Abstract:
A decision maker (DM) contemplates whether to take a costly action. The DM does not know the action's value and relies on data and unbiased statistical inference to estimate it. The data are Bernoulli experiments governed by the action's value. A designer, who wishes the DM to take the action, controls the size of the data, i.e., the sample size, available to the DM. We establish that in many environments the designer's optimal sample size is the largest one satisfying that either a single --- or a simple majority --- of favorable realizations would persuade the DM to take the action.