In a famous article “Agreeing to Disagree,” Robert J. Aumann (1976) proved with a very elegant Bayesian argument that people with the same priors cannot agree to disagree. (Aumann went on to win a Nobel prize in economics.) His "result implies that the process of exchanging information on the posteriors for A will continue until these posteriors are equal." (1238) And this result fits a widespread intuition that in science (unlike say much of the history of philosophy) there is essentially agreement. (This idea has had unfortunate impact on economists who tried to make their field look scientific by suppressing disagreement.) Aumann tacitly assumes an efficient (scientific) 'market' for information exchange. As regular readers of this blog know by now, I am no fan of the uses people put the Bayesian machinery, so I return to Aumann's argument below. The economist Ali Khan reminded me of Aumann's piece after he read a draft-paper I co-authored with a terrific young Flemish PhD Student, Merel Lefevere, “Private Epistemic Virtue, Public Vices: Moral Responsibility in Policy Sciences.” (What follows draws on our joint research.) A lot of philosophers also assume without argument that scientific communities are like Aumann's efficient market for information exchange.
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