Choosing The Best Incentives for Belief Elicitation with an Application to Political Protests

Many experiments elicit subjects' prior and posterior beliefs about a random variable to assess how information affects one's own actions. However, beliefs are multi-dimensional objects, and experimenters often only elicit a single response from subjects. In this paper, we discuss how the incentives offered by experimenters map subjects' true belief distributions to what profit-maximizing subjects respond in the elicitation task. In particular, we show how slightly different incentives may induce subjects to report the mean, mode, or median of their belief distribution. If beliefs are not symmetric and unimodal, then using an elicitation scheme that is mismatched with the research question may affect both the magnitude and the sign of identified effects, or may even make identification impossible. As an example, we revisit Cantoni et al.'s (2019) study of whether political protests are strategic complements or substitutes. We show that they elicit modal beliefs, while modal and mean beliefs may be updated in opposite directions following their experiment. Hence, the sign of their effects may change, allowing an alternative interpretation of their results.