probability and decision theory

From: Wei Dai <weidai.domain.name.hidden>
Date: Sun, 15 Mar 1998 23:43:08 -0800

On what basis do we choose a theory of probability? Does probability have
any meaning outside the context of decision theory? It seems to me the
answer is no. If this is true then the real question is how do we choose a
decision theory. Is decision theory a positive theory? Is it supposed to
make predictions about agents in the real world? At first I thought yes,
we can accept or reject decision theory based on whether or not it makes
correct predictions about real agents. But if probability theory is part
of decision theory, then it would be circular to use probabilistic
arguments on decision theory itself.

Does anyone see a way out of this?

P.S.

Maybe the answer is that a decision theory has two roles, one as a
normative theory about how one should act, and the other as a positive
theory about how others do act. Perhaps the two roles could even be filled
with two different theories. Once we accept a decision theory as a
normative theory, the probability theory part of it would tell us which
decision theory we should accept as a positive theory.

If this is the right way to think about probability theory, then we should
make clear in our discussions whether we're talking about it as a positive
theory or a normative theory. But it is still not clear on what basis we
should choose a normative probability (or decision) theory.
Received on Sun Mar 15 1998 - 23:43:37 PST