroscience. Each of these two fields have their own traditions and practical common sense. Typically, studies in perceptual decision making employ a small number of extensively trained participants (approximately 6–10 individuals). Social neuroscience studies, on the other hand, recruit larger samples (often more than 20 participants) without extensive training protocols. We therefore needed to strike a balance in this trade-off between number of participants and number of data points (e.g. trials) obtained from each participant. Note, for example, that each of our participants underwent around 4000 training trials. Importantly, our initial study (N=12) yielded robust results that showed the hypothesized effects nearly completely, supporting the adequacy of our power estimate. However, we decided to replicate the findings in a new sample with N=15 participants to enhance the reliability of our findings and examine our hypothesis in a stringent discovery-replication design. In Figure 4—figure supplement 5, we provide the results of a power analysis that we applied on the data from study 1 (i.e. the discovery phase). These results demonstrate that the sample size of study 2 (i.e. replication) was adequate when conditioned on the results from study 1.

Finally, one natural limitation of our experimental setup is that the situation being studied is very specific to the design choices made by the experimenters. These choices were made in order to operationalize the problem of social interaction within the psychophysics laboratory. For example, the joint decisions were not an agreement between partners (Bahrami et al., 2010; Bahrami et al., 2012). Instead, following a number of previous works (Bang et al., 2017; Bang et al., 2020), joint decisions were automatically assigned to the most confident choice. In addition, partner’s confidence and choice were random variables drawn from a distribution prespecified by the experimenter and therefore, by design, unresponsive to the participant’s behavior. In this sense, one may argue that the interaction partner’s behavior was not ‘natural’ since they did not react to the participant’s confidence communications (note however that the partner’s response times and accuracy were not entirely random but matched carefully to the participant’s behavior prerecorded in the individual session). How much of the findings are specific to these experimental setting and whether the behavior observed here would transfer to other real-life settings is an open question. For example, it is plausible that participants may show some behavioral reaction to the response time variations since there is some evidence indicating that for binary choices like here, response times also systematically communicate uncertainty to others (Patel et al., 2012). Future studies could examine the degree to which the results might be paradigm-specific.

Data that supports the findings of the study can be found here: https://osf.io/v7fqz/.

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Author details

1. Jamal Esmaily

   1. Department of General Psychology and Education, Ludwig Maximillian University, Munich, Germany
   2. Faculty of Computer Engineering, Shahid Rajaee Teacher Training University, Tehran, Islamic Republic of Iran
   3. Graduate School of Systemic Neurosciences, Ludwig Maximilian University Munich, Munich, Germany

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Validation, Visualization, Methodology, Writing – original draft, Writing – review and editing

   For correspondence

   jimi.esmaily@gmail.com

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-5529-6732

2. Sajjad Zabbah

   1. School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Islamic Republic of Iran
   2. Wellcome Centre for Human Neuroimaging, University College London, London, United Kingdom
   3. Max Planck UCL Centre for Computational Psychiatry and Aging Research, University College London, London, United Kingdom

   Contribution

   Conceptualization, Data curation, Software, Methodology, Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

3. Reza Ebrahimpour

   Institute for Convergent Science and Technology, Sharif University of Technology, Tehran, Islamic Republic of Iran

   Contribution

   Conceptualization, Software, Supervision, Funding acquisition, Validation, Investigation, Methodology, Project administration, Writing – review and editing

   Contributed equally with

   Bahador Bahrami

   For correspondence

   ebrahimpour@sharif.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-7013-8078

4. Bahador Bahrami

   1. Department of General Psychology and Education, Ludwig Maximillian University, Munich, Germany
   2. Centre for Adaptive Rationality, Max Planck Institute for Human Development, Berlin, Germany

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Validation, Investigation, Visualization, Writing – original draft, Project administration, Writing – review and editing

   Contributed equally with

   Reza Ebrahimpour

   For correspondence

   bbahrami@gmail.com

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-0802-5328

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