Quantifying the effects of social influence

Abstract

How do humans respond to indirect social influence when making decisions? We analysed an experiment where subjects had to guess the answer to factual questions, 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 regularity. It holds across all questions analysed, even though the correct answers differ by several orders of magnitude. Our finding supports the assumption that individual diversity does not affect the response to indirect social influence. We argue that the nature of the response crucially changes with the level of information aggregation. This insight contributes to the empirical foundation of models for collective decisions under social influence.

Figure 1. Scatter plots for questions 1 (first and third column) and 3 (second and fourth column).

The green lines show median smoothing: the x-axis has been split into equally sized bins of size 10 (arbitrary), and the medians in each bin are plotted. The bottom row shows median smoothing with shaded areas corresponding to error bars between the first and third quartile of each bin. Note the scaling of the x- and y-axis.

Figure 2. Residuals vs. fitted values for both information conditions and all questions.

The first two rows show the no-information condition, while the last two – the aggregate information condition. Questions are numbered from left to right and top to bottom. The mutual information (MI) is shown on top of each plot (see Methods for definition of MI).

Figure 3. QQ Plots.

Theoretical quantiles of a normal distribution versus sample quantiles for all six questions. There are outliers in the data resulting in non-normal residuals. Question numbers (Q) are indicated on the top left corner of each plot.