Thinking and Deciding

DESCRIPTIVE MODELS AND HEURISTICS 53
point here is not to evaluate behavior, it is to improve it. We would not know what
improvement is without a standard that is separate from behavior.
Descriptive models and heuristics
Two types of descriptive models are common in the study of decisions. One type
involves mathematical models, much like those used in physics, chemistry, or economics.
For example, in Chapter 11, we shall discuss a descriptive model of decision
making for people told the probabilities of various outcomes of a decision. The
model says that people do not use the probabilities as given but, instead, transform
them according to a certain function. The form of the function explains many of the
discrepancies between the normative model and actual decisions.
Another type is to describe judgment and decisions in terms of heuristic methods.
Our modern concept of heuristic methods was devised by George Polya, an eminent
mathematician born in Hungary in 1887, who moved to Stanford University in 1940.
There he began the task of trying to set down what he had learned over the years
about the methods of mathematics, as distinct from its content. His first book on
this subject, How to Solve It (1945), brought into common use the term “heuristic,”
an adjective originally meaning “serving to discover.” The term is often used in the
expression “heuristic method” or simply as a noun meaning “heuristic method.” The
use of heuristics, or heuristic methods, constitute “heuristic reasoning,” which Polya
defines (p. 115) as “reasoning not regarded as final and strict but as provisional and
plausible only, whose purpose is to discover the solution of the present problem.”
Heuristic methods are likely to help solve many different problems, but no one can
specify exactly when each method will help.
Polya’s heuristics can be understood as suggestions to facilitate more extensive
search for useful possibilities and evidence. They encourage active open-mindedness
in mathematical problem solving. An example, is: Could you imagine a more accessible
related problem? Suppose you were asked to solve the equation:
x 4 − 13x 2 +36=0
If you use this heuristic, the attempt to think of a related problem might make you
think of an ordinary quadratic equation, which (let us suppose) you know how to
solve. You might then see that you could make this problem into the simpler one by
letting y = x 2 , which changes the equation into an ordinary quadratic equation in y.
Once the values of y are found, the values of x can be determined.
Beginning with Kahneman and Tversky (1972) researchers have used the idea
of heuristics to explain departures from normative models. The problem described
at the very beginning of this chapter is an example. The idea captures much of the
theorizing in this field. People develop heuristics exactly because they are often
useful. But the use of these heuristics leads to biases. The question is whether we
can learn better heuristics, or other ways around the problems they cause. That is the
prescriptive question.