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". |