The Dos And Don’ts Of Decision Theory
Unlike Savage, Jeffrey does not make a distinction between the objects
of instrumental and non-instrumental desire (acts and outcomes
respectively) and the objects of belief (states of the world).
There are more complicated choice rules that depend on a richer
representation of uncertainty involving a notion of
confidence.
For instance, if preferences merely represent choice behaviour or
choice dispositions, as they do according to the revealed
preference theory popular amongst economists (see Sen 1973),
then Completeness is automatically satisfied, on the assumption that a
choice must inevitably be made.
There is a more straightforward defence of Transitivity in preference;
a defence that hinges on the sure losses that may befall anyone who
violates the axiom. The lesson here may
simply be that the theories in question require development; any
mature ethical theory owes us an account of how to act under risk or
uncertainty. You read this know how to apply Bayes Theorem in making a decision.
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We have looked in detail at the discrete applications of Bayesian Decision Theory. .