Adam Elga, Princeton, Philosophy Department
Fragmented decision theory

Bayesian decision theory assumes that its subjects are perfectly coherent: logically omniscient and able to perfectly access their information. Since imperfect coherence is both rationally permissible and widespread, it is desirable to extend decision theory to accommodate incoherent subjects. New 'no-go' proofs show that the rational dispositions of an incoherent subject cannot in general be represented by a single assignment of numerical magnitudes to sentences (whether or not those magnitudes satisfy the probability axioms). Instead, we should attribute to each incoherent subject a whole family of probability functions, indexed to choice conditions. If, in addition, we impose a "local coherence" condition, we can make good on the thought that rationality requires respecting easy logical entailments but not hard ones. The result is an extension of decision theory that applies to incoherent or fragmented subjects, assimilates into decision theory the distinction between knowledge-that and knowledge-how, and applies to cases of "in-between belief".

This is joint work with Agustin Rayo (MIT).