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. (shrink)

Policy disputes arise at all scales of governance: in clubs, non-profits, firms, nations, and alliances of nations. Both the means and ends of policy are disputed. While many, perhaps most, policy disputes arise from conflicting ends, important disputes also arise from differing beliefs on how to achieve shared ends. In fact, according to many experts in economics and development, governments often choose policies that are “inefficient” in the sense that most everyone could expect to gain from other feasible policies. Many (...) other kinds of experts also see existing policies as often clearly inferior to known alternatives. (shrink)

In practice, scoring rules elicit good probability estimates from individuals, while betting markets elicit good consensus estimates from groups. Market scoring rules combine these features, eliciting estimates from individuals or groups, with groups costing no more than individuals. Regarding a bet on one event given another event, only logarithmic versions preserve the probability of the given event. Logarithmic versions also preserve the conditional probabilities of other events, and so preserve conditional independence relations. Given logarithmic rules that elicit relative probabilities of (...) base event pairs, it costs no more to elicit estimates on all combinations of these base events. (shrink)

Contributors to the recent disagreement debate have sought to provide a uniform response to cases in which epistemic peers disagree about the epistemic import of a shared body of evidence, no matter what kind of evidence they are disagreeing about. The varied cases addressed in the literature have included examples of disagreement about restaurant bills, court verdicts, weather forecasting, chess, morality, religious beliefs, and even disagreements about philosophical disagreements. The equal treatment of these varied cases has motivated the search for (...) a uniform response to peer disagreement wherever it is encountered. In this article I challenge this prevalent approach in the literature. I grant the notion of epistemic peer and accept that being a peer may amount to the same thing in different domains; nonetheless I contend that different domains appear to call for different responses to disagreement. I argue that the appropriate response to finding out about a disagreement with a peer is different in different domains. (shrink)