Social Prevalence Is Rationally Integrated in Belief Updating

People rely on social information to inform their beliefs. We ask whether and to what degree the perceived prevalence of a belief influences belief adoption. We present the results of two experiments that show how increases in a person’s estimated prevalence of a belief led to increased endorsement of said belief. Belief endorsement rose when impressions of the belief’s prevalence were increased and when initial beliefs were uncertain, as predicted by a Bayesian cue integration framework. Thus, people weigh social information rationally. An implication of these results is that social engagement metrics that prompt inflated prevalence estimates in users risk increasing the believability and adoption of viral misinformation posts.


ii. Participants revise their beliefs in line with new prevalence information
As predicted, participants' ratings of the likelihood of these beliefs increased by a mean of 5.19% in the Higher Prevalence condition and remained relatively stable (decreased by 0.32%) in the Control condition (95% CI = [4.97, 6.04]; t(5489) = 20.19, p < 0.001, d = 0.272).

iii. Belief change is commensurate with change in prevalence estimate
We ran a linear mixed-effects model predicting belief change with condition and change in prevalence estimate as fixed effects and random intercepts per participant and item. This model revealed significant main effects of condition (β = 1.75, t = 5.21, p < 0.001) and change in prevalence estimate (β = 0.14, t = 8.15, p < 0.001). The interaction between condition and prevalence change was not significant (p = 0.25). This model predicted 13.5% of the variance (conditional R 2 ).

iv. Belief change is dependent on initial certainty
We fit a linear mixed-effects model with standardized certainty and prevalence condition as fixed effects and random intercepts per participant and item. The model revealed main effects of both scaled certainty (β = 1.51, t = 7.49, p < .001) and prevalence condition (β = 5.49, t = 20.54, p < .001), as well as a significant interaction (β = -2.87, t = -10.66, p < .001).
We replicated our predicted effect of certainty with an additional linear mixed-effects model using change in prevalence estimate as a continuous predictor instead of the dichotomous condition variable. This model had an otherwise identical structure to the first. Again, main effects of standardized certainty (β = 0.41, t = 2.76, p < .01) and change in prevalence estimate (β = 0.18, t = 26.64, p < .001) were significant. Crucially, the same significant interaction was observed (β = -1.98, t = -15.10, p < .001).
A confound explains the unexpected positive relationship between certainty and belief change in the Control condition. Estimates of prevalence differed more from participant's own initial beliefs when those beliefs were more certain. As a result of this pattern, the data shown in the Control condition differed more from participant's own beliefs under conditions of high certainty, potentially leading to higher belief change. To control for this confound, we added the raw difference between initial prevalence estimate and initial belief as a fixed effect to the previous model, and used it to predict belief change in the Control condition. With the addition of the confound to the model, the main effect of scaled certainty disappeared (p = 0.14). The model also revealed a significant effect of prevalence change (β = 0.23, t = 14.30, p < .001), a significant effect of the difference between initial prevalence estimate and initial belief (β = 5.15, t = 26.52, p < .001), and a significant, negative interaction between certainty and prevalence change (β = -1.92, t = -11.34, p < .001).

D. Evidence Against the Effect of Demand Characteristics in Experiment 2
Analyses of participants' open-ended responses about their perceived purpose of the study support the idea that demand characteristics are not a primary driver of the results in Experiment 2. First, many participants' responses suggested that they believed the memory cover task (e.g. "The ability of someone to remember a surprising result."; "how distraction from random questions affects short term memory over an extended time frame"). Second, we sorted participants into groups based on whether they gave any indication that they suspected the study had something to do with their beliefs being influenced by the prevalence data (e.g. "Social influence on people's endorsement of or belief in different ideas"; N = 68) or did not (N = 134). A linear mixed-effects model with prevalence condition and mention of social influence in the open-ended response as fixed effects and random intercepts per participant and item found no significant effect of this awareness (p = 0.13) and no significant interaction (p = 0.64). Belief change was the same between the two groups, suggesting that even explicit awareness of the intended purpose of the study did not affect behavior.