  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
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.
