Two Bayesian agents with a common prior and common knowledge of each other's posteriors cannot agree to disagree.
Aumann proved in 1976 that agents with a common prior whose posteriors are common knowledge must hold equal posteriors, even where their private information differs. Persistent disagreement therefore shows that one of the assumptions fails; it does not by itself say which.
In practice
- Two analysts with the same data and the same model who still disagree have learned that one of the theorem's assumptions does not hold, and not yet which one.
- Two forecasters both saying 30% who cannot converge after comparing notes are not disagreeing about the world but about what counts as evidence.
- Further reading
- Wikipedia
- Subject
- Games & Strategic Interaction
- Essay
- What is provable, and what people actually do