Thinking and Deciding

Practically all thinking involves beliefs in some way. We make decisions on the
basis of beliefs about the outcomes of each option. If I want to drive to the city, I
choose my route according to my beliefs about speed and safety. When we think
about the strengths of our goals, such as the relative importance of speed and safety,
we do this as well on the basis of beliefs, for example, beliefs about what it would
feel like to have an automobile accident. Beliefs themselves can be the objects of
thought. I can think about how much the construction on the expressway is likely to
slow me down, given that it is Saturday afternoon. (Is there a sports event in town?)
Part II explores three major approaches to the analysis of belief formation: probability
theory, the theory of hypothesis testing, and the theory of correlation. It concludes
with a chapter on biases in belief formation in general.
Probability theory (Chapter 5) is a normative theory for evaluating numerically
the strengths of our beliefs in various propositions. Like logic, it is a theory of
inference, but unlike logic, it concerns degrees of belief rather than certainty. In
Chapter 6, we shall see that our belief strengths, as manifest in our judgments of
probability, violate this normative model seriously. It is not just that our numbers
are not exactly correct. They are often systematically out of order. We believe that
one event is more likely than another when the rest of our beliefs imply the opposite.
We can take steps to guard against these violations. Actively open-minded thinking
can help. When probability judgments are very important, computers can help us as
well.
The theory of hypothesis testing (Chapter 7) concerns the selection of evidence:
asking the right question to find out how much to believe some hypothesis. If we
ask questions well, we can make inferences from their answers that bring our beliefs
into line with the available evidence as efficiently as possible. Scientists try to
do this when they design experiments, and physicians try to do it when they order
tests. Again, we shall find certain biases that cause us to depart from the normative
model. Some of these biases can be ameliorated by actively open-minded thinking,
especially by considering other hypotheses than those we favor.
Chapter 8 deals with beliefs that concern the correlation between two variables.
We tend to perceive data as showing correlations when we already believe that we
will find a correlation. Chapter 9 shows that this distorting effect of prior belief
occurs throughout our thinking, and the chapter also explores the causes of this bias
and the conditions under which it occurs. The existence of this bias is the main
justification for my claim that we need to remind ourselves to be open to new beliefs
and to evidence against our old ones: Our natural tendency is often the opposite.