Agreeing to Disagree with Limit Knowledge
The possibility for agents to agree to disagree is considered in an extended epistemic-topological framework. In such an enriched context, Aumann’s impossibility theorem is shown to no longer hold. More precisely, agents with a common prior belief satisfying limit knowledge instead of common knowledge of their posterior beliefs may actually entertain distinct posterior beliefs. Hence, agents can actually agree to disagree. In particular, agreeing to disagree with limit knowledge is illustrated within a representative epistemic-topological situation.
Keywordsagreeing to disagree agreement theorems limit knowledge interactive epistemology
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