Introduction

Social animals have evolved sophisticated mechanisms for cooperation. To coordinate, individuals exchange information, enabling independent and group regulation (Emerson, 1956; Wheeler, 1911). Interaction provides the self with insights about others and, simultaneously, about its own state within the environment. In humans, this psychological differentiation begins in utero (Ciaunica et al., 2021) and continues into adulthood. This prolonged differentiation facilitates the distinction between self and others, allowing grounded social orientation and flexible adaptation. Early psychological theorists highlighted the importance of healthy social exchange in humans for integrating constructive relational blueprints, noting that disruptions during sensitive periods can impair the formation of trusting, safe social bonds (e.g., Fairbairn, 1952; 1994) and foster less adaptable interpersonal beliefs (Young et al., 2006).

At the individual level, humans must manage information exchange to navigate and reduce relational uncertainty. When faced with external uncertainty about others’ characteristics, prior knowledge can swiftly and effectively guide predictions. When uncertainty arises regarding one’s own internal state, external cues can provide anchoring information to support self-through-other calibration. To reduce uncertainty about others, theories of the relational self (Anderson & Chen, 2002) suggest that the self is the most extensive and well-grounded representation available, leading to a readily accessible initial belief (Kreuger & Clement, 1994) that can be projected or integrated into social learning. Conversely, to address uncertainty about the self, individuals can generalize information from others to themselves—this social contagion facilitates adaptation to social groups and is a crucial component of interpersonal cohesion that relies on trust (Frith & Frith, 2012).

Computational modelling has advanced our understanding of how humans engage in self-insertion and social contagion to achieve efficient prediction and adaptation. By integrating self-preferences into prior beliefs, self-insertion models account for increased reaction times at the onset of learning and enhanced predictive accuracy as a function of interpersonal similarity (Tarantola et al., 2017; Barnby et al., 2022). Conversely, uncertain self-preferences can be influenced by observing others’ intertemporal discounting behavior (Garvert et al., 2015; Moutoussis et al., 2016; Thomas et al., 2022).

However, critical questions remain: How do humans adjudicate between self-insertion and contagion during interaction to manage interpersonal generalization? Does the uncertainty in self-other beliefs affect their generalizability? How can disruptions in interpersonal exchange during sensitive developmental periods (e.g., childhood maltreatment) inform models of psychiatric disorders? Understanding the computational processes humans use in social exchange has broad implications for theories of healthy childhood development, group cohesion, reputation management, interpersonal synchrony, and the breakdown of social bonds.

In this study, we present a formal account of self-other generalization in healthy individuals and those seeking psychiatric support, tested through an interactive social economic paradigm—the Intentions Game—and a computational model that concurrently allows for self-insertion and social contagion. We evaluate our model using data from matched participants with and without a diagnosis of Borderline Personality Disorder (BPD). BPD is characterized by interpersonal sensitivity, relational instability, emotional dysregulation, impulsivity, paranoia, and severe fear of abandonment (e.g., Gunderson et al., 2018; Euler et al., 2021). It is strongly associated with early childhood adversity, such as psychological, physical, and sexual abuse or neglect (Afifi et al., 2011; Bateman et al., 2023), and inconsistent parenting experiences (Crawford et al., 2009), particularly during sensitive developmental periods (Fonagy & Bateman, 2008). Early adversity interacts with pre-existing variations in stress-homeostasis mechanisms, exacerbating interpersonal disruptions (Pratt et al., 2017), underpinned by difficulties in mentalizing and trust appraisal, leading to disruptions in social learning (e.g., Fonagy & Luyten, 2009; Nolte et al., 2023) and representations of self and other (Hanegraaf et al., 2021).

Computational models have probed social processes in BPD, linking the BPD phenotype to a potential over-reliance on social versus internal cues (Henco et al., 2020), ‘splitting’ of social latent states that encode beliefs about others (Story et al., 2023), negative appraisal of interpersonal experiences with heightened self-blame (Mancinelli et al., 2024), inaccurate inferences about others’ irritability (Hula et al., 2018), and reduced belief adaptation in social learning contexts (Siegel et al., 2020). Previous studies have typically overlooked how self and other are represented in tandem, prompting further investigation into why any of these BPD phenotypes manifest.

We propose a theory with testable predictions to begin addressing this question, outlining that information generalization is foundational to healthy and evolving social bonds, and that the BPD phenotype may arise from an infraction to this process. To foreshadow our results we discover that healthy participants employ a mixed process of self-insertion and contagion to predict and align with the beliefs of their partners in the Intentions Game. In contrast, individuals with BPD exhibit distinct, disintegrated representations of self and other, despite showing similar average accuracy in their predictions about partners. Our model and data suggest that the previously observed computational characteristics in BPD, such as reduced self-anchoring during ambiguous learning and a relative impermeability of the self, arise from the failure of information about others to transfer and inform the self. By integrating separate computational findings, we provide a foundational model and a concise, dynamic paradigm to investigate uncertainty, generalization, and regulation in social interactions. Additionally, we examine the extent to which self-reported complex trauma and its sequelae are linked to these computational processes.

Results

Healthy participants (CON; n=53) and participants diagnosed with BPD (n=50), matched on age, gender, education, and social deprivation indices (Table 1), were invited to participate in a three-phase social value orientation paradigm—the Intentions Game (Figure 1A)—with virtual partners. In the first phase, participants made forced choices between two options for splitting points with an anonymous partner. In the second phase, participants learned to predict the decisions of a new anonymous partner using the same forced-choice setup, receiving feedback on the accuracy of their successive predictions. Notably, using a novel server architecture (Burgess et al., 2023), partners in phase 2 were configured to be approximately 50% different from the participants in terms of their choices, ensuring that all participants had to learn about their phase 2 partner. The third phase mirrored the first, with participants informed that they were matched with a third anonymous partner, unrelated to those in phases 1 and 2. Detailed descriptions of the task can be found in the methods section.

Psychometric and Behavioural Results

Participants with BPD, compared to CON, reported significant childhood trauma, epistemic disruptions (including mistrust and credulity), elevated referential and persecutory beliefs, and demonstrated ineffective trait mentalizing (Table 1). The groups did not differ in trait measures of certainty regarding self and others’ mental states, nor in elevated trust.

We analyzed the ‘types’ of choices participants made in each phase (Supplementary Table 1). For example, a participant could make prosocial (self=5; other=5) versus individualistic (self=10; other=5) choices, or prosocial (self=10; other=10) versus competitive (self=10; other=5) choices. There were 12 types of pairs in phases 1 and 3 (individualistic vs. prosocial; prosocial vs. competitive; individualistic vs. competitive).

In phase 1, both CON and BPD participants made prosocial choices over competitive choices with similar frequency (CON=9.67[3.62]; BPD=9.60([3.57]). However, CON participants made significantly fewer prosocial choices when individualistic choices were available (CON=2.87[4.01]; BPD=5.22[4.54]; t=2.75, p=0.007). Both groups favored individualistic over competitive choices with similar frequency (CON=11.03[1.95]; BPD=10.34([2.63]). Examining reaction times (in milliseconds; ms) in phase 1 by choice type revealed that, compared to competitive choices, individualistic choices were made faster (linear estimate = -880.60, 95%CI: -1385.42, -376.2; t = -3.42, p < 0.001), and prosocial choices were made fastest (linear estimate = -1171.1, 95%CI: -1701.97, -640.71; t = -4.32, p < 0.001) irrespective of the type of choice pair. Prosocial choices were made significantly faster than individualistic choices (linear estimate = -290.70,95%CI: -548.50, -32.91; t = -2.21, p = 0.027). There was no difference in reaction times between CON and BPD participants in phase 1.

In phase 2 each group showed good predictive accuracy (CON=77.2%[13.9%]; BPD=72.7%[15.6%]). There was no difference in overall predictive accuracy between BPD and CON (linear estimate=2.44, 95%CI: -0.67, 5.54; t=1.56; p=0.12), nor when analysed on a trial-by-trial basis (linear estimate=0.26, 95%CI: -0.06, 0.59; z=1.61, p=0.11) using a random effects models. All participants showed an effect of time on accuracy, such that participants became more accurate in predicting their partner over the course of phase 2 (linear estimate=0.013, 95%CI: 0.008, 0.017; z=6.01; p<0.001). There was no impact of choice type on reaction times in phase 2.

In phase 3, both CON and BPD participants continued to make equally frequent prosocial versus competitive choices (CON=9.15[3.91]; BPD=9.38[3.31]), and CON participants continued to make significantly less prosocial versus individualistic choices (CQN=2.03[3.45]; BPD=3.78 [4.16]; t=2.31, p=0.02). Both groups chose equally frequent individualistic versus competitive choices (CON=10.91 [2.40]; BPD=10.18[2.72]). Reaction times in phase 3 revealed that compared to competitive choices, individualistic choices were made faster (linear estimate = -528.50, 95%CI: - 943.60, -114.6; t = -2.50, p = 0.012), and prosocial choices were made fastest (linear estimate = -693.5, 95%CI: -1137.65, -250.39; t = -3.07, p = 0.002), irrespective of the type of choice pair. Prosocial choices were no longer executed significantly faster than individualistic choices. All participants made faster choices in phase 3 compared to phase 1 (linear estimate = -242.02, 95% CI: -332.64, -151.41; t = -5.24, p = 0.001). There was no significant effect of group on reaction times between phases 1 and 3, nor within phase 3 when analyzed independently.

Table 1.

Figure 1.

Computational Analysis

Over all three phases, we assumed participants and their partners used a Fehr-Schmidt utility function (Fehr & Schmidt, 1999) to calculate the utility of two options , based on the joint rewards available for both the participant, R_ppt = and their partner, . The utility of each option was weighted based on absolute-reward gain α (how much participants care about selfearnings) and relative reward β along a prosocial-competitive axis (how much participants care about equality of outcomes); β < 0 is prosocial, whereas β > 0 is competitive.

We then constructed four models to explain how participants used their own preferences and uncertainty over these preferences * to predict and learn about the preferences of their partner (θ_par; Figure 1B; see methods). Model M1 (Figure 1C) suggests that participants initially use their own preferences as a prior belief about their partner (self-insertion), which is gradually diminished during the learning process in phase 2. M1 also posits that, following learning, the inferred beliefs about a partner will influence participants’ own preferences, making them more similar to their partner’s preferences following observation (social contagion). According to this model, participants shift towards their partner based on their uncertainty about self and others (Figure 1E): greater uncertainty over self-preferences and increased precision in representing the other cause stronger social contagion effects.

Model M4 (Figure 1D), on the other hand, suggests that participants do not engage in these generalization processes: predictions about others are not grounded in the self, and observing others does not alter self-preferences. Models M2 and M3 allow for either self-insertion or social contagion to occur independently. Consistent with prior research, we also constructed a model that assumes the same insertion and contagion processes as M1, but along a single prosocial-competitive axis (‘Beta model’; Barnby et al., 2022). The ‘Beta model’ accommodates the possibility that participants might only consider a single dimension of joint reward allocation, which is typically emphasized in previous studies (e.g., Hula et al., 2018).

Table 2.

Model Comparison – BPD Participants Hold Disintegrated Self-Other Beliefs

We found that CON participants were best fit at the group level by M1 (Frequency = 0.59, Protected Exceedance Probability = 0.98), whereas BPD participants were best fit by M4 (Frequency = 0.54, Protected Exceedance Probability = 0.86; Figure 2A). Consequently, we analyzed common parameters between groups, assuming that M1 and M4 best fitted the CON and BPD groups, respectively. It is worth noting that a minority of participants were best fit by M3 (CON: Frequency = 0.32; BPD: Frequency = 0.39), which assumes that participants were influenced by their partner but were not subject to self-insertion biases. We therefore also examined the change in beliefs between phases 1 and 3 under the assumption that M3 was accurate. Anticipating this analysis, we find that our main conclusions hold, showing that BPD participants were significantly less influenced by their partner compared to CON participants.

Generative Accuracy and Recovery

We simulated data for each participant using their individual parameters from the winning model within each group and refitted our models using this simulated data. Model comparison yielded very similar results (Figure 3A), with CON synthetic participants best fit at the group level by M1 (Frequency = 0.58, Protected Exceedance Probability = 0.98) and BPD synthetic participants best fit by M4 (Frequency = 0.57, Protected Exceedance Probability = 0.85). The simulated data closely matched the actions of participants across all three phases (median accuracy = 0.8, SD = 0.12). In phase 2, the model-predicted total correct scores were not significantly different from observed scores (Figure 3E). Both model responsibility and common parameters within each dominant model were strongly and significantly associated (model confusion p = 0.46–0.97, p < 0.001; parameter recovery p = 0.70–0.94, p < 0.001; Figure 3C). Given the very good to excellent performance of the models, we continued to analyze individual parameters and simulations across each group.

Figure 2.

Phase 1 - BPD Participants Are More Certain About Themselves

We first examined self-representations of participants in phase 1. CON participants and BPD participants were equally prosocial (CON mean = -7.50; BPD mean = -6.59; Δμ = 0.92, 95%HDI: -1.24, 3.12) – both groups valued equal allocation of reward between themselves and their partners. BPD participants had lower preferences for earning higher absolute rewards (CON mean = 18.41 ; BPD mean = 10.57; Δμ = -7.83, 95%HDI: -11.06, -4.75). BPD participants were also more certain about both types of preference (Δμ = -0.89, 95%HDI: -1.01, - 0.75; Δμ = -0.32, 95%HDI: -0.60, -0.04) versus CON participants (Figure 2B).

Phase 2 – BPD Participants Use Neutral Priors And Form Rigid Beliefs

We next assessed how participants generated their prior beliefs about a partner in phase 2. CON participants were best fit by M1 which assumes the same median belief participants use in phase 1 is identical to their median prior belief about their partners. In contrast, BPD participants were best fit by M4 and generated a new median prior belief about their partners.

In BPD participants, only new beliefs about the relative preferences of partners (prosocial-competitive axis) differed - new median priors were larger than median preferences in phase 1 (mean = -0.47; Δμ = -6.10, 95%HDI: -7.60, -4.60). BPD priors about their partner’s relative preferences were also centred closely around 0 (Δμ = -0.39, 95%HDI: -0.77, -0.05), suggesting that BPD participants entered into the interaction with very neutral priors about their partner.

BPD participants were equally flexible around their prior beliefs about a partner’s relative reward preferences (Δμ = -1.60, 95%HDI: -3.42, 0.23), and were less flexible around their beliefs about a partner’s absolute reward preferences (Δμ=- 4.09, 95%HDI: -5.37, -2.80), versus their CON counterparts. (Figure 2B).

Belief updating in phase 2 was substantially less adaptive in BPD participants across the board. The median change in beliefs (from priors to posteriors) about a partner’s preferences was lower versus, controls (Δμ = -5.53, 95%HDI: -7.20, -4.00; Δμ = -10.02, 95%HDI: -12.81, -7.30). Posterior beliefs about partner were also more rigid in BPD versus CON (Δμ = -0.94, 95%HDI: -1.50, -0.45; Δμ = - 0.70, 95%HDI: -1.20, -0.25). This is perhaps unsurprising given the disintegrated priors of the BPD group, meaning they need to ‘travel less’ and thus have longer to converge on the beliefs of their partner.

Analysing belief updating on a more granular trial-by-trial basis revealed axial and group differences in belief refinement over the course of phase 2 (Figure 2C). We examined this by analysing the Kullback-Leibler divergence (D_KL) of beliefs between each trial in Phase 2, from t-1 to t over trial 1–54, using random-effect linear models.

Across both groups and belief types, the magnitude of belief updating reduced over time (linear estimate[D_KL] = -0.007,95%CI: -0.008, -0.005; t = -7.60, p < 0.001). Beliefs about a partner’s relative reward preferences were updated more vs. absolute reward preferences (linear estimate= 0.54, 95%CI: 0.47, 0.62; t = 14.00, p < 0.001). These interacted, such that initial flexibility over relative vs. absolute beliefs reduced over the course of phase 2 (linear estimate = -0.013, 95%CI: -0.015, -0.011; t = -10.81, p < 0.001).

CON participants remained more flexible than BPD participants along both axes (linear estimate = 0.40, 95%CI: 0.29, 0.51, t = 7.18, p < 0.001; linear estimate = 0.17, 95%CI: 0.29, 0.51, t=3.06, p=0.002). This interacted over time, such that the difference between groups, and the magnitude of belief updates decreased over time (linear estimate = -0.009, 95%CI:-0.012,-0.006, t = - 5.30, p < 0.001; linear estimate = -0.004, 95%CI:-0.008,-0.001, t = -2.78, p = 0.005) - CON participants and BPD participants eventually converged to an equivalent updating schedule (Figure 2C). Analyses of phase 2 belief updating suggests posterior beliefs are generally less sensitive to change in BPD versus CON.

Beliefs in phase 2 penetrated into reaction times (Figure 2D): all participants were slower at the start of phase 2 and sped up over time (linear estimate = -15.03, 95%CI: -21.06, -8.99; t = -4.88, p < 0.001). Baseline participant-partner similarity did not have an overall effect on reaction time but did interact with trial - as participant-partner similarity increased, reaction times early in phase 2 were significantly slower and this effect attenuated over time (linear estimate = -0.53, 95%CI: -0.75, -0.32; t = -4.91, p < 0.001). Reaction time did not vary between groups: both BPD and CON participants displayed the same effect. We also show that reaction times and belief updates in phase 2 were significantly coupled, such that larger shifts in posterior beliefs along both axes were associated with larger reaction times (linear estimate = 0.044, 95%CI: 0.027, 0.06, t = 5.01, p < 0.001; linear estimate = 0.021, 95%CI: 0.005, 0.039, t = 2.49, p = 0.012; Figure S9).

Phase 3 – BPD Participants Are Less Influenced by Partners

In the dominant model for the BPD group—M4—participants are not influenced in their phase 3 choices following exposure to their partner in phase 2. To further confirm this conclusion, we also analyzed participants under the assumption that M3 was the dominant model for both groups, considering that a minority of participants were best explained by this model. This analysis aligns with our primary model comparison (Figure 2E). CON participants altered their absolute median beliefs in phase 3 (linear estimate = 1.75, 95% CI: 0.73, 2.79; t = 3.36, p < 0.001) and increased their precision (linear estimate = 1.53, 95% CI: 0.65, 2.40; t = 3.43, p < 0.001) more than BPD participants. There was also an interaction with the type of belief: CON participants changed their median beliefs about relative reward along the prosocial-competitive axis more than their beliefs about absolute reward (linear estimate = 2.13, 95% CI: 0.09, 4.18; t = 2.06, p = 0.041), and became more precise along the same axis (linear estimate = 3.01,95% CI: 1.30,4.71; t = 3.47, p < 0.01), compared to BPD participants. This suggests that relative reward preferences are particularly resistant to change in BPD participants.

Figure 3.

Parameter Associations with Reported Trauma, Paranoia, and Attributed Intent

We collected psychometric data from participants prior to entering the task, and then additionally asked participants to attribute explicit intentions to their partner after phase 2. Attributions varied along two axes: the degree to which they believed their partner was motived by harmful intent (HI) and self-interest (SI).

Reported persecutory ideation (RGPTSB) and childhood trauma (CTQ) across both groups were associated with lower self-preferences for absolute reward (RGPTSB: ρ= -0.27, p = 0.007, CTQ: ρ= -0.25, p = 0.001) and higher competitive selfpreferences (RGPTSB: ρ = 0.29, p = 0.003, CTQ: ρ = 0.23, p = 0.02). Both the CTQ and RGPTSB were also associated with more rigid self-preferences about absolute reward (RGPTSB: ρ = -0.30, p = 0.003, CTQ: ρ = -0.50, p < 0.001), but not relative reward.

Reported CTQ was associated with a reduction in prior belief uncertainty (ρ = - 0.26, p = 0.008) and updating (ρ = -0.37, p < 0.001) about a partner’s relative preferences (Figure 4A). There was no association of reported childhood trauma and beliefs about a partner’s absolute preferences. In contrast, baseline reported RGPTSB was associated with a reduction in prior belief uncertainty and updating across the board (ρ = -0.28, p = 0.004; ρ = -0.22, p = 0.03; ρ = -0.30, p = 0.002; ρ = -0.25, p = 0.01).

Regarding participants’ mentalizing capacity assessed by the MZQ (higher scores equate to worse trait mentalizing), total scores were negatively associated with belief updating in phase 2 (ρ = -0.35, p < 0.001; ρ = -0.34, p < 0.001), but only increased prior belief uncertainty about a partner’s absolute preferences (ρ = - 0.25, p = 0.009). The MZQ was also negatively associated with social contagion along the prosocial-competitive axis (ρ = -0.43, p < 0.001). The credulity (ETMCQ) of participants was negatively associated with belief updating (ρ = -0.25, p = 0.013; ρ = -0.35, p<0.001), but was not associated with prior belief uncertainty about self-other disparity, nor with social contagion. See Supplementary Figure 7 for full correlations of parameters with all measures.

We also show how social contagion may be restricted as a result of trauma, paranoia, and less effective trait mentalizing. By assessing all participants under the assumption of M3 (where everyone is able to be influenced by their partner) allows a test of psychometric scores on preferences changes between phase 1 and 3 across our total population. We found a negative association between CTQ scores and absolute changes in self-preferences across the board (ρ = -0.26, p = 0.010; ρ = -0.22, p = 0.031), whereas RGPTSA and RGPTSB scores were only negatively associated with changes in self-preferences about relative reward (RGPTSA: ρ = -0.33, p < 0.001; RGPTSB: ρ = -0.31, p = 0.002). The MZQ was also associated with reduced social contagion effects for relative reward preferences (ρ =-0.43, p< 0.001). No other scale was affiliated with social contagion under M3 (see Supplementary Figure 8). Controlling for trait mentalizing (MZQ) nullified the relationship between RGPTS scores and social contagion, as well as CTQ scores and social contagion but only for relative reward. Thus, childhood trauma and trait paranoia may only result in less self-change when trait mentalizing is impacted.

We then tested parameter influences on explicit intentional attributions in Phase 2. Uncertainty about the self in phase 1 was not associated with either HI or SI attributions. Greater participant-partner disparity at baseline (before interaction) was distinctly associated with HI and SI (Figure 4B). Greater disparity of absolute preferences before learning was associated with reduced attributions of SI (ρ* = -0.22, p = 0.03), and greater disparity of relative preferences before learning exaggerated attributions of HI (ρ = 0.22, p = 0.03). This is likely due to partners being significantly less individualistic and prosocial on average compared to participants (Δρ[α] = -5.50, 95%HDI: -7.60, -3.60; Δμ[β] = 12, 95%HDI: 9.70, 14.00), thus partners are correctly recognised as less selfish and more competitive.

Greater prior uncertainty (before interaction) over a partner’s relative preferences was associated with increased HI (ρ = 0.26, p = 0.007) but not SI, according with prior work (Barnby et al., 2022). There was no association between prior uncertainty over absolute preferences with either attribution. Controlling for total belief updating about a partner’s relative reward preferences and baseline similarity * did not remove the association with HI (ρ = 0–21, P = 0.03). This suggests that expectations of greater difference, irrespective of one’s true difference between self-other, may exaggerate beliefs about the intentional harm of others.

Figure 4.

Discussion

We built and tested a theory of interpersonal generalization in a population of matched participants with (BPD) and without (CON) a diagnosis of borderline personality disorder using the Intentions Game, a three-phase social value orientation task. Both groups demonstrated equivalent behavioral accuracy but employed opposite strategies. CON participants used a process of self-other generalization to predict and align with their partners, while BPD participants maintained distinct representations of self and other. In phase 2, CON participants exhibited greater belief sensitivity to new information during observational learning, eventually adopting a similar updating regime to those with BPD. Our findings also indicate that reported childhood trauma and persecutory beliefs were linked to reduced flexibility when learning about partners, diminishing the influence of a partner’s behavior on self-change. Collectively, our results integrate prior computational and behavioral findings in BPD and provide a formal account of social information generalization in humans, alongside a concise social paradigm to test these processes.

The data replicate models of social generalization that have focused on individual processes of self-insertion and contagion, extending these theories by demonstrating both processes in conjunction. Models of self-insertion directly map participant preferences onto prior beliefs about others, which has been used to explain increased reaction times in observational learning of others’ snack food preferences (Tarantola et al., 2017), as well as improved predictive accuracy when matched with individuals of similar social values (Barnby et al., 2022). Both findings are replicated in this study. Although we did not explicitly model reaction times, we observed an interaction between reaction time reductions over time and interpersonal similarity at baseline. In tandem, models of social contagion have focused on intertemporal discounting and explain shifts in self-preferences as a function of uncertainty regarding self and others (Moutoussis et al., 2016). In both the dominant (M1) and sub-dominant (M3) models that best explained data in healthy participants, shifts in self-beliefs were also influenced by representational uncertainty of self and other: greater self-uncertainty and reduced other uncertainty led to larger shifts in self-beliefs.

The data also align with prior research on social impression formation, which suggests that humans form rapid evaluations of others that are refined over time (Bone et al., 2021; Moutoussis et al., 2023). This initial ‘heating’ and subsequent ‘cooling’ of beliefs corresponds to the computational complexity employed: model-based strategies are typically used early in interactions, transitioning to simpler, model-free computations once a partner’s behavior becomes predictable (Gęsiarz & Crockett, 2015; Guennouni & Speekenbrink, 2022). Our findings support this framework, demonstrating initial variability early in interactions followed by steady, minimal updating. Notably, participants with a BPD diagnosis exhibit a less sensitive updating profile compared to CON participants.

Disruptions in self-to-other generalization provide an explanation for previous computational findings related to task-based mentalizing in BPD. BPD is characterized by early life adversity and neglect, which result in diminished representations of self and other (Fonagy & Bateman, 2008). Studies tracking observational mentalizing reveal that individuals with BPD, compared to those without, place greater emphasis on social over internal cues when learning (Henco et al., 2020; Fineberg et al., 2018) and demonstrate reduced belief adaptation (Siegel et al., 2020), along with ‘splitting’ of latent social representations (Story et al., 2024). This heightened focus on others often leads to perceiving them as harmful. From the perspective of our model, those with BPD intensely focus on social information (Henco et al., 2020) due to the adoption of a new, neutral belief about others. The absence of constrained self-insertion may predispose them to ‘split’ beliefs (Story et al., 2024), as individuals with BPD reach the beliefs of their partner more rapidly, are less receptive to new information, and adopt greater belief precision (Siegel et al., 2020). This may represent an attempt to quickly reduce the uncertainty of a neutral prior. Essentially, individuals with BPD assume ambiguity and are quicker to settle on an explanation given limited data. Although self-insertion may intuitively seem counter to rational belief formation, it has important implications for sustaining trusting social bonds through moderation of information in the face of uncertainty.

Those with a diagnosis of BPD also show reduced permeability in generalising from other to self. While prior research has predominantly focused on how those with BPD use information to form impressions, it has not typically examined whether these impressions affect the self. In interactive trust paradigms, neural responses to monetary offers from others to the self were substantially blunted in individuals with BPD compared to those without (King-Casas et al., 2008). Similarly, in non-social reward tasks, those with BPD show reduced neural feedback-related negativity amplitudes, which obstructs feedback-related self-change (Stewart et al., 2019; Vega et al., 2013). Our results suggest a mechanistic basis for social contagion, indicating that self-rigidity prevents observed social behaviors from generalizing to the self, potentially exacerbated by childhood trauma, paranoia, and impaired mentalizing capabilities. Resistance to social influence may serve as a protective response but can also contribute to the pervasive loneliness experienced by individuals with BPD, even in the absence of social isolation (Liebke et al., 2017).

Clinical implications of our work underscores the importance of consistency and stability in clinical support for individuals with a diagnosis of BPD. Encouragingly, we found that those with BPD were not entirely impermeable to observed behavior, suggesting that consistent external models of trust could be internalized over time. Restoring a stable sense of self through social learning and effective mentalizing, along with a consistent focus on differentiating self from other (de Meulemeester et al., 2021), are central to mentalization-based therapies (Bateman & Fonagy, 2010; Smits et al., 2024) and other evidence-based treatments for BPD. We hope that our paradigm and model can offer insights into the effectiveness of these and other therapies in driving mechanistic psychological change.

More broadly, our model bridges formal theories of associative learning and social cognition. Reinforcement learning approaches have effectively organized theories around uncertainty navigation in non-social contexts (Piray et al., 2021; Zika, 2023). However, humans do not function in isolation. Bayesian models of internal and external social beliefs are better suited to capture the dynamic nature of time, context, and uncertainty during interactions (FeldmanHall & Nassar, 2021; Velez & Gweon, 2021). This is particularly important for understanding psychiatric disorders (Barnby et al., 2023). Our paradigm is concise, visually engaging, includes straightforward rules and instructions, and allows for tight experimental control over partner similarity to promote learning. Our model and paradigm effectively capture core social psychological principles grounded in general computational approaches to learning and uncertainty, elucidating key aspects of human social interaction and exchange.

We note some limitations to our study. Primarily, we focused on the ability of individuals to integrate their self-concept into beliefs about others. It is also possible that humans possess strong, salient representations of others (or groups of others) that serve as dominant templates for learning. This may be particularly relevant for individuals with BPD, who will often have interpersonal experiences of abuse, neglect, or other forms of distress. The use of a salient, negative other-prior as a basis for learning was not measured in this study, but it may explain the ambivalent prior observed in phase 2, where a mixture of self and notional other influences belief formation, leading to rigid belief updating. Individuals with BPD may integrate priors from different sources as a mixture. We can simulate this by modelling a causal framework that incorporates priors based on both self and a strong memory impression of a notional other (Figure S3). However, a strength of our data is that we observed impression formation independent of valence—impressions were formed regardless of whether a partner was more or less prosocial or selfish than the participant (Figure S4). This supports our hypothesis that a vulnerable self-model and lack of self-insertion contribute to the formation of overly precise beliefs during learning as a means of rapidly reducing uncertainty. Even if a mixture model better explains the ambivalent prior in phase 2, it would still support a general hypothesis about the fractured concept of self and other in BPD.

Another strength of our work is demonstrating processes of self-insertion and contagion under minimal interaction conditions: simple observation alone was sufficient to elicit both processes. However, this is also a limitation. While we predict that these processes will apply in more naturalistic settings, this has yet to be tested, and it remains unclear whether these effects will persist in richer conditions, particularly when higher affective arousal and challenges to mentalising are present. Lastly, the action space and parameters governing choice in our study were quite simple—two actions influenced by two parameters. This was a deliberate computational choice to avoid overly complex action spaces that may be difficult to fit to real human data, and which might fail to capture how these mechanisms operate in the context of increasing action and model complexity.

Our findings open new possibilities for testing how social uncertainty across the lifespan, and in the context of ill-health, may explain the formation and maintenance of healthy social bonds as well as their disruption. We make two key predictions: 1. The self is an evolving and dynamic concept, particularly susceptible to peer influence during adolescence. We predict that adolescents will use self-insertion to a lesser degree (if at all) than adults in our sample, and that the extent of social contagion in our paradigm will correlate with reported peer influence in other areas. We further predict that the degree of social contagion will correspond to brain regions associated with self-processing (Sebastian, Burnett & Blakemore, 2008), and that these contagion effects will diminish as individuals progress into emerging and full adulthood. 2. Psychosis is conceptualized as a heightened absorption in self-generated conscious experiences, leading to a collapse of the internal and external boundaries of self and other (Humpston, 2018). We predict that in our paradigm, this will manifest as an exaggeration of self-insertion when predicting others, accompanied by low learning rates and minimal social contagion effects.

Materials and methods

Participants

We used a case-control, between-subjects design with 103 participants: a control group from the general population (N = 53) and a clinical group diagnosed with BPD (N = 50). Both groups were recruited for a larger study investigating social exchanges in BPD and Anti-Social Personality Disorder (approved by the Research Ethics Committee for Wales, 12/WA/0283). The control and clinical groups were matched on age, sex, years in education, and the English Indices of Deprivation based on the 2019 census (loD 2019; Ministry of Housing, Communities & Local Government, 2019). Participants received £70 compensation for completing questionnaires and online tasks which included the Intentions Game. They also received a performance bonus if they were entered into the lottery for surpassing 1000 points over the course of the game.

Participants for the control group were recruited through an advertisement on the Call For Participants website (https://www.callforparticipants.com), local community services and adult schools. Inclusion criteria required control participants to have no pre-existing or current diagnoses of mental health disorders, neurological disorders, or traumatic brain injuries. Additionally, control participants must not have been currently in therapy or taking medication for any psychiatric disorders.

BPD participants were recruited through referrals by psychiatrists, psychotherapists, and trainee clinical psychologists within personality disorder services across 9 NHS Foundation Trusts in the London, and 3 NHS Foundation Trusts across England (Devon, Merseyside, Cambridgeshire). Participants were also recruited through the UCLH website, where the study was advertised. Individuals who discovered the study through this platform and were interested in participating initiated contact themselves. To be included in the study, all participants needed to have, or meet criteria for, a primary diagnosis of BPD (or emotionally-unstable personality disorder or complex emotional needs) based on a clinical assessment and be under the care of one of the trusts collaborating in recruitment or have a general practitioner whose details they were willing to provide. Clinical participants with recent psychotic episodes, severe learning disability, or current or past neurological disorders were excluded.

Psychometric Measures

Green et al. Paranoid Thought Scale (GPTS).

The GPTS assesses paranoid thoughts, including ideas of social reference (scale A) and persecution (scale B), in both general and clinical populations (Green et al., 2008). Each item is scored from 0 (not at all) to 5 (totally) concerning endorsement of each item. We retained items from the GPTS that were consistent with the revised version outlined in Freeman et al., 2021 (Revised GPTS; R-GPTS). The R-GPTS has demonstrated excellent psychometric properties (Freeman et al., 2021), making it a reliable and valid tool for assessing trait paranoid thoughts in non-clinical and clinical populations.

Childhood Trauma Questionnaire (CTQ)

The Childhood Trauma Questionnaire is used to screen for maltreatment history (Bernstein et al., 2003). Each item is scored from 1 (never true) to 5 (very often true). The CTQ has showed good internal consistency reliability across the five scales (Sacchi et al., 2018) and good construct validity based on significant associations with stress responsivity (McMahon et al., 2022), and dissociation (Nobakht et al., 2021).

Certainty About Mental States Questionnaire (CAMSQ)

The CAMSQ assesses one’s certainty in classifying the mental states of oneself and others at an abstract level (Müller et al., 2023), e.g. ‘I know what other people think of me’ and ‘I know my feelings’. Each subscale is scored from 1 (never) to 7 (always). In US and German samples, the CAMSQ showed high internal consistency for Self-Certainty (ω = .90/.88) and Other-Certainty (ω = .91/.89) subscales, and high two-week test-retest reliability for Self-Certainty (r = .85), Other-Certainty (r = .78), and Other-Self-Discrepancy (r = .82) scores (Müller et al., 2023).

Mentalisation Questionnaire (MZQ)

The MZQ is a 15-item questionnaire assessing an individual’s trait mentalizing, i.e., one’s ability to understand and interpret their own and others’ mental states (Hausberg et al., 2012). The MZQ demonstrated good internal consistency (a = .81) and test-retest reliability (r = .76), and was sensitive to change over a 6-month follow-up period and showed good criterion-related validity, distinguishing individuals with BPD from those without BPD (Hausberg et al., 2012). A higher score reflects worse trait mentalizing.

Epistemic Trust, Mistrust and Credulity Questionnaire

The ETMCQ is a 15-item measure calibrated to assess trust (e.g. ‘I usually ask people for advice when I have a personal problem), mistrust (e.g. Td prefer to find things out for myself on the internet rather than asking people for information), and credulity (e.g. ‘I am often considered naive because I believe almost anything that people tell me’; Campbell et al., 2021). Each item is scored from 1 (Strongly Disagree) to 7(Strongly Agree).

Paradigm, procedure and server architecture

The Intentions Game is a repeated social-value orientation paradigm with three phases.

In Phase 1 of the Intentions Game, participants take on the role of the decider with an anonymous partner over 36 trials. In each trial, participants choose between two options to distribute points between themselves and their partners. Participants make 12 choices each between prosocial and competitive (e.g. Option 1 =[10,10], Option 2 = [10,5]) individualistic and competitive (e.g. Option 1=[10,5], Option 2=[8,1]), and prosocial and individualistic options (e.g. Option 1 =[5,5], Option 2=[10,5]). Phase 1 choices allowed experimenters to classify participants’ social preferences as prosocial (preferring equal outcomes), individualistic (maximising own payoff), or competitive (maximising relative payoff difference at the cost of lower self-gain).

We included a task environment that balanced each type of choice pair (see Supplementary Table 1).

In phase 2 of the game, participants were matched with a new anonymous partner and played the role of the recipient over 54 trials. In this phase, the participants predicted which of the two options their partner would choose on each trial. Trial numerical values for self and other were identical to Phase 1. Partners’ decisions were determined via a dynamic algorithm (Burgess et al., 2023) to ensure partners were approximately ~50% different from the participants’ based on participants’ choices in phase 1. To surmise this architecture, we implemented a version of the client-server paradigm hosted on an Amazon Web Service (AWS) LightSail server, where the web-based behavioural task (implemented with JavaScript in Gorilla.sc) acted as the client and exchanged information with a remote AWS server. The server received all anonymised behavioural data following phase 1. The Application Programming Interface (API) to interact with the server used a customizable R script (v4.3) to process the received data from the participant, and additional R scripts were used to process and generate output for the participant. A function within the backend scripts first used Bayesian inference to approximate a participant’s parameters for phase 1. It then simulated what choices the participant would have made in phase 2 had the participant been in the role of the partner. The algorithm then sought to find parameters that would be at least 50% dissimilar from participant parameters with respect to the generated choices of those parameters. This allowed the task behaviour of phase 2 to be dynamically updated in response to participant choices in phase 1. This facilitated tight control over the state of the task and enabled advanced computations to be performed on participant data beyond the capabilities of a web browser.

Participants were incentivised in phase 2 to predict accurately, as accurate predictions would contribute to their total point scores (total correct answers were multiplied by 10 and added to their points) and determined their entry into the lottery to win an extra £20 Amazon voucher. After participants had made their predictions, they were given feedback informed on whether their predictions were accurate.

At the end of phase 2, participants were asked to rate (1) the extent to which they thought their partner was driven by the desire to earn points in this task overall (self-interest) and (2) the extent to which they thought their partner was driven by the desire to reduce the participant’s points in this task overall (attribution of harmful intent). The answers were presented using two separate sliders from 0 to 100; the sliders were initialised to be invisible until the participants made the first click.

Phase 3 was identical to phase 1 except that participants were matched with a new anonymous partner. Participants would take on the decider role similar to phase 1 which allowed experimenters to estimate whether the observation of their partner in phase 2 had an influence on participants in phase 3.

Behavioural Analysis

All analysis was conducted in R (v. 4.3.3) on a macbook pro (M2 Max; OS=Ventura13.5). All individual numeric values extraneous of statistical tests are reported with their mean and standard deviation (mean=KCWM8V4, SD=YY). All statistical tests where dependent variables mapped one value to one participant (e.g. trait psychometric scores) were conducted as linear models, with the regression coefficient, 95% confidence interval (95%CI), t-value and p-value reported like so (linear estimate=KCWM8V4, 95%CI:AA,BB; t=CC, p=DD). When dependent variables mapped multiple values to each participant (e.g. trial-by-trial accuracy or reaction time) random-effects linear modelling was used. All correlations used Pearson estimates (r) unless distributions were non-normal, in which case Spearman-ranked correlations (ρ) were performed.

Model space and Computational Analysis

We apply four computational hypotheses (M1-M4) which could explain the data collected from the Intentions Game (Figure 1), centred around formal principles of self-insertion and social contagion. Self-insertion states that a self inserts their own preferences into their beliefs about others (Anderson & Chen, 2002; Kreuger & Clement, 1994); Social Contagion states that a self’s preferences will change when exposed to the preferences of an other (Frith & Frith, 2012). In each case, cognitive representations of self and other are allowed to intermingle to form a new hybrid of the two for the purposes of computational efficiency and/or social bonding.

We note some important assumptions in our notation going forward. In dyadic social interaction, both parties are trying to estimate and predict the true state (θ) of the self (θ_S) and the other (θ_o). However, this estimation is inherently imperfect. Theories of social inference need to consider three sources of noisy estimation of this quantity: a self’s (s) metacognitive model of their own state, , their partner’s (o) state, , and finally the experimenter’s approximation of both quantities, (Barnby et al., 2024). In this work we consider the experimenter’s approximation of the self’s state (phasel), the self’s approximation of their other (phase 2), and how exposure to a partner may influence (phase 3). We term the self the participant (ppt) and the other the partner (par) and assume in phase 1, in phase 2, and are the shifted participant preferences following exposure to the partner.

All models assumed a constricted Fehr-Schmidt utility function was used by participants and partners to calculate the utility of two options in each trial within the task.

In phase 1, participants made binary choices c^t, t = {1… T} about whether option 1 or option 2 should be chosen given the returns for each option pair, R^t = {R^t;1: R^t;2} =.

Here, α_ppt describes the weight a participant places on their own payoff (in one reduced model we set α_ppt =1), and β_ppt, the weight a participant places on their payoff relative to the payoff of their partner. Large positive or negative values of β_ppt indicate respectively that participants like or dislike earning more than their partner.

We can therefore describe these terms α and β as reflecting preferences for absolute and relative payoffs, respectively. For efficiency we discretised states of α_ppt from 0- 30 (increments of 0.125) and β_ppt from -30 to 30 (increments of 0.25).

Over this state space we can construct a belief that participants are estimated to hold which generate their choices, C. Herein, we refer to this belief as θ_ppt, where θ_ppt is a matrix over a fixed grid of α_ppt and β_ppt values. In the models, θ_ppt is drawn from a normal distribution made from a central tendency, , and a standard deviation, . The standard deviation around the central tendency allows for stochastic choice behaviour consistent with random utility models (Block, 1974; McFadden, 1974). We invert the model to estimate θ_ppt based on a participant’s choices given their likelihood of choosing c^t= 1 :

When is larger, a participant’s choices in Phase 1 are estimated to be less deterministic and more stochastic - i.e. they are less sure about their preferences along each dimension. This consideration will become important for choices made in phase 3.

In phase 2, over 54 trials, we then model the participants binary predictions , t = {1… T) about whether option 1 or 2 would be chosen by their partner given the returns R^t = {R^t;1; R^t;2} = for each pair of options. They then were given feedback about the partner’s true decision which we note as d^f. We assumed the participant predict the partner in the same way they would themselves, ranging along two dimensions, α_par and β_par which was needed to be inferred through observation, using a likelihood for d^t of LL = log [p(d^t = 1|α_par, β_par, R^t)] using the same formula as phase 1. We note the belief about α_par and β_par together as θ_par, represented as a matrix over a fixed grid of α_par and β_par values.

The partner decisions, D^t = {d¹,d² …,d^T} are then used to update the participants beliefs about the partner, written as p(θ_par|D^t), starting with prior p(θ_par |D⁰). Both M1 and M2 assume participants use their own central tendency, , as a starting point for their prior beliefs about their partner as theoretically outlined as a self-insertion bias (Barnby et al., 2024) which draws from past computational work (Barnby et al., 2022; Tarantola et al., 2017). We also assumed participants used a new standard deviation which allowed for participants to believe their partner may be different from them (belief flexibility). Therefore we have:

In models M3 and M4, we assume participant’s may instead use a new central tendency (rather than their own) as prior beliefs over their partner. This are free parameters to be approximated, .

In all cases, we assume participants update their beliefs about their partner’s social preferences given their partner’s decisions D along trials 1–54 according to Bayes rule:

We can then marginalise over to calculate the belief participants had over their participant’s social value preferences.

We assume that participants predict the partner’s decision in the next trial by calculating the probability determined by the utility differences ΔU_α,β(R^t+1) as in phase 1, summed over the joint distribution of partner parameters, :

And then performed probability matching, so that:

In the third phase participants are once again asked to make choices for themselves and a new anonymous partner over 36 trials with an assumed identical utility function as in phase 1. In model M1 and M3 we assume participants use a combination of their own preferences and the posterior beliefs about their partner to form a new distribution to select between the two options available on each trial. This draws from the same formulation used previously (Moutoussis et al. 2016). In essence, we state that participants know their true preferences in phase 1 but are unsure about them. The inferred partner beliefs provides information to the participant about some common preference distribution both share, which in turn informs the participant’s own choices ć^t, t = {1 … T} in the form of an adjusted belief along each dimension for phase 3, and (eq. 7), using a log likelihood of . We refer to and together as for convenience, where is a matrix over a grid of fixed values of and . To note: models M2 and M4 do not assume participants undergo this change, and instead use their original phase 1 beliefs to make choices .

Where and are the standard deviation and central tendency of the final posterior inference about the partner, .

All computational models were fitted using a Hierarchical Bayesian Inference (HBI) algorithm which allows hierarchical parameter estimation while assuming random effects for group and individual model responsibility (Piray et al., 2019). During fitting we added a small noise floor to distributions (2.22e^-16) before normalisation for numerical stability. Parameters were estimated using the HBI in native space drawing from broad priors (μM=0, σ²M = 6.5; where M={M1, M2, M3, M4}). This process was run independently for each group. Parameters were transformed into model-relevant space for analysis. All models and hierarchical fitting was implemented in Matlab (Version R2022B). All other analyses were conducted in R (version 4.3.3; arm64 build) running on Mac OS (Ventura 13.0).

To conduct model recovery we simulated synthetic participants (CON=53; BPD=50) using their fitted parameters from the dominant model of the group (CON=M1; BPD=M4). We then performed model fitting with an identical procedure to the real behavioural data. We tested associations between model responsibility and individual parameters for the real and recovered models, as well as the association between choices and predictions made by the model from simulation and the choices and predictions made by participants in each trial.

Differences between groups for individual-level parameters were estimated using hierarchical Bayesian t-tests (Bååth, 2014). This used JAGS as a backend MCMC sampler; differences in mean between groups (Δμ) are additionally reported with their corresponding posterior 95% High Density Interval (95%HDI). Belief updates were calculated as the Kullback-Leibler Divergence between probabilities (P) from trial t-1 to t, marginalised along all possible states, S={s¹,s²,…,sⁿ}: *.

Supplementary materials

Supplementary Figure 1.

Supplementary Figure 2.

Supplementary Figure 3.

Supplementary Figure 4.

Supplementary Figure 5.

Supplementary Figure 6.

Supplementary Figure 7.

Supplementary Figure 8.

Supplementary Figure 9.

Supplementary Table 1.

Open data and code

https://github.com/josephmbarnby/SocialTransfer_Barnby_etal_2024

Acknowledgements

We would like to greatly thank all participants who took part in the research.

Additional information

CRediT

JMB: Conceptualisation, Data Curation, Investigation, Formal Analysis, Methodology, Project Administration, Software, Supervision, Visualisation, Writing – Original Draft, Writing – Review and Editing. JN: Investigation, Methodology, Writing – Original Draft, Writing – Review and Editing. JG: Conceptualisation, Investigation, Project Administration, Resources, Writing – Review and Editing. MW: Project Administration. HB: Software, Writing – Review and Editing. LR: Resources, Writing – Review and Editing. GC: Validation, Writing – Review and Editing. JK: Supervision, Writing – Review and Editing. PRM: Resources, Writing – Review and Editing. PD: Conceptualisation, Formal Analysis, Writing – Review and Editing. TN: Conceptualisation, Project Administration, Resources, Supervision, Writing – Review and Editing. PF: Conceptualisation, Resources, Supervision, Writing – Review and Editing.

Funding

JMB is supported by a Wellcome Trust award (228268/Z/23/Z) and as a scholar within the FENS-Kavli Network of Excellence. Funding for PD was from the Max Planck Society and the Humboldt Foundation. PD is a member of the Machine Learning Cluster of Excellence, EXC number 2064/1 – Project number 39072764 and of the Else Kroner Medical Scientist College “ClinbrAln: Artificial Intelligence for Clinical Brain Research”.