Optimal Sample Sizes and Statistical Decision Rules

A statistical decision rule is a mapping from data to actions induced by statistical inference on the data. We characterize these rules for data that are chosen strategically in persuasion environments. A designer wishes to persuade a decision maker (DM) to take a particular action and decides how many Bernoulli experiments about a parameter of interest the DM can obtain. After obtaining these data and estimating the parameter value, the DM chooses to take the action if the estimated value exceeds some threshold. We establish that as the threshold changes, the resulting statistical decision rules in many environments are either simple majority or reverse unanimity.