What is decision theory?
Decision theory is theory about decisions. The subject is not a very unified
one. To the contrary, there are many different ways to theorize about
decisions, and therefore also many different research traditions. This text
attempts to reflect some of the diversity of the subject. Its emphasis lies on
the less (mathematically) technical aspects of decision theory.
The following are examples of decisions and of theoretical problems that
they give rise to.
Shall I bring the umbrella today? – The decision depends on
something which I do not know, namely whether it will rain or not.
I am looking for a house to buy. Shall I buy this one? – This
house looks fine, but perhaps I will find a still better house for the
same price if I go on searching. When shall I stop the search
Am I going to smoke the next cigarette? – One single cigarette is
no problem, but if I make the same decision sufficiently many times
it may kill me.
The court has to decide whether the defendent is guilty or not. –
There are two mistakes that the court can make, namely to convict
an innocent person and to acquit a guilty person. What principles
should the court apply if it considers the first of this mistakes to be
more serious than the second?
A committee has to make a decision, but its members have
different opinions. – What rules should they use to ensure that they
can reach a conclusion even if they are in disagreement?