Earlier social information has a stronger influence on judgments

People’s decisions are often informed by the choices of others. Evidence accumulation models provide a mechanistic account of how such social information enters the choice process. Previous research taking this approach has suggested two fundamentally different cognitive mechanisms by which people incorporate social information. On the one hand, individuals may update their evidence level instantaneously when observing social information. On the other hand, they may gradually integrate social information over time. These accounts make different predictions on how the timing of social information impacts its influence. The former predicts that timing has no impact on social information uptake. The latter predicts that social information which arrives earlier has a stronger impact because its impact increases over time. We tested both predictions in two studies in which participants first observed a perceptual stimulus. They then entered a deliberation phase in which social information arrived either early or late before reporting their judgment. In Experiment 1, early social information remained visible until the end and was thus displayed for longer than late social information. In Experiment 2, which was preregistered, early and late social information were displayed for an equal duration. In both studies, early social information had a larger impact on individuals’ judgments. Further, an evidence accumulation analysis found that social information integration was best explained by both an immediate update of evidence and continuous integration over time. Because in social systems, timing plays a key role (e.g., propagation of information in social networks), our findings inform theories explaining the temporal evolution of social impact and the emergent social dynamics.


Response
Predictor   There was a strong positive correlation between the generated and the recovered parameter for all parameters, but not across different parameters.The parameters are thus interpretable and capture distinct processes.To conduct the recovery analysis, we repeatedly (30 times) generated data with random input parameters and recovered them with the same hierarchical model used to analyse the empirical data.The input parameters were sampled with a quasirandom number generator (using the sobol sequence), ensuring an even distribution across a large multidimensional parameter space.Using these input parameters, we sampled confidence judgments from computed probabilities that take the stimulus difficulty and social information characteristics (presence, validity, and timing) observed by the participant at a given trial into account.The generated data thus have the same hierarchical structure as the empirical data in Experiment 1, with 99 participants, each conducting 100 trials (excluding filler trials).We report the mean of the posterior distributions and the 95% CI of the higher order group-level estimate.To measure the relationship between input and recovered parameters, we calculated the square of the Pearson correlation coefficient r 2 for each parameter combination.

Figure S3 .
Figure S3.Parameter recovery analysis.(a) Relationship of the input parameters (x-axis) and the recovered parameter estimates.(b) Correlation matrix of input parameters and recovered parameter estimates.There was a strong positive correlation between the generated and the recovered parameter for all parameters, but not across different parameters.The parameters are thus interpretable and capture distinct processes.To conduct the recovery analysis, we repeatedly (30 times) generated data with random input parameters and recovered them with the same hierarchical model used to analyse the empirical data.The input parameters were sampled with a quasirandom number generator (using the sobol sequence), ensuring an even distribution across a large multidimensional parameter space.Using these input parameters, we sampled confidence judgments from computed probabilities that take the stimulus difficulty and social information characteristics (presence, validity, and timing) observed by the participant at a given trial into account.The generated data thus have the same hierarchical structure as the empirical data in Experiment 1, with 99 participants, each conducting 100 trials (excluding filler trials).We report the mean of the posterior distributions and the 95% CI of the higher order group-level estimate.To measure the relationship between input and recovered parameters, we calculated the square of the Pearson correlation coefficient r 2 for each parameter combination.

Figure S4 .
Figure S4.The average reported confidence on a scale from 60% to 100% for different social information conditions (50% confidence was excluded because no choice can be assigned to it).The numbers indicate the proportion of choices within a social information condition.Error bars indicate standard error.

Figure S5 .
Figure S5.Accuracy over time in Exp. 1. Accuracy over time by (a) difficulty level and (b) dominant color.Dots show the raw means; lines show the regression model predictions by treatment.

Figure S6 .
Figure S6.Confidence-accuracy relationship in Experiment 1.(a) There was a positive confidence-accuracy relationship in trials without social information (SI).This relationship (b) was stronger in trials with correct social information but (c) disappeared and tended to reverse in trials with wrong social information.Black dots indicate raw means; error bars indicate twice the standard error.Red dots indicate accuracy predicted by the signal detection analysis.

Figure S7 .
Figure S7.Posterior estimates of all subjects from Experiment 1.The black dots indicate the average parameter estimates for each subject for color bias (positive values indicate an orange bias), personal drift, social shift and social drift (see Table1for a description of parameters).The red and black error bars indicate the 80% and 95% credibility intervals.The estimates were ordered according to the strength of the social shift.

Figure S8 .Figure S9 .
Figure S8.Distribution of confidence judgments as (a) observed in Exp. 1 and (b) predicted by the cognitive model in Exp. 1. Proportions of confidence judgments by treatment.Blue/red color shows proportions of confidence judgments for correct/wrong choices.Gray indicates neutral choices (i.e., 50%).The cognitive model reproduces the empirical patterns well, including the positive/negative influence of correct/wrong social information and the stronger influence of early social information.

Figure S10 .
Figure S10.Confidence-accuracy relationship in Experiment 2. (a) There was a positive confidence-accuracy relationship in trials without social information (SI).This relationship (b) was stronger in trials with correct social information but (c) tended to reverse in trials with wrong social information.Black dots indicate raw means; error bars indicate twice the standard error.Red dots indicate accuracy predicted by the signal detection model.

Figure S11 .Figure S12 .
Figure S11.Posterior estimates of all subjects from Experiment 2. The black dots indicate the average parameter estimates for each subject for color bias (positive values indicate an orange bias), personal drift, social shift and social drift (see Table1for a description of parameters).The red and black error bars indicate the 80% and 95% credibility intervals.The estimates were ordered according to the strength of the social shift.

Table S2 .
Bayesian Signal Detection results analyzing the effect of timing (Exp.1).

Table S3 .
Comparison of different models based on LOOIC with different combinations of the main parameters of interest (Exp.1+2).

Table S4 .
Priors and estimates of the group-level parameters of the cognitive model (Exp.1+2).

Table S6 .
Bayesian Signal Detection results analyzing the effect of timing (Exp.2).