Schematic overview of the experimental design.

(A) The baseline donation phase. Participants were presented with twenty charities, each accompanied by a brief description. For each charity, they were asked to decide how much they were willing to donate within the specified range. These initial responses provided a baseline measure of individual giving preferences in the absence of social information. (B) The observation of others’ donations and the second donation phase. For each charity, participants engaged in five sequential trials in which they first predicted the donation of another individual and then received feedback about the actual donation. This procedure exposed participants to a distribution of others’ giving behavior. After completing all five trials for a given charity, participants made a second donation decision for that same charity, allowing assessment of changes in giving following social information. The set of charities in this phase was identical to that in the baseline phase. (C) The experimental manipulation. The distribution of others’ donations was manipulated along two dimensions - mean level and variability (SD) - in a 2 * 2 between-subject design. Participants were randomly assigned to one of four conditions: Low Mean-Low SD (LM-LSD); Low Mean-High SD (LM-HSD); High Mean-Low SD (HM-LSD); High Mean-High SD (HM-HSD). The histogram and table display the distributions and descriptive statistics of the manipulated donation values in Experiment 1.

Overview of the four experiments.

Experiment 1-3 recruited college students and involved hypothetical donation decisions with ranges of $0-$2, $0-$10, and $0-$100, respectively. Experiment 4 recruited participants from the U.S. general population via Prolific and implemented an incentive-compatible design in which donations ranged from 0 to 100 points (equivalent to $1). Across all experiments, the mean and standard deviation of observed others’ donations were experimentally manipulated (Fig. S1). In Experiment 1, we manipulated the overall mean ($0.6 vs. $1.4) and standard deviation (0.1 vs. 0.3) of others’ donations, computed by pooling donation amounts across all charities. Experiment 2 adopted the same distributional structure as Experiment 1, with all donation values scaled by a factor of 5. Experiment 3 further extended the donation range ($0-$100) and increased the contrast in the standard deviation of others’ donations between the Low-SD and High-SD conditions. Finally, Experiment 4 implemented an incentive-compatible design with more fine-grained donation settings, ensuring that the mean of others’ donations was matched across SD conditions at the charity level while their standard deviation varied (Method S3 and Fig. S2).

The mean of observed others’ donations robustly modulated shifts in individual donation amounts.

Across all four experiments, a significant interaction between the mean of others’ donations and phase was found across all four experiments (Exp 1: b = -0.34, SE = 0.023, t (12652) = -14.83, p < 0.001; Exp 2: b = -1.83, SE = 0.10, t(13432) = -18.16, p < 0.001; Exp 3: b = -18.03, SE = 1.02, t(13627) = -17.71, p < 0.001; Exp 4: b = -15.42, SE = 0.87, t(14563) = -17.63, p < 0.001; Table S4). Specifically, participants significantly increased their own donation amounts after observing generous donations from others, but significantly decreased their donations after observing stingy donations of others. (A - D) displayed the results from Experiments 1 - 4. Group averages are shown as colored dots with error bars indicating ± 1 standard error of the mean (SEM), whereas faint lines and dots represent individual participants.

Variations of individual donation amounts decreased after observing others, with a stronger reduction in Low-SD groups.

The standard deviation of individual donation amounts significantly decreased following observing others’ donations across all experiments (Exp1: F(1, 321) = 146.63, p < 0.001; Exp2: F(1, 341) = 260.99, p < 0.001; Exp3: F(1, 346) = 144.57, p < 0.001; Exp4: F(1, 370) = 73.18, p < 0.001 ; Table S4). This reduction was more pronounced when others’ donations were less variable (Low-SD conditions). This pattern was significant in Experiments 2 - 4 and marginal in Experiment 1 (Exp1: F(1, 321) = 2.87, p = 0.09; Exp2: F(1, 341) = 14.64, p < 0.001 ; Exp3: F(1, 346) = 18.44, p < 0.001; Exp4: F(1, 370) = 14.55, p < 0.001). The results from Experiments 1 - 4 were displayed in (A - D). Group averages are shown as colored dots with error bars indicating ± 1 standard error of the mean (SEM), whereas faint lines and dots represent individual participants.

The mean and variability effects of others’ donations generalized to novel charitable giving.

(A) After the observation of others’ donation and second donation phase, participants in High-Mean conditions donated more to novel charities than those in Low-Mean conditions, despite the absence of further social input (b = 16.94, SE = 3.37, t(370) = 5.03, p < 0.001; Table S6). (B) The standard deviation of individual novel donations was significantly smaller in Low-SD conditions relative to High-SD conditions, an effect most evident in Low-Mean contexts (F (1,370) = 9.87, p = 0.002; Table S7). Group averages are shown as colored dots with error bars indicating ± 1 standard error of the mean (SEM), whereas faint dots represent individual participants.

Formal model comparison.

(A) The schematic of the reinforcement learning model used to fit participants’ choices. This model assumes that individuals updated their beliefs about others’ donations through prediction errors, anchored to participants’ initial donations as geometrically weighted references, and subsequently integrated these learned estimates with their own preferences to determine their second donations. (B - E) For each experiment, we computed the summed AIC (Akaike Information Criterion), the summed BIC (Bayesian Information Criterion) and the PXP (protected exceedance probability) for each candidate model (Table S8). The model with lowest summed AIC and BIC were treated as the reference model, and ∆AIC and ABIC values were computed by subtracting the information criterion of the reference model from that of each competing model. Smaller ∆AIC/∆BIC values indicate better fit, and PXP values indicate stronger evidence in favor of that model at the group level. In Experiment 1 - 3, the Hybrid of D1 and Prediction model (Model 3) provided the best account of participants’ behaviors, as indicated by converging evidence from all three model comparison metrics. Though a variant of the Hybrid of D1 and Prediction model (Model 3b) yielded the lowest AIC and BIC in Experiment 4, the Hybrid of D1 and Prediction model (Model 3) showed a higher PXP value, suggesting greater population-level support. Collectively, these model comparison results indicate that participants relied on both their initial donation and the updated prediction of others’ donation to guide their second donation, and used feedback about others’ actual donations to update their predictions. Asterisks (*) denote the best-fitting model according to each model comparison metric.

Positive association between psychopathy and the social information weight parameter.

The total score of psychopath was positively associated with the social information weight parameter across all experiments (Exp1: Spearman ρ = 0.11, p = 0.046; Exp2: Spearman ρ = 0.18, p = 0.001; Exp3: Spearman ρ = 0.14, p = 0.011; Exp4: ρ = 0.28, p < 0.001). (A - D) presented the results from Experiment 1 - 4.

Positive association between psychopathy and the social information weight in a perceptual task.

(A) Example trial of the BEAST Task (Berlin Estimate AdjuStment Task). Participants were presented with an image of animals, and then estimated the number of animals displayed. They then observed another person’s estimate and were given a chance to adjust their estimate. (B) The total psychopathy score was positively associated with the social information weight in this perceptual task (Spearman ρ = 0.15, p = 0.004).

The distribution of social information across conditions in all experiments.

Histograms depict the distribution of donation amounts provided by others, presented as social information to participants. In each experiment (A - D), participants were randomly assigned to one of four conditions in a 2 (Mean: Low vs. High) × 2 (SD: Low vs. High) between-subjects design. The distributions reflect the experimental manipulation of the mean and variability of social information in each condition (Experiment 1: LM-Low-SD condition: Mean = 0.593, SD = 0.103; Low-Mean-High-SD condition: Mean = 0.604, SD = 0.284; High-Mean-Low-SD condition: Mean = 1.400, SD = 0.115; High-Mean- High-SD condition: Mean = 1.401, SD = 0.292; Experiment 2: LSD-LSD condition: Mean = 3.00, SD = 0.514; LM-HSD condition: Mean = 3.02, SD = 1.418; HM-LSD condition: Mean = 7.00, SD = 0.576; HM-HSD condition: Mean = 7.00, SD =1.460; Experiment 3: LM-LSD condition: Mean = 29.76, SD = 4.035; LM-HSD condition: Mean = 30.74, SD = 16.089; HM-LSD condition: Mean = 70.30, SD = 4.049; HM-HSD condition: Mean = 69.42, SD = 16.466; Experiment 4: LM-LSD condition: Mean = 29.65, SD = 4.191; LM-HSD condition: Mean = 29.65, SD = 15.456; HM-LSD condition: Mean = 69.65, SD = 4.191; HM-HSD condition: Mean = 69.65, SD = 15.456).

Item-level social information values across charity items and conditions in all experiments.

Each panel displays the observed donation amounts presented as social information for each charity item (Items 1-20) across four conditions (LowMean-LowSD, LowMean-HighSD, HighMean-LowSD, HighMean-HighSD). The x-axis represents the value of others’ donation amounts, and the y-axis represents the charity item. Gray dots denote individual observed donations (five per item), and red dots represent the average of the five observed donations for each charity item. In Experiment 1 - 3 (A - C), the mean and standard deviation of social information were manipulated at the aggregate level across items. At the group level, HighMean conditions had larger average donation amounts than LowMean conditions, and HighSD conditions had greater variability than LowSD conditions. However, these constraints were implemented across items rather than within each item, such that item-level means differed between SD groups. In Experiment 4 (D), social information was manipulated at the charity-item level to eliminate this potential confound. Specifically, for each charity item, the mean of the five observed donations was held constant between LowSD and HighSD conditions, while the standard deviation of the five observed donations was systematically larger in HighSD than LowSD conditions. This design ensured that variability effects could be examined independently of the mean-related effects.

Exposure to others’ donations promoted convergence of individual donations toward group giving, especially when others’ donations were consistent.

The pseudo-SD of individual donations, indexing dispersion of individual donations around others’ mean donations, significantly decreased after observing others’ donations in all experiments ((Expl: F(1, 321) = 372.79,p < 0.001, partial η2 = 0.54; Exp2: F(1, 341) = 464.22,p < 0.001, partial η2 = 0.58; Exp3: F(1, 346) = 397.08,p < 0.001, partial η2 = 0.53; Exp4: F(1, 370) = 238.73,p < 0.001, partial η2 = 0.39; Table S5). This convergence effect was significantly larger in Low-SD conditions in Experiment 2 - 4 and marginal in Experiment 1 (Exp1: F(1, 321) = 3.56, p = 0.06, partial η2 = 0.01; Exp2: F(1, 341) = 7.82, p = 0.005, partial η2 = 0.02; Exp3: F(1, 346) = 10.43, p = 0.001, partial η2 = 0.03; Exp4: F(1, 370) = 10.72, p = 0.001, partial η2 = 0.03). Group averages are shown as colored dots with error bars indicating ± 1 standard error of the mean (SEM), whereas faint lines and dots represent individual participants.

Model recovery.

To assess whether our tested models could be reliably distinguished, model recovery analyses were performed (A - D). For each experiment, simulated datasets were generated from each candidate model (N = 360 artificial agents; 85 simulated agents per condition), and Gaussian noise was added. All candidate models were fitted to the simulated data and compared. Values in the confusion matrices reflect the probabilities that a candidate model is selected as the best-fitting model for data generated from a given model, according to BIC. Across all experiments, the confusion matrices exhibited strong diagonal dominance, demonstrating great model recovery and clear separation among models.

Parameter recovery.

To examine whether parameters of the winning model are recoverable, parameter recovery analyses were performed (A - D). For each experiment, we generated datasets from the winning model (N = 360 artificial agents; 85 simulated agents per condition) with added Gaussian noise. The winning model was then fitted to the simulated data. Parameter recovery was quantified by computing the correlation between true and fitted parameter values, with higher correlations indicating better recovery. Across all experiments, parameter recovery was strong: Spearman correlations between true and recovered values for the learning rate (α), relative weight on initial donations (λ), and social information weight (w) all exceeded 0.89.

Posterior predictive check: the predicted donation amount.

The linear mixed-effects model conducted on donation amounts simulated from the winning model revealed a significant interaction between the mean of others’ donations and the phase across all four experiments (Exp 1: b = - 0.29, SE = 0.021, t(12613) = -13.96,p < 0.001, 95% CI = [-0.34, -0.25]; Exp 2: b = -1.68, SE = 0.09, t(13432) = -18.06,p < 0.001, 95% CI = [-1.87, -1.50]; Exp 3: b = -15.66, SE = 0.94, t(13627) = -16.74,p < 0.001, 95% CI = [-17.49, -13.82]; Exp 4: b = -14.44, SE = 0.79, t(14563) = -18.27,p < 0.001, 95% CI = [-16.00, -12.90]). This pattern mirrors the real data, indicating that the winning model successfully captures the changes in the central tendency of individual donations. Solid lines indicate the observed donation behaviors, and dashed lines indicate model predictions generated using the best-fitting parameters of the winning model. Magenta dots represent the simulated values from the winning model.

Posterior predictive check: the standard deviation of the predicted donation amount.

Mixed-effects ANOVAs conducted on the SD of predicted donation amounts revealed a significant main effect of the phase across all four experiments (Expl: F(1, 320) = 833.875,p < 0.001, partial η2 = 0.72; Exp2: F(1, 341) = 927.77,p < 0.001, partial η2 = 0.73; Exp3: F(1, 346) = 766.36,p < 0.001, partial η2 = 0.69; Exp4: F(1, 370) = 443.04,p < 0.001, partial η2 = 0.55). Moreover, the between the phase and the variability of others’ donations was significant across all experiments (Exp1: F(1, 320) = 6.34, p = 0.01, partial η2 = 0.02; Exp2: F(1, 341) = 14.64,p < 0.001, partial η2 = 0.04; Exp3: F(1, 346) = 18.44,p < 0.001, partial η2 = 0.05; Exp4: F(1, 370) = 14.55,p < 0.001, partial η2 = 0.04). These results suggest that the winning model captures the variability dynamics observed in the real data. Solid lines indicate the observed donation behaviors, and dashed lines indicate model predictions generated using the best-fitting parameters of the winning model. Magenta dots represent the simulated values from the winning model.

Posterior predictive check: the Pseudo SD of the predicted donation amount.

Mixedeffects ANOVAs conducted on the Pseudo SD of predicted donation amounts revealed a significant main effect of the phase across all four experiments (Exp1: F(1, 320) = 833.875,p < 0.001, partial η2 = 0.72; Exp2: F(1, 341) = 927.77,p < 0.001, partial η2 = 0.73; Exp3: F(1, 346) = 766.36,p < 0.001, partial η2 = 0.69; Exp4: F(1, 370) = 443.04,p < 0.001, partial η2 = 0.55). Moreover, we observed a significant interaction between the phase and the variability of others’ donations (Exp1: F(1, 320) = 6.34, p = 0.01, partial η2 = 0.02; Exp2: F(1, 341) = 14.64,p < 0.001, partial η2 = 0.04; Exp3: F(1, 346) = 18.44,p < 0.001, partial η2 = 0.05; Exp4: F(1, 370) = 14.55,p < 0.001, partial η2 = 0.04). These results demonstrate that the winning model generates variability patterns closely matching those observed in the real data. Solid lines indicate the observed donation behaviors, and dashed lines indicate model predictions generated using the best-fitting parameters of the winning model. Magenta dots represent the simulated values from the winning model.

Relationships between psychopathy and absolute donation changes from the first to the second individual donations, per experiment.

The total psychopathy scores were positively correlated with the absolute donation changes in Experiment 2 - Experiment 4, with a marginally significant association observed in Experiment 1 (Expl: Spearman ρ = 0.10, p = 0.071, 95% CI: [-0.01, 0.21]; Exp2: Spearmanρ = 0.17,p = 0.002, 95% CI: [0.06, 0.27]; Exp3: Spearman ρ = 0.14,p = 0.009, 95% CI: [0.03, 0.24]; Exp4: p = 0.19,p < 0.001, 95% CI: [0.09, 0.29]).

Relationships between empathy and absolute donation changes from the first to the second individual donations.

The total empathy scores showed no significant associations with the absolute donation changes across all experiments (Expl: Spearman ρ = -0.04, p = 0.51, 95% CI: [-0.15, 0.08]; Exp2: Spearman ρ = -0.03, p = 0.57, 95% CI: [-0.14, 0.08]; Exp3: Spearman ρ = -0.03, p = 0.58, 95% CI: [-0.14, 0.08]; Exp4: ρ = 0.09, p = 0.086, 95% CI: [-0.02, 0.19]).

Association between empathy and the social information weight parameters, per experiment.

The total empathy scores were not significantly associated with the social information weight parameter (Expl: Spearman ρ = -0.01, p = 0.81, 95% CI: [-0.13, 0.10]; Exp2: Spearman ρ = -0.10, p = 0.062, 95% CI: [-0.21, 0.01]; Exp3: Spearman ρ = -0.06, p = 0.24, 95% CI: [-0.17, 0.05]; Exp4: ρ = 0.09, p = 0.091, 95% CI: [-0.02, 0.19]).

Association between psychopathy and baseline donation amounts, per experiment.

The total psychopathy scores were significantly negatively associated with the baseline donation amount in Experiment 1-3, but not in Experiment 4 (Exp1: Spearman ρ = -0.15, p = 0.006, 95% CI: [-0.26, -0.04]; Exp2: Spearman ρ = -0.12, p = 0.024, 95% CI: [-0.23, -0.01]; Exp3: Spearman ρ = -0.11, p = 0.038, 95% CI: [-0.22, 0]; Exp4: ρ = 0.09, p = 0.07, 95% CI: [-0.01, 0.20]).

Association between empathy and the baseline donation amounts, per experiment.

Significant positive associations between the total empathy scores and the baseline donation amounts emerged in Experiment 1, 3 and 4, whereas this association was not observed in Experiment 2 (Expl: Spearman ρ = 0.17, p = 0.002, 95% CI: [0.06, 0.28]; Exp2: Spearman ρ = 0.02, p = 0.71, 95% CI: [-0.09, 0.13]; Exp3: Spearman ρ = 0.13,p = 0.014, 95% CI: [0.02, 0.24]; Exp4: ρ = 0.22,p < 0.001, 95% CI: [0.12, 0.32]).

No association between psychopathy and the initial estimate of the number of animals.

The total psychopathy scores were not associated with the first estimate of the number of animals in the perceptual-based social influence task (Spearman ρ = -0.03, p = 0.51, 95% CI: [-0.14, 0.07]).

No association between empathy and the social information weight in a perceptual task.

The total empathy scores were not correlated with the social information weight in the perceptual-based social influence task (Spearman ρ = 0.07, p = 0.18, 95% CI: [-0.03, 0.17]).

No association between empathy and the initial estimate of the number of animals.

The total empathy scores were not correlated with the first estimate of the number of animals in the perceptual-based social influence task (Spearman ρ = 0.06, p = 0.23, 95% CI: [-0.04, 0.17]).

Linear mixed-effects model results predicting individual donation amounts as a function of the Mean and SD of Others’ donations and Phase

Individual donation amount ~ 1 + Mean Cond + SD Cond + Phase + Mean Cond * SD Cond + Mean Cond * Phase + SD Cond * Phase + Mean Cond * SD Cond * Phase + (1 | SubID) + (1 | Charity Item)

Mixed ANOVA on the averaged individual donation amount

Control analysis: The linear mixed-effects model predicting individual donation amounts as a function of the Mean and SD of Others’ donations in the Baseline Phase

Individual donation amount ~ 1 + Mean Cond + SD Cond + Mean Cond * SD Cond + (1 | SubiD) + (1 | Charity Item)

Mixed ANOVA on the SD of the individual donation amounts

Mixed ANOVA on the ‘pseudo-SD of individual donation’ amounts

Linear mixed-effects model predicting individual novel donation amounts as a function of the Mean and SD of Others’ donations

Individual novel donation amount ~ 1 + Mean Cond + SD Cond + Mean Cond * SD Cond + (1 | SublD) + (1 | Charity Item)

Mixed ANOVA on the standard deviation of individual novel donation amounts

Summary table of model comparison results.

AIC and BIC were calculated and then summed across participants. PXP (protected exceedance probability) was calculated among all models. Model 0 is the Intercept Only Model; Model 1 is the D1 Only Model; Model 2 is the Prediction Only Model; Model 2b is a variant of the Prediction Only model with a free initial prediction; Model 3 is a Hybrid of D1 and Prediction Model; Model 3b is a variant of Hybrid of D1 and Prediction Model with a free initial prediction. #param means the number of parameters.

Linear mixed-effects model predicting absolute donation changes from psychopathy scores, after controlling for confounding variables

|D2 — D1|~1 + Psychopathy Score + Age + Gender + Mean Cond + SD Cond + + Mean Cond * SD Cond + (1|SubID) + (1|Charity Item)

Linear regression predicting the social information weight from psychopathy scores, after controlling for other modeling parameters and confounding variables

w ~ 1 + Psychopathy Score + α + λ + Age + Gender + Mean Cond + SD Cond + + Mean Cond * SD Cond

Linear mixed-effects model predicting absolute donation changes from empathy scores, after controlling for confounding variables

|D2 — D1|~1 + Empathy Score + Age + Gender + Mean Cond + SD Cond + + Mean Cond * SD Cond + (1 | SublD) + (1 | Charity item)

Linear regression predicting the social information weight from empathy scores, after controlling for other modeling parameters and confounding variables

w ~ 1 + Empathy Score + α + λ + Age + Gender + Mean Cond + SD Cond + + Mean Cond * SD Cond

Linear regression predicting the social information weight from psychopathy scores in the perceptual task, after controlling for confounding variables

SocWeight ~ 1 + Psychopathy Score + Age + Gender

Linear regression predicting empathy scores from the social information weight in the perceptual task, after controlling for confounding variables

SocWeight ~ 1 + Empathy Score + Age + Gender