Posts on: Preference
A common assumption in economics is that utilities are reducible to choice
dispositions. The story goes something like this. Suppose we know what an agent
would choose if she were asked to pick one from a range of goods. If the agent
is disposed to choose X, and Y was an available alternative, we say that the
agent prefers X over Y. One can show that if the agent's choice
dispositions satisfy certain formal constraints, then they are "representable"
by a utility function in the sense that whenever the agent prefers X over Y,
the function assigns greater value to X than to Y. This utility function is
assumed to be the agent's true utility function, telling us how much the agent
values the relevant goods.
The decision-theoretic concept of preference is linked to the concepts
of subjective probability and utility by the expected utility
principle:
(EUP) A rational agent prefers X to Y iff the expected
utility of X exceeds the expected utility of Y.
Economists usually take preference to be the more basic concept and
interpret the EUP as an implicit definition of the agent's utilities
(and sometimes also her probabilities).
Decision theory comes in many flavours. One of the most important
but least discussed divisions concerns the individuation of
outcomes. There are basically two camps. One side -- dominant in
economics, psychology, and social science -- holds that in a
well-defined decision problem, the outcomes are exhausted by a
restricted list of features: in the most extreme version, by the
amount of money the agent receives as the result of the relevant
choice. In less extreme versions, we may also consider the agent's
social status or her overall well-being. But we are not allowed to
consider non-local features of an outcome such as the act that brought
it about, the state under which it was chosen, or the alternative acts
available at the time. This doctrine doesn't have a name. Let's call
it localism (or utility localism).
Decision theoretic representation theorems show that one can read
off an agent's probability and utility functions from their
preferences, provided the latter satisfy certain minimal rationality
constraints. More substantive rationality constraints should therefore
translate into further constraints on preference. What do these
constraints look like?
Here are a few steps towards an answer for one particular
constraint: a simple form of the Principal Principle. The Principle
states that if cr is a rational credence function and ch=p is the
hypothesis that p is the chance function, then for any E in the domain
of p,
In The Logic of Decision, Richard Jeffrey pointed out that
the desirability (or "news value") of a proposition can be usefully
understood as a weighted average of the desirability of different ways
in which the proposition can be true, weighted by their respective
probability. That is, if A and B are incompatible propositions,
then
(1) Des(AvB) = Des(A)P(A/AvB) + Des(B)P(B/AvB).
So desirabilities are affected by probabilities. If you prefer A
over B and just found out that conditional on their disjunction, A is
more likely then B, then the desirability of the disjunction goes
up. That seems right.
It is well-known that humans don't conform to the model of rational
choice theory, as standardly conceived in economics. For example, the
minimal price at which people are willing to sell a good is often much
higher than the maximal price at which they would previously have been
willing to buy it. According to rational choice theory, the two prices
should coincide, since the outcome of selling the good is the same as
that of not buying it in the first place. What we philosophers call
'decision theory' (the kind of theory you find in Jeffrey's Logic
of Decision or Joyce's Foundations of Causal Decision
Theory) makes no such prediction. It does not assume that the
value of an act in a given state of the world is a simple function of
the agent's wealth after carrying out the act. Among other things, the
value of an act can depend on historical aspects of the relevant
state. A state in which you are giving up a good is not at all
the same as a state in which you aren't buying it in the first place,
and decision theory does not tell you that you must assign equal
value to the two results.
One of the novelties in Richard Jeffrey's "Logic of Decision"
(1965) was to unify the space over which probabilities and values are
defined: both probability and desirability are distributed over the
space of possible worlds, of ways things might be. By contrast, in
earlier theories like that of Savage, probabilities were defined over
states (or events) and utilities over
consequences, which were taken to be distinct kinds of
things. Technically, this difference between Savage and Jeffrey isn't
terribly important as long as anything an agent may care about can be
found in the set of 'consequences'. However, the distinction and the
labeling in Savage's treatment carries a danger to overlook the
complexity of human values. This has, I believe, led to a number of
serious mistakes.