# INST 354 Lecture Notes - Lecture 13: Decision Analysis, Rational Expectations, Mental ModelExam

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The decision tree diagrams remind us that the crucial first step in understanding any decision is

to describe the situation in which the decision occurs. That step may sound trivial, but the

attempt to construct a summary diagram forces us to answer difficult questions about what to

include and, more difficult, what to exclude. Then the diagram prompts us to solve the

challenging problem of quantifying the uncertainties and values that define the decision. Solving

the problem of inferring how another person has conceptualized a decision situation is usually

the toughest part of psychological research or applied decision analysis. (Much of the craft of

research design involves creating experimental situations in which the researcher restricts the

subject’s thought processes and understands the effects of those restrictions on the subject’s

mental model of the experimental situation.)

If we believe that we have captured our subject’s situation model in a decision tree diagram, it

is relatively easy to calculate the decision that leads to the highest expected outcome by

applying a rule that follows from decision theory (the four rational assumptions introduced in

Chapter 1). This rule is called the rational expectations principle, and it is usually summarized

as an equation:

Utility = S (probabilityi × valuei).

The equation prescribes that for each alternative course of action under consideration (each

major branch of the decision tree), we need to weight each of the potential consequences by its

probability of occurrence, and then add up all the component products to yield a summary

evaluation called an expected utility for each alternative course of action (each initial left-

hand branch). In our example medical decision (Figure 2.1), the calculations specify the

expected utility for “have the operation” as +52 ([+80 × .65] + [0 × .35]) and for “do not operate”

as +44 ([+100 × .30] + [+20 × .70]), implying that the rational decision would be to have the

operation. In the case of the gamble (Figure 2.2), if we assume that the dollar values represent

the decision maker’s true personal values for those consequences (an assumption that needs to

be carefully examined), the expected utility for gamble (a) is $9.00 ([$45 × .20] + [0 × .80]) and

for gamble (b) is $7.50 ([$30 × .25] + [0 × .75]), implying the decision maker should choose to

play gamble (a), if the expected value is the only consideration.

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