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For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No. 1Introduction2The Finite Case 2.1Polarization2.2Dilation2.3Global polarization3The General Case 3.1Merging of opinions3.2The Bayesian consensus-or-polarization law4DiscussionAppendix

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In a recent paper, Pettigrew (2021) reports a generalization of the celebrated accuracy-dominance theorem due to Predd et al. (2009). But Pettigrew’s proof is incorrect. I will explain the mistakes and provide a correct proof.