Elias Tsakas

Department of Economics
Maastricht University

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Robust scoring rules

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 to (a) not update his beliefs as a response to the incentives provided by the mechanism itself, and (b) report his beliefs truthfully. Such non-invasive mechanisms are called robust scoring rules, and they are useful in a number of settings. First, their existence guarantees that the usual assumption of stationary beliefs (that we often explicitly or implicitly impose, e.g., in revealed preference tests or in experimental designs) is at least theoretically plausible. Second, robust scoring rules are needed for eliciting unbiased estimates of population beliefs in surveys. We prove that robust scoring rules exist under mild assumptions. Our existence proof is constructive, thus identifying an entire class of robust scoring rules. Subsequently, we show that commonly-used scoring rules (viz., the quadratic and the discrete) are approximately robust in the sense that they can arbitrarily approximate the beliefs the subject would have had, if elicitation had not taken place. In this sense, our results imply that the quadratic scoring rule that we typically use in the literature can effectively  elicit the subject's beliefs without distorting them.