Aumann's agreement theorem states that rational agents can not indefinitely disagree about a matter of fact if they are able to freely exchange beliefs. Nonetheless, persistent and often bitter disagreement about factual questions is common place despite ever increasing opportunities to freely exchange information. I will present a model in which rational agents can agree to disagree if they believe they do not have identical preferences, and show how agents may mistakenly come to believe that others have goals that are fundamentally opposed to their own, leading to persistent polarisation.
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