Robust scoring rules

Is it possible to guarantee that the mere exposure of a subject to a belief elicitation task will not affect the very same beliefs that we are trying to elicit? 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 prove that robust scoring rules always exist under mild assumptions on the subject's costs for acquiring information. Moreover, every scoring rule can become approximately robust, in the sense that if we scale down the incentives sufficiently, we will approximate with arbitrary precision the beliefs that the subject would have held if he had not been confronted with the belief-elicitation task.