Choice by Heuristics
Eduard Brandstätter
Johannes Kepler University of Linz
Austria
Conference of the Economic Science Association,
Rome, June 30, 2007
Overview
• Expectancy-value theories
• Problems
• Priority Heuristic
• Conclusion
Expectancy-Value Theories
Utility = ∑ Probability x Value
•
•
•
•
•
•
•
•
•
Expected-value theory
Expected-utility theory
Prospect theory
Cumulative prospect theory
Security-potential/aspiration theory
Transfer of attention exchange model
Disappointment theory
Regret theory
Decision affect theory
Heuristics!
Three Steps
1) Check for dominance
2) Check for easy choice
3) Employ the priority heuristic
Brandstätter, E., Gigerenzer, G., & Hertwig, R. (2006). The
priority heuristic: Making choices without trade-offs.
Psychological Review, 113, 409-432.
Problem
A
80% chance
20% chance
to win $5,000
to win $0
B
2% chance
98% chance
to win $4,010
to win $4,000
What would you choose? A or B?
OA
OB
Priority Heuristic
A
80% chance
20% chance
to win $5,000
to win $0
B
2% chance
98% chance
to win $4,010
to win $4,000
Three Reasons
• Minimum gains
• Chances of the minimum gains
• Maximum gains
Priority Heuristic
A
80% chance
20% chance
to win $5,000
to win $0
STOP
B
2% chance
98% chance
to win $4,010
to win $4,000
Priority Rule
1) Do the minimum gains differ?
Problem
C
40% chance
60% chance
to win $5,000
to win $0
D
80% chance
20% chance
to win $2,500
to win $0
What would you choose? C or D?
OC
OD
Priority Heuristic
C
D
40% chance
60% chance
80% chance
20% chance
to win $5,000
to win $0
to win $2,500
to win $0
Priority Rule
1) Do the minimum gains differ?
2) Do the chances of the minimum gains differ?
STOP
Problem
E
0.001% chance
99.999% chance
to win $5,000
to win $0
F
0.002% chance
99.998% chance
to win $2,500
to win $0
What would you choose? E or F?
OE
OF
Priority Heuristic
E
0.001% chance
99.999% chance
to win $5,000
to win $0
Choose E!
F
0.002% chance
99.998% chance
to win $2,500
to win $0
Priority Rule
1) Do the minimum gains differ?
2) Do the chances of the minimum gains differ?
3) Choose the gamble with the higher maximum gain!
Questions
When do the minimum gains differ?
When do the chances differ?
Aspiration Levels
Minimum Gains
10% of the highest gain
of the decision problem
Chances
10%
E
0.001% chance
99.999% chance
to win $5,000
to win $0
F
0.002% chance
99.998% chance
to win $2,500
to win $0
Aspiration Levels: $500, 10%
Results
Correct Predictions (%)
(Kahneman & Tversky, 1979)
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
Equi- Equalprobable weight
Minimax
Maximax
Better Tallying Most Lexico- Least Probable
than
likely graphic likely
average
Results
Correct Predictions (%)
(Kahneman & Tversky, 1979)
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
TAX
Equi- Equalprobable weight
Minimax
Maximax
Better Tallying Most Lexico- Least Probable
than
likely graphic likely
average
Results
Correct Predictions (%)
(Kahneman & Tversky, 1979)
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
SPA
TAX
Equi- Equalprobable weight
Minimax
Maximax
Better Tallying Most Lexico- Least Probable
than
likely graphic likely
average
Results
Correct Predictions (%)
(Kahneman & Tversky, 1979)
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
CPT
SPA
Erev et al.
(2002)
TAX
Equi- Equalprobable weight
Minimax
Maximax
Better Tallying Most Lexico- Least Probable
than
likely graphic likely
average
Results
Correct Predictions (%)
(Kahneman & Tversky, 1979)
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
CPT
CPT
SPA
T&K Erev et al.
(1992) (2002)
TAX
Equi- Equalprobable weight
Minimax
Maximax
Better Tallying Most Lexico- Least Probable
than
likely graphic likely
average
Results
Correct Predictions (%)
(Kahneman & Tversky, 1979)
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
CPT
L&O
(1999)
CPT
CPT
SPA
T&K Erev et al.
(1992) (2002)
TAX
Equi- Equalprobable weight
Minimax
Maximax
Better Tallying Most Lexico- Least Probable
than
likely graphic likely
average
Results
Correct Predictions (%)
(Kahneman & Tversky, 1979)
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
Priority
CPT
L&O
(1999)
CPT
CPT
SPA
T&K Erev et al.
(1992) (2002)
TAX
Equi- Equalprobable weight
Minimax
Maximax
Better Tallying Most
than
likely
average
Lexico- Least Probable
graphic likely
Results
100
90
Correct Predictions (%)
80
70
60
LL
BTA
50
PROB
EQUI
LEX
MINI
ML
GUESS
MAXI
40
EQW
30
20
10
0
0
10
20
30
40
50
60
70
Information Ignored (%)
80
90 100
Results
100
Correct Predictions (%)
90
80
SPA
CPT
70
TAX
TALL
60
LL
BTA
50
PROB
EQUI
LEX
MINI
ML
GUESS
MAXI
40
EQW
30
20
10
0
0
10
20
30
40
50
60
70
Information Ignored (%)
80
90 100
Results
100
Correct Predictions (%)
90
PRIORITY
80
SPA
CPT
70
TAX
TALL
60
LL
BTA
50
PROB
EQUI
LEX
MINI
ML
GUESS
MAXI
40
EQW
30
20
10
0
0
10
20
30
40
50
60
70
Information Ignored (%)
80
90 100
Conclusion
• Expectancy-value theories rest on untested
assumptions
• Priority Heuristic
Minimum gain, chances of minimum gain, maximum gain
• New way to think about risky choice in the future
Eduard Brandstätter
Johannes Kepler University of Linz, Austria
Choice by Heuristics
Eduard Brandstätter
Johannes Kepler University of Linz
Austria
Conference of the Economic Science Association,
Rome, June 30, 2007
Computer Experiment
Choices between 2 gambles
Dependent variable
Decision time
Decision time (sec)
3 Reasons
Independent variables
• Number of consequences
(2 or 5)
1 Reason
2
Consequences
•
5
Number of reasons
(1 or 3)
Range of Application
100
Correct Predictions (%)
90
80
70
60
PRIORITY
TAX
SPA
50
CPT
EV
40
2
Ratio of Expected Values
2
Results
Mellers et al. (1992)
100
90
80
Correct Predictions (%)
70
60
50
40
30
PRIORITY
20
TAX
SPA
10
CPT
EV
0
1
2
3
4
Ratio Between Expected Values
5
6
Results
Correct Predictions (%)
Gambles with five consequences (Lopes & Oden, 1999)
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
Priority
CPT
T&K
(1992)
CPT
Erev et al.
(2002)
TAX
Equiprobable
Equalweight
Minimax Maximax
Better
than
average
Most
likely
Lexicographic
Least
likely
Probable
Results
Correct Predictions (%)
Choices between a gamble and a sure amount
(Tversky & Kahneman, 1992)
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
Priority
CPT
CPT
L&O Erev et al.
(1999)
(2002)
SPA
Equiprobable
Equalweight
Minimax Maximax
Better
than
average
Tallying
Most
likely
Lexicographic
Least
likely
Probable
Results
Randomly generated gambles (Erev et al., 2002)
100
90
80
Correct Predictions (%)
70
60
50
40
30
20
10
0
Priority
CPT
L&O
(1999)
CPT
T&K
(1992)
SPA
TAX
Equi- Equalprobable weight
Minimax
Maximax
Better Tallying
than
average
Most
likely
Lexicographic
Least Probable
likely
Results
Priority Heuristic
Correct Predictions
Kahneman & Tversky (1979)
100%
Lopes & Oden (1999)
87%
Tversky & Kahneman (1992)
89%
Erev et al. (2002)
85%
Priority Heuristic For Losses?
Gains
1) Do the minimum gains differ?
2) Do the probabilities of the minimum gains differ?
3) Choose the gamble with the higher maximum gain!
Losses
1) Do the minimum losses differ?
2) Do the probabilities of the minimum losses differ?
3) Choose the gamble with the lower maximum loss!
AL: 10% of highest gain/loss, 10%
Transitivity?
Transitivity: If A > B and B > C then A > C
Transitivity?
A
29% chance
71% chance
to win $5.00
to win $0
B
38% chance
62% chance
to win $4.50
to win $0
A>B
Choose A!
Transitivity?
A
29% chance
71% chance
to win $5.00
to win $0
B
38% chance
62% chance
to win $4.50
to win $0
C
46% chance
54% chance
to win $4.00
to win $0
A > B, B > C
Choose B!
Transitivity?
A
29% chance
71% chance
to win $5.00
to win $0
B
38% chance
62% chance
to win $4.50
to win $0
C
46% chance
54% chance
to win $4.00
to win $0
A > B, B > C, but C > A
STOP
Transitivity?
Empirical Pattern
A-B:
68% A
B-C:
65% B
A-C
37% A
Prioirty heuristic predicts intransitivies
Going to Court?
A plaintiff can either accept a €200,000 settlement or
face a trial with a 50% chance of winning €420,000,
otherwise nothing.
A defendant can either pay for a €200,000 settlement or
face a trial with a 50% chance of losing €420,000,
otherwise nothing.
Example
A defendant can either pay for a $200,000 settlement or
face a trial with a 50% chance of losing $420,000,
or a 50% chance of losing nothing.
STOP
Losses
1) Do the minimum losses differ? AL: $42,000
Decision Making
In real life, many risky choice situations. Whether to
•
approach an attractive boy/girl or not
•
operate one’s knee or not
•
take job offer A or B
•
invade a country or not
•
put sanctions on a country or not
•
go to court or not
Outcome-Heuristics
•
Maximax
Select the gamble with the highest
maximum outcome.
•
Better-than-average
Calculate the grand mean of all outcomes of all gambles. For each
gamble calculate the number of outcomes equal or above the grand mean.
Choose the gamble with the highest
number of such outcomes.
A
80% chance
20% chance
4 000
0
B
For sure
3 000
Dual-Heuristics
•
Least-Likely
Identify each gamble‘s worst payoff. Select the
gamble with the lowest probability of the worst
payoff.
•
Probable
Categorize probabilities as probable (i.e. p ≥ .5
for two-outcome gambles) and improbable.
Cancel improbable outcomes. Calculate the
mean of all probable outcomes for each gamble.
Select the gamble with the highest mean.
A
80% chance
20% chance
4 000
0
B
For sure
3 000
Dual-Heuristics
•
Most-likely
Determine the most likely outcome of each
gamble and their respective payoffs. Then
select the gamble with the highest, most likely
payoff.
•
Lexikographic
Like most-likely. If two outcomes are equal,
determine the second most likely outcome of
each gamble and select the gamble with the
(second most likely) payoff. Proceed, until a
decision is reached.
A
80% chance
20% chance
4 000
0
B
For sure
3 000
Computerexperiment: Decision Time
A 20% chance 5,000
80% chance 2,000
C 25% chance 4,000
75% chance 3,000
B 50% chance 4,000
50% chance 1,200
D 20% chance 5,000
80% chance 2,800
AL
€ = 500
p = 10%
AL
€ = 500
p = 10%
Prediction
People need less time for choice between A and B than
between C and D
Zentrale Fragen:
Wie gut schneidet die Prioritäts-Heuristik im Vergleich zu …
1) einfachen Entscheidungs-Heuristiken, und
2) komplexen Entscheidungstheorien
a) Kumulative Prospekt-Theorie (CPT)
b) Security-Potential/Aspiration Theorie (SPA) ab
c) Transfer of attention exchange model?
Datensatz
Klassische Entscheidungsprobleme (14)
(Kahneman & Tversky, 1979)
Vier heterogene Datensätze
1) Klassische Entscheidungsprobleme (14)
(Kahneman & Tversky, 1979)
Vier heterogene Datensätze
1) Klassische Entscheidungsprobleme (14)
(Kahneman & Tversky, 1979)
2) Spiele, mit fünf Ausgängen (90)
(Lopes & Oden, 1999)
A
200
150
100
50
0
mit p = 0.04
mit p = 0.21
mit p = 0.50
mit p = 0.21
mit p = 0.04
B
200
165
130
95
60
mit p = 0.04
mit p = 0.11
mit p = 0.19
mit p = 0.28
mit p = 0.38
Vier heterogene Datensätze
1) Klassische Entscheidungsprobleme (14)
(Kahneman & Tversky, 1979)
2) Spiele, mit fünf Ausgängen (90)
(Lopes & Oden, 1999)
3) Entscheidungsprobleme zwischen Spiel und sicherem Betrag (56)
(Tversky & Kahneman, 1992)
A
50
100
mit p = 0.1
mit p = 0.9
B
95
sicher
Vier heterogene Datensätze
1) Klassische Entscheidungsprobleme (14)
(Kahneman & Tversky, 1979)
2) Spiele, mit fünf Ausgängen (90)
(Lopes & Oden, 1999)
3) Entscheidungsprobleme zwischen Spiel und sicherem Betrag (56)
(Tversky & Kahneman, 1992)
4) Spiele mit ungleichem Erwartungswert (100)
(Erev et al., 2002)
A
77 mit p = 0.49
0 mit p = 0.51
EV = 37.7
B
98 mit p = 0.17
0 mit p = 0.83
EV = 16.7
Prospekt-Theorie
Kahneman & Tversky (1979)
U = (pi) v(xi)
1
(p)
v(x)
(-x)
0
Probability (p)
1
Wahrscheinlichkeits-GewichtungsFunktion
Problem
x
Multiplikation
Werte-Funktion
Expectancy Value Theories
Dependent Variable = Probability x Value
Choice Difficulty
EV
A
99% chance
1% chance
to win €5,000
to win €0
€4,950
B
100 % chance
to win €3
€3
C
80% chance
20% chance
to win €5,000
to win €0
€4,000
D
2% chance
98% chance
to win €4,010
to win €4,000
€4,000
Results
100
Correct Predictions (%)
90
PRIORITY
80
SPA
CPT
70
TAX
TALL
60
LL
BTA
50
PROB
EQUI
LEX
MINI
ML
GUESS
MAXI
40
EQW
30
20
10
0
0
10
20
30
40
50
60
70
Information Ignored (%)
80
90 100
Results
100
90
Correct Predictions (%)
80
70
60
GUESS
50
40
30
20
10
0
0
10
20
30
40
50
60
70
Information Ignored (%)
80
90 100
Results
Correct Predictions (%)
(Kahneman & Tversky, 1979)
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
Results
100
90
Correct Predictions (%)
80
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
70
Information Ignored (%)
80
90 100
Utility = ∑ Probability x Value
Three Steps: Easy Choice
A
29% chance
71% chance
to win $3.00
to win $0
B
17% chance
83% chance
to win $56.70
to win $0
What would you choose? A or B?
OA
OB
Correct Predictions (%)
Results
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
Equiprobable
Equalweight
Minimax
Maximax
Better
than
average
Tallying
Most
likely
Lexicographic
Least
likely
Probable
Correct Predictions (% )
Results
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
CPT
SPA
Equiprobable
Equalweight
Minimax
Maximax
Better
than
average
Tallying
Most
likely
Lexicographic
Least
likely
Probable
Correct Predictions (%)
Results
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
Priority
CPT
SPA
Equiprobable
Equalweight
Minimax Maximax
Better
than
average
Tallying
Most
likely
Lexicographic
Least
likely
Probable