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Robust scoring rules

Elias Tsakas
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Elias Tsakas: General Economics 1 (Micro)

No 23, Research Memorandum from Maastricht University, Graduate School of Business and Economics (GSBE)

Abstract: We study elicitation of latent (prior) beliefs when the agent can acquire information via a costly attention strategy. We introduce a mechanism that simultaneously makes it strictly dominant to (a) not acquire any information, and (b) report truthfully. We call such a mechanism a robust scoring rule. Robust scoring rules are important for different reasons. Theoretically, they are crucial both for establishing that decision-theoretic models under uncertainty are testable. From an applied point of view, they are needed for eliciting unbiased estimates of population beliefs. We prove that a robust scoring rule exists under mild axioms on the attention costs. These axioms are shown to characterize the class of posterior-separable cost functions. Our existence proof is constructive, thus identifying an entire class of robust scoring rules. Subsequently, we show that we can arbitrarily approximate the agent's prior beliefs with a quadratic scoring rule. The same holds true for a discrete scoring rule. Finally, we show that the prior beliefs can be approximated, even when we are uncertain about the exact specification of the agent's attention costs.

Keywords: belief elicitation; prior beliefs; rational inattention; hidden information costs; posterior-separability; Shannon entropy; population beliefs; testing decision-theoretic models (search for similar items in EconPapers)
JEL-codes: C91 D81 D82 D83 D87 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-des, nep-gth, nep-mic and nep-ore
Date: 2018-10-08
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