Robust Scoring Rules

Abstract

Does the mere exposure of a subject to a belief elicitation task affect the very same beliefs that we are trying to elicit? Is it theoretically possible to guarantee that this will not be the case? In this paper, we introduce mechanisms that make it simultaneously strictly dominant for the subject (a) not to acquire any information that could potentially lead to belief updating as a response to the incentives provided by the mechanism itself, and (b) to report his beliefs truthfully. Such mechanisms are called robust scoring rules. We argue that robust scoring rules are needed for eliciting unbiased estimates of population beliefs in surveys, and we prove that they exist under mild assumptions on the subject’s costs for acquiring information. Although not all standard scoring rules are robust, it is still the case that every scoring rule is approximately robust in the following sense: we can weaken the incentives enough so that the subject will want to acquire only limited amount of information (thus updating only to nearby posterior beliefs), but not enough so that the incentives to report truthfully vanish. As a result, any scoring rule can approximate with arbitrary precision the beliefs that the subject would have held if he had not been confronted with the belief-elicitation task.

Keywords: Non-invasive belief elicitation, prior beliefs, rational inattention, posterior-separability, Shannon entropy, population beliefs

JEL Classification: C91, D81, D82, D83, D87