Review of Symbolic Logic 8 (1):11-45 (2015)

Harvey Lederman
Princeton University
Robert Aumann presents his Agreement Theorem as the key conditional: “if two people have the same priors and their posteriors for an event A are common knowledge, then these posteriors are equal” (Aumann, 1976, p. 1236). This paper focuses on four assumptions which are used in Aumann’s proof but are not explicit in the key conditional: (1) that agents commonly know, of some prior μ, that it is the common prior; (2) that agents commonly know that each of them updates on the prior by conditionalization; (3) that agents commonly know that if an agent knows a proposition, she knows that she knows that proposition (the “K K” principle); (4) that agents commonly know that they each update only on true propositions. It is shown that natural weakenings of any one of these strong assumptions can lead to countermodels to Aumann’s key conditional. Examples are given in which agents who have a common prior and commonly know what probability they each assign to a proposition nevertheless assign that proposition unequal probabilities. To alter Aumann’s famous slogan: people can “agree to disagree”, even if they share a common prior. The epistemological significance of these examples is presented in terms of their role in a defense of the Uniqueness Thesis: If an agent whose total evidence is E is fully rational in taking doxastic attitude D to P, then necessarily, any subject with total evidence E who takes a different attitude to P is less than fully rational.
Keywords agreement theorem  common priors  Aumann  disagreement  common knowledge
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DOI 10.1017/s1755020314000380
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References found in this work BETA

The Skeptic and the Dogmatist.James Pryor - 2000 - Noûs 34 (4):517–549.
Reflection and Disagreement.Adam Elga - 2007 - Noûs 41 (3):478–502.
Knowledge and its Limits.Timothy Williamson - 2000 - Tijdschrift Voor Filosofie 64 (1):200-201.
Ifs and Oughts.Niko Kolodny & John MacFarlane - 2010 - Journal of Philosophy 107 (3):115-143.

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Standard State Space Models of Unawareness.Peter Fritz & Harvey Lederman - 2015 - Theoretical Aspects of Rationality and Knowledge 15.
Agreement Theorems for Self-Locating Belief.Michael Caie - 2016 - Review of Symbolic Logic 9 (2):380-407.

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