Transcript Development of Decision Analysis

The Development of
Decision Analysis
Jason R. W. Merrick
Based on Smith and von Winterfeldt (2004). Decision Analysis in
Management Science. Management Science 50(5) 561-574.
Why making decisions can be hard?

There are trade-offs between the alternatives


There is uncertainty about the outcomes


Consider choosing a major and then a career
There are disagreements between stakeholders


Consider playing the lottery, investing in the stock market,
or choosing health insurance
There is a sequence of decisions to make


Consider buying a car, a computer or a phone
Consider making any decision with your spouse or
significant other
There is a large range of alternatives available
confined by constraints

Go see Drs. Brooks, Hardin, and McLay!
Elements of a Decision

Values and Objectives


Decisions and Alternatives


What you are trying to achieve?
What you are choosing between to get what you
want?
Uncertainties and Probabilities

The uncertain events that affect you getting what
you want?
The Decision Context

Keeney (1992) uses the concept of a decision frame
to explain the decisions that people make.


Suppose you are looking for a car.


A decision frame consists of a decision maker’s set of
alternatives and the objectives that the decision maker is
attempting to achieve when choosing.
What objectives might you have if you wanted a car to get
to work, go shopping, and get around town?
Suppose you are looking transportation for the same
purpose

How does this change your objectives for just the car
choice?
Development of Decision Analysis
Bernoulli
Bayes
Ramsey
DeFinetti
1738
1763
1931
1937
von
Neumann
Morgenstern
Savage
1954
1944
• Concerned with the fact that people generally do not follow the expected value
model when choosing amongst gambles (e.g. buying insurance).
• Proposed the expected utility model with a logarithmic utility function to
explain the deviations from the expected value model.
Development of Decision Analysis
Bernoulli
Bayes
Ramsey
DeFinetti
1738
1763
1931
1937
von
Neumann
Morgenstern
Savage
1954
1944
• Interested in the revision of probability based on observations and proposed
the updating procedure that is now known as Bayes Theorem
P( A | B) 
P( B | A) P( A)
P( B | A) P( A)  P( B | A) P( A)
Development of Decision Analysis
Bernoulli
Bayes
Ramsey
DeFinetti
1738
1763
1931
1937
von
Neumann
Morgenstern
Savage
1954
1944
• Recognized the notion of probability and utility as intrinsically intertwined and
showed that subjective probabilities and utilities can be inferred from
preferences among gambles.
Development of Decision Analysis
Bernoulli
Bayes
Ramsey
DeFinetti
1738
1763
1931
1937
von
Neumann
Morgenstern
Savage
1954
1944
• Followed a similar path as Ramsey by developing a system of assumptions
about preferences among gambles that allowed him to derive subjective
probabilities for events.
• DeFinetti’s interest was primarily in the representation of beliefs as subjective
probabilities, not in the derivation of utilities.
Development of Decision Analysis
Bernoulli
Bayes
Ramsey
DeFinetti
1738
1763
1931
1937
von
Neumann
Morgenstern
Savage
1954
1947
• “Theory of Games and Economic Behavior”: Primary purpose was to lay the
foundation for the study of games, but also established foundations for
decision analysis.
• Provided an axiomization of the expected utility model showing that the
cardinal utility function could be created from preferences among gambles.
• Analysis took the probabilities as a given and their axioms led to the
conclusion that decision makers should make decisions to maximize their
expected utility.
• This is now referred to as the expected utility model.
Development of Decision Analysis
Bernoulli
Bayes
Ramsey
DeFinetti
1738
1763
1931
1937
von
Neumann
Morgenstern
Savage
1954
1944
• Extended the work of von Neumann and Morgenstern to consider cases in
which the probabilities are not given.
• Savage’s goal was to provide a foundation for a “theory of probability based
on the personal view of probability derived mainly from the work of DeFinetti.”
• Savage proposed a set of axioms about preferences among gambles that
enabled him to simultaneously derive the existence of subjective probabilities
for events and utilities for outcomes
• Combined the ideas of utility theory from economics and subjective
probability from statistics in to the subjective expected utility model.
Lotteries

Let’s see what your answers would be
?
1

$0

1-?
$30,000
-$10,000
What would your answer be?
1
$500

$30,000
1-?
-$10,000


What would your answer be?
Etc…
How should we decide?

Complete Ordering Axiom
r1  r2
or r1  r2
or r1  r2
r1  r2 and r2  r3  r1  r3


These are the minimal mathematical conditions
for a complete ordering
What does this mean?
How should we decide?

Continuity Axiom
r1  r2 and r2  r3   c  0 s.t.
c
1


r2

1-c
r1
r3
This is rather like the mean value theorem in
calculus
What does this mean?
How should we decide?

Independence Axiom
if r1  r2 then r3 and c
c
1-c

r1
c

r3
What does this mean?
1-c
r2
r3
How should we decide?

Unequal Probability Axiom
if r1  r2 and p  q then
p
1-p

r1
q

r2
What does this mean?
1-q
r1
r2
How should we decide?

Compound Lottery Axiom
p
1
r1

1-p
r2
r3
p
q


1-q
r1
q

r4
What does this mean?
1-p
1-q
r4
r2
r3
Expected Utility Wins
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Criteria that don’t satisfy these axioms
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Maximin
Maximax
Minimax regret
They fail the continuity, unequal probability and
the compound lottery axioms
Criteria that do satisfy these axioms
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Expected value
Expected utility
Three Viewpoints
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There are three major angles of study about gambles and
decisions
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Normative: the study of rational choice.

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
Descriptive: the study of how people actually think and behave.

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
Normative models are built on basic assumptions (axioms) that
people consider as providing logical guidance for their decisions.
Examples include the expected utility model and the subjective
expected utility model.
Descriptive studies may develop mathematical models of behavior,
but such models are judged by the extent to which their predictions
correspond to the actual choices people make.
Major example is prospect theory.
Prescriptive: focused on helping people make better decisions.

Uses normative models, but with awareness of the limitations and
descriptive realities of human judgment.
Decision Analysis

Focused on the prescriptive power of the subjective
expected utility model and Bayesian statistics.


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Robert Schlaifer at Harvard wrote “Probability and Statistics
for Business Decisions” in 1959.
Howard Raiffa and Schlaifer wrote “Applied Statistical
Decision Theory” in 1961.
Ron Howard at Stanford first used the term decision
analysis.
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Howard (1966) “Decision Analysis: Applied Decision Theory”.
Howard (1968) “The Foundations of Decision Analysis”.