Defining Decision Theory - Behavioral Mathematics for Game AI - page 48

D ESCRIPTIVE D ECISION T HEORY
The other side of the decision theory coin is the realm of positive or descriptive
decision theory. In this case, positive is not the antonym of negative , but rather spun
off the word posit, that is, to lay down an assumption or theory. In fact, despite the
affirmative nature of the word, positive decision theory deals in such a manner as
to not make a judgment about what should be done.
The other choice of words, descriptive, is somewhat clearer in this respect.
Descriptive decision theory simply describes a correlation, for example, between cause
and effect or other such relationships. This is the realm of study of what people tend
to do, rather than what they should do (Figure 4.2).
FIGURE 4.2 Positive decision theory uses historical observations of behavior,
and summarizes and analyzes that data to express what has been done in the past.
Part of the problem is that of converting scale. In Isaac Asimov's Foundation
trilogy, the character Hari Seldon was a proponent of what he called “psychohis-
tory.� He believed that by studying the past actions of large groups of people, you
could predict the future actions of large groups of people. Notice that the first part
of that sentence looks much like our descriptive decision theory, that is, studying
the past actions of large groups of people. However, Seldon was very aware that the
data from psychohistory could not predict the actions of a single person. Asimov's
example (which actually is borrowed from real-world physicist Daniel Bernoulli)
was that of the action of molecules of a gas. While science has a pretty good handle
on how large quantities of gaseous molecules act in concert, they can't predict the
action of any single one of those molecules. Therefore, while psychohistory is valu-
able for predicting the path of masses, it doesn't help us determine what may hap-
pen on a more granular scale—such as that of the individual.