Suppose you are offered a free choice between two identical gambles,
one a gamble on the hypothesis P and the other a gamble on the
hypothesis Q.  What should decide the choice for you?  Here is a
pretty compelling answer: you should prefer the gamble on P to the
gamble on Q if and only if you are more confident in the truth of P
than you are in the truth of Q.  That is to say, the following
principle seems to hold:

Your state of confidence and preference is open to rational
criticism if the following condition is not satisfied: where P and Q
are any hypotheses, you prefer a gamble on P to an identical gamble
on Q if and only if you are more confident that P than you are that
Q.

This insight into the relation between confidence and preference is
surely a modest one.  But, modest though it may be, it opens up a
distinct approach to epistemology.  It has been a traditional
concern of epistemology to say, in some general way, by what
principles the opinions of a rational person ought to be
constrained.  Epistemologists have sought such principles, and
evidence for their legitimacy, in various places—from analyses of
the nature of justification, from reflections on metaphysical
structure of the world, from the findings of cognitive psychology,
from the application of evolutionary biology to human cognition.
Our principle suggests a different place to look.  The principle
tells us that, on pain of opening our states of confidence and
preference to criticism, our states of confidence must mirror our
preferences: we must invest more confidence in P than in Q just if
we prefer a gamble on P to an identical gamble on Q.  This suggests
that, if we can find a theory that says something useful about when
(on pain of inviting such criticism) we ought to prefer one gamble
to another, it will turn out to be a theory that tells us something
useful about when (on pain of inviting such criticism) we ought to
invest more confidence in one hypothesis than in another  a theory
that will constitute a genuine contribution to epistemology.
The partisans of Bayesian decision theory claim to have found just
such a theory.  The purpose of this course will be to evaluate that
claim.  This will involve examining both the foundations of Bayesian
decision theory and the way in which the results of that theory have
been (and might be) deployed to deal with familiar (and some
unfamiliar) epistemological problems.