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Published June 2014 | Submitted + Published
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Merging and testing opinions

Pomatto, Luciano ORCID icon
Al-Najjar, Nabil
Sandroni, Alvaro
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Abstract

We study the merging and the testing of opinions in the context of a prediction model. In the absence of incentive problems, opinions can be tested and rejected, regardless of whether or not data produces consensus among Bayesian agents. In contrast, in the presence of incentive problems, opinions can only be tested and rejected when data produces consensus among Bayesian agents. These results show a strong connection between the testing and the merging of opinions. They also relate the literature on Bayesian learning and the literature on testing strategic experts.

Additional Information

© 2014 Institute of Mathematical Statistics. Received August 2013; revised December 2013. First available in Project Euclid: 20 May 2014. Supported by a grant from the NSF. We thank Ehud Kalai, Wojciech Olszewski, Eran Shmaya, Marciano Siniscalchi and Rakesh Vohra for useful discussions. We are grateful to the Editor and the referees for their thoughtful comments, for simplifying Example 1 and for stimulating the results in Section 6. We also thank the seminar audiences at the Fifth Transatlantic Theory Workshop, the Summer meeting of the Econometric Society 2012, XIII Latin American Workshop in Economic Theory, the 4th Workshop on Stochastic Methods in Game Theory, the Washington University seminar series and the Paris Game Theory Seminar. All errors are ours.

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