Our opinions, which things we like or dislike, depend on the opinions of those around us. Nowadays, we are influenced by the opinions of online strangers, expressed in comments and ratings on online platforms. Here, we perform novel academic A/B testing experiments with over 2,500 participants to measure the extent of that influence. In our experiments, the participants watch and evaluate videos on mirror proxies of YouTube and Vimeo. We control the comments and ratings that are shown underneath each of these videos. Our study shows that from 5$%$ up to 40$%$ of subjects adopt the majority opinion of strangers expressed in the comments. Using Bayes theorem, we derive a flexible and interpretable family of models of social influence, in which each individual forms posterior opinions stochastically following a logit model. The variants of our mixture model that maximize Akaike information criterion represent two sub-populations, i.e., non-influenceable and influenceable individuals. The prior opinions of the non-influenceable individuals are strongly correlated with the external opinions and have low standard error, whereas the prior opinions of influenceable individuals have high standard error and become correlated with the external opinions due to social influence. Our findings suggest that opinions are random variables updated via Bayes rule whose standard deviation is correlated with opinion influenceability. Based on these findings, we discuss how to hinder opinion manipulation and misinformation diffusion in the online realm.
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