Scoring Rules and Epistemic Compromise

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Formal models of epistemic compromise have several fundamental applications. Disagreeing agents may construct a compromise of their opinions to guide their collective action, to give a collective opinion to a third party, or to determine how they should update their individual credences. Recent literature on disagreement has focused on certain questions about epistemic compromise: when you find yourself disagreeing with an epistemic peer, under what circumstances, and to what degree, should you change your credence in the disputed proposition? Elga (2006) and Christensen (2007) say you should compromise often and deeply; Kelly (2010) disagrees. But these authors leave open another question: what constitutes a perfect compromise of opinion? In the disagreement literature, it is sometimes assumed that if we assign different credences ca and cb to a proposition p, we reach a perfect compromise by splitting the difference in our credences. In other words: to adopt a perfect compromise of our opinions is to assign (ca+cb)/2 credence to p. For instance, Kelly (2010) says that when peers assign 0.2 and 0.8 to a proposition, to adopt a compromise is to split the difference with one’s peer and believe the hypothesis to degree 0.5.2 But why does 0.5 constitute a perfect compromise? Of course, 0.5 is the arithmetic mean of 0.2 and 0.8. But why must a compromise of agents’ opinions always be the arithmetic mean of their prior credences? In other cases of compromise, we do not simply take it for granted that the outcome that constitutes a perfect compromise is determined by the arithmetic mean of quantities that reflect what individual agents most prefer. Suppose