Computational Modeling Approach
to Decision Making
1. Measurement of Preference
·
Decision making theories
begin with the concept of a preference relation.
A,
B, C are alternatives (or options)
–
Gambles, Cars,
Jobs, Houses, Medical Treatments
A ³p B means
A is preferred or indifferent to B
·
Preference
relations can be measured by
Choice (choose between
A or B)
Certainty Equivalents (what is the dollar equivalent of
each option)
Ratings (rate how strongly you like each option on a 10
point scale)
·
Different
Measures of Preference do not always yield the same order
Producing
preference reversals
e.g.,
Gamble
A: .95 chance of winning $4 vs. nothing
Gamble
B: .60 chance of winning $16 vs. .4
chance of losing $8
Choice
Frequency A > Choice Frequency B
Certainty
Equivalent for B > Certainty Equivalent for A
(see Slovic & Tversky, 1993, for a review)
·
Most theorists
believe that choice is the most basic measure of preference (see Luce, 2000)
2. Conflict and the Probabilistic Nature of
Preference
•
Suppose a person
is given a choice between two options that are approximately equal in weighted
average value, inducing some type of conflict.
•
The same pair of
options is presented on two different occasions.
•
The probability
of making an inconsistent choice is .33. In other words, the person changes his
or her mind 1 out of 3 times! (see, e.g., Starmer,
2000)
•
The test – retest
(within one week) correlation for selling prices is generally below .50 (less
than 25% predictable across time). (Hershey & Schoemaker,
1989)
•
This is a
ubiquitous property of human behavior, but standard utility theories consider
it an irrational aspect of human choice.
3. Biological and Evolutionary Explanations
for the Probabilistic Choice
·
Exploratory
Behavior
o
We need to
continuously learn about uncertain probabilities of payoffs in a changing,
non-stationary environment.
·
Unpredictable
Behavior
o
We do not want
our competitors to be able to perfectly predict our behavior and use this to
take advantage of us.
·
Dynamic
Motivational Systems
o
Our needs or
goals change over time like hunger, thirst, sex
4. Psychological Explanations for
Probabilistic Choice
·
Fundamental
Preference Uncertainty
o
We have fuzzy
beliefs and uncertain values.
·
Constructive
Evaluations
o
We need to
construct evaluations online, and the frame may change, and attention may
fluctuate.
·
Changing Strategies
o
Using different
choice rules can change preferences
5. Implications for Standard Utility Theory
·
Suppose we
assume: Choose A over B à A ³p B à u(A) > u(B)
o
What problems
does this generate?
·
MaCrimmon (1968) asked 38 business managers to respond to 3
sets of choices, and 8 managers exhibited intransitivity’s. Should we reject
utility theory?
·
Absolutely not (e.g.,says Luce, 2000) these are
just errors. After all, the nature of choice is probabilistic.
·
Thus, standard
utility theorists define
A ³p B à Pr[ A | {A,B} ] ³ .50
·
In the end,
standard utility models are actually founded on probabilistic choice
assumptions. Axioms must be tested using statistical models.
·
But why is a
.00002 change in probability from .49999 to .50001 more important than a .48
change in probability from .51 to .99 or .49 to .01?
·
A model that
accounts for the entire continuous range of probabilities is superior to one
that only accounts for two categories [0,.5) vs (.5, 1] of probabilities.
6. Decisions take time
·
Decision time is
systematically related to choice probability
o
Petrusic and Jamieson (1978)
o
Dror, Busemeyer, & Baselo al (1999)
·
Choice
probabilities become more extreme with longer deliberations
o
Simonson (1989)
compromise effect
o
Dhar (2000) attraction effect
·
Preferences can
be reversed under time pressure
o
Edlund and Svenson (1993)
o
Diederich (2000)
·
Preferences are
dynamically inconsistent (Plans are not followed)
o
Ainslie (1975)
o
Busemeyer et al.
(2000)
o
Trope et al
(2002)
7. Goals of Computational Models of Choice
·
Explain how
conflicts are resolved
o
the deliberation
process described by William James
·
Account for the
entire continuous range of choice probabilities [0,1]
o
Not simply
categorize whether they are above or below 50%
o
Explain
paradoxical choice behavior
·
Account for other
manifestations of choice
o
Choice response
time
o
Confidence
Ratings
·
Account for other
manifestations of preference
o
Certainty
equivalents
o
Buying or selling
prices
·
Explain the
origins of weights and values
·
Build on
principles from both cognitive psychology and neuro-psychology
·
Examples
o
Decision Field
Theory (Busemeyer & Townsend, 1993)
o
Neural
Computational Model of Usher & McClelland (2002)
o
Constraint
Satisfaction model of Guo and Holyoak
(2002)