How do humans respond to indirect social influence when making decisions? We analysed an experiment where subjects had to repeatedly guess the correct answer to factual questions, while having only aggregated information about the answers of others. While the response of humans to aggregated information is a widely observed phenomenon, it has not been investigated quantitatively, in a controlled setting. We found that the adjustment of individual guesses depends \emph{linearly} on the distance to the mean of all guesses. This is a remarkable, and yet surprisingly simple, statistical regularity. It holds across all questions analysed, even though the correct answers differ in several orders of magnitude. Our finding supports the assumption that individual diversity does not affect the response to indirect social influence. It also complements previous results on the nonlinear response in information-rich scenarios. We argue that the nature of the response to social influence crucially changes with the level of information aggregation. This insight contributes to the empirical foundation of models for collective decisions under social influence.
