In the last four months I wrote a draft of a possible textbook on
decision theory. Here it is.
I've used these notes as basis for my honours/MSc course "Belief,
Desire, and Rational Choice". They're tailored to my usage, but they
might be useful to others as well.
The main difference to other textbooks is that I talk at length
about the structure and interpretation of subjective probabilities and
utilities. In part, this is because it makes a great difference to the
plausibility of the expected utility norm whether, say, utilities are
defined in terms of individual welfare, in terms of choice
dispositions, or taken as primitive. But I also think these are
independently interesting philosophical topics.
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).
According to a popular picture, some beliefs are justified by "seemings": under
certain conditions, if it seems to you that P, then you are justified
to believe that P, without the assistance of other beliefs. So
seemings provide a kind of foundation for belief, albeit a fallible
kind of foundation.
But most of our beliefs are not justified by seemings (or by
beliefs which are justified by seemings, etc.). I once learned that
Luanda is the capital of Angola and I've retained this belief for many
years, although I rarely think about Angola and thus rarely experience
any relevant seemings that could justify the belief.
Friends of primitive powers and dispositions often contrast their
view with an alternative view, usually attributed to Lewis, on which
modal facts about powers, dispositions, laws, counterfactuals etc. are
grounded in facts about other possible worlds. But Lewis never held
that alternative view – nor did anyone else, as far as I
know. The allegedly mainstream alternative is entirely made of
straw. The real alternative that should be addressed is the
reductionist view that powers and dispositions are reducible to
ultimately non-modal elements of the actual world.
In his "Dicing
with Death" (2014), Arif Ahmed presents the following scenario as
a counterexample to causal decision theory (CDT):
You are thinking about going to Aleppo or staying in
Damascus. Death has predicted where you will be and is waiting for
you there. For a small fee, you can delegate your choice to a coin
toss the outcome of which Death can't predict.
Tossing the coin promises to reduce the chance of death from about
1 to 1/2. Nonetheless, CDT seems to suggest that you shouldn't toss
the coin. To illustrate, suppose you are currently completely
undecided and thus give equal credence to Death being in Aleppo and to
Death being in Damascus. Then you're 50 percent confident that if you
were to stay in Damascus, you would survive; similarly for
going to Aleppo. You're also 50 percent confident that you would
survive if you were to toss the coin, but in that case you'd have
to pay the small fee. So it's not worth paying.
Bob's favourite piano piece is Beethoven's Moonlight Sonata. Alice
would like to play Bob's favourite piece, and she can play the
Moonlight Sonata, but she doesn't know that it is Bob favourite piece,
nor can she find out that it is. Can Alice play Bob's favourite
piano piece?
In one sense yes, in another no. It's a kind of de re/de dicto
ambiguity. Alice can play what is in fact Bob's favourite piece, but
she can't play it "under that description", loosely speaking.
In decision theory, the available options are often glossed informally
as the acts the agent can perform, or the propositions she can make
true. But this yields implausible results in cases where an agent has
doubts about what she can do.
For example, assume Bob suspects that the button in front of him
functions as a light switch, as in fact it does. Then Bob can turn
on the light by pressing the button. But if he is not certain that
the button is a light switch, decision theory should consider the
consequences of pressing the button if it has some other function. So
turning on the light by pressing the button should not count as
an option.
It is tempting to think that there is nothing more to physical
quantities than their nomic role: that to have a certain mass just is
to behave in such-and-such a way under such-and-such conditions.
But it is also tempting to think that the "Galilean equivalence" of
inertial mass and gravitational mass is a true identity; i.e.,
that
Inertial mass = gravitational mass.
However, the role associated with "inertial mass" is completely
different from the role associated with "gravitational mass". So if
having such-and-such inertial mass is having the relevant
dispositions associated with "inertial mass", and likewise for
gravitational mass, then the Galilean equivalence could not be an
identity. It would rather state an empirical law, according to which
two distinct quantities always have the same value.
In chapter 8 of Doing Good Better, William MacAskill argues
that we should not make a great effort to reduce our carbon emissions,
to buy Fairtrade coffee, or to boycott sweatshops. The reason is that
these actions have at best a small impact on improving other people's
lives and so the cost and effort is better spent elsewhere.
From a strictly utilitarian perspective, there is nothing to
complain about this. But strict utilitarianism is a highly
counterintuitive position. In fact, MacAskill himself rejects it when
he says that it would not be OK to consume meat from factory farms and
"offset" by donating to animal welfare organisations, even if the net
result would be less animal suffering. I agree. Whether a course of
action is right or wrong is not just a matter of the net difference it
makes to the amount of suffering in the world. But then we also have
to reconsider MacAskill's conclusions about carbon offsetting,
fairtrade, and sweatshops.
You observe a process that generates two kinds of outcomes, 'heads'
and 'tails'. The outcomes appear in seemingly random order, with
roughly the same amount of heads as tails. These observations support
a probabilistic model of the process, according to which the
probability of heads and of tails on each trial is 1/2, independently
of the other outcomes.
How observations about frequencies confirm or disconfirm
probabilistic models is well understood in Bayesian epistemology. The
central assumption that does most of the work is the Principal
Principle, which states that if a model assigns (objective)
probability x to some outcomes, then conditional on the model, the
outcomes have (subjective) probability x. It follows that models that
assign higher probability to the observed outcomes receive a greater
boost of subjective probability than models that assign lower
probability to the outcomes.