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Choice by Heuristics
Eduard BrandstätterJohannes 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.
What would you choose? A or B?
O A O B
A 80% chance to win $5,00020% chance to win $0
B 2% chance to win $4,01098% chance to win $4,000
Problem
Priority Heuristic
Three Reasons• Minimum gains• Chances of the minimum gains• Maximum gains
A 80% chance to win $5,00020% chance to win $0
B 2% chance to win $4,01098% chance to win $4,000
Priority Heuristic
Priority Rule1) Do the minimum gains differ?
STOP
A 80% chance to win $5,00020% chance to win $0
B 2% chance to win $4,01098% chance to win $4,000
Problem
What would you choose? C or D?
O C O D
C 40% chance to win $5,00060% chance to win $0
D 80% chance to win $2,50020% chance to win $0
Priority Heuristic
C 40% chance to win $5,00060% chance to win $0
D 80% chance to win $2,50020% chance to win $0
Priority Rule1) Do the minimum gains differ?2) Do the chances of the minimum gains differ?
STOP
Problem
E 0.001% chance to win $5,00099.999% chance to win $0
F 0.002% chance to win $2,50099.998% chance to win $0
What would you choose? E or F?
O E O F
Priority Heuristic
E 0.001% chance to win $5,00099.999% chance to win $0
F 0.002% chance to win $2,50099.998% chance to win $0
Priority Rule1) Do the minimum gains differ?2) Do the chances of the minimum gains differ?3) Choose the gamble with the higher maximum gain!
Choose E!
Questions
When do the minimum gains differ?
When do the chances differ?
Aspiration Levels
Minimum Gains 10% of the highest gainof the decision problem
Chances 10%
E 0.001% chance to win $5,00099.999% chance to win $0
F 0.002% chance to win $2,50099.998% chance to win $0
Aspiration Levels: $500, 10%
Results
(Kahneman & Tversky, 1979)
0
10
20
30
40
50
60
70
80
90
100
Equi-probable
Equal-weight
Mini-max
Maxi-max
Betterthan
average
Tallying Mostlikely
Lexico-graphic
Leastlikely
Probable
Cor
rect
Pre
dict
ions
(%)
100
50
40
30
20
10
0
60
80
90
70
Results
(Kahneman & Tversky, 1979)
0
10
20
30
40
50
60
70
80
90
100
TAX Equi-probable
Equal-weight
Mini-max
Maxi-max
Betterthan
average
Tallying Mostlikely
Lexico-graphic
Leastlikely
Probable
Cor
rect
Pre
dict
ions
(%)
100
50
40
30
20
10
0
60
80
90
70
Results
(Kahneman & Tversky, 1979)
0
10
20
30
40
50
60
70
80
90
100
SPA TAX Equi-probable
Equal-weight
Mini-max
Maxi-max
Betterthan
average
Tallying Mostlikely
Lexico-graphic
Leastlikely
Probable
Cor
rect
Pre
dict
ions
(%)
100
50
40
30
20
10
0
60
80
90
70
Results
(Kahneman & Tversky, 1979)
0
10
20
30
40
50
60
70
80
90
100
CPTErevet al.
(2002)
SPA TAX Equi-probable
Equal-weight
Mini-max
Maxi-max
Betterthan
average
Tallying Mostlikely
Lexico-graphic
Leastlikely
Probable
Cor
rect
Pre
dict
ions
(%)
100
50
40
30
20
10
0
60
80
90
70
Results
(Kahneman & Tversky, 1979)
0
10
20
30
40
50
60
70
80
90
100
CPTT&K
(1992)
CPTErevet al.
(2002)
SPA TAX Equi-probable
Equal-weight
Mini-max
Maxi-max
Betterthan
average
Tallying Mostlikely
Lexico-graphic
Leastlikely
Probable
Cor
rect
Pre
dict
ions
(%)
100
50
40
30
20
10
0
60
80
90
70
Results
(Kahneman & Tversky, 1979)
0
10
20
30
40
50
60
70
80
90
100
CPTL&O
(1999)
CPTT&K
(1992)
CPTErevet al.
(2002)
SPA TAX Equi-probable
Equal-weight
Mini-max
Maxi-max
Betterthan
average
Tallying Mostlikely
Lexico-graphic
Leastlikely
Probable
Cor
rect
Pre
dict
ions
(%)
100
50
40
30
20
10
0
60
80
90
70
Results
(Kahneman & Tversky, 1979)
0
10
20
30
40
50
60
70
80
90
100
P riority CP TL& O
(1999)
CP TT& K
(1992)
C P TE rev et a l.
(2002)
S P A TA X E qui-probable
E qual-weight
M in i-m ax
M ax i-m ax
B etterthan
average
Tally ing M os tlik ely
Lex ic o-graphic
Leas tlik e ly
P robable
Cor
rect
Pre
dict
ions
(%)
100
50
40
30
20
10
0
60
80
90
70
Results
BTA
EQUI
LL
MLLEX
MAXI
EQW
GUESSPROB MINI
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Information Ignored (%)
Co
rrec
t Pre
dic t
ions
(%
)
Results
TAX
TALL
BTA
EQUI
LL
MLLEX
MAXI
EQW
GUESSPROB MINI
SPACPT
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Information Ignored (%)
Co
rrec
t Pre
dic t
ions
(%
)
Results
TAX
TALL
PRIORITY
BTA
EQUI
LL
MLLEX
MAXI
EQW
GUESSPROB MINI
SPACPT
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Information Ignored (%)
Co
rrec
t Pre
dic t
ions
(%
)
Conclusion
• Expectancy-value theories rest on untested assumptions
• Priority HeuristicMinimum 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 BrandstätterJohannes 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
Independent variables
• Number of conse-quences(2 or 5)
• Number of reasons(1 or 3)
2 5
Ausgänge
11
12
13
14
En
tsch
eid
un
gsz
eit
(sec
)
Benötigte Schritte1
3
3 Reasons
1 Reason
2 Consequences 5
Dec
isio
n t
ime
(sec
)
40
50
60
70
80
90
100
Ratio of Expected Values
Cor
rect
Pre
dict
ions
(%)
PRIORITY
TAX
SPA
CPT
EV
2 2
Range of Application
0
10
20
30
40
50
60
70
80
90
100
1 2 3 4 5 6
Ratio Between Expected Values
Cor
rect
Pre
dict
ions
(%
)
PRIORITY
TAX
SPA
CPT
EV
Results
Mellers et al. (1992)
Results
Gambles with five consequences (Lopes & Oden, 1999)
0
10
20
30
40
50
60
70
80
90
100
Priority CPTT&K
(1992)
CPTErev et al.
(2002)
TAX Equi-probable
Equal-weight
Minimax Maximax Betterthan
average
Mostlikely
Lexico-graphic
Leastlikely
Probable
Cor
rect
Pre
dict
ions
(%)
50
40
30
20
10
0
60
70
80
90
100
Results
Choices between a gamble and a sure amount(Tversky & Kahneman, 1992)
0
10
20
30
40
50
60
70
80
90
100
Priority CPTL&O
(1999)
CPTErevet al.
(2002)
SPA Equi-probable
Equal-weight
Minimax Maximax Betterthan
average
Tallying Mostlikely
Lexico-graphic
Leastlikely
Probable
Cor
rect
Pre
dict
ions
(%)
50
60
70
80
90
100
10
0
20
30
40
Results
Randomly generated gambles (Erev et al., 2002)
0
10
20
30
40
50
60
70
80
90
100
Priority CPTL&O
(1999)
CPTT&K
(1992)
SPA TAX Equi-probable
Equal-weight
Mini-max
Maxi-max
Betterthan
average
Tallying Mostlikely
Lexico-graphic
Leastlikely
Probable
Cor
rect
Pre
dict
ions
(%
)
ResultsPriority Heuristic
Correct Predictions
Kahneman & Tversky (1979) 100%
Lopes & Oden (1999) 87%
Tversky & Kahneman (1992) 89%
Erev et al. (2002) 85%
Priority Heuristic For Losses?
Gains1) Do the minimum gains differ?2) Do the probabilities of the minimum gains differ?3) Choose the gamble with the higher maximum gain!
Losses1) 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 > B
A 29% chance to win $5.0071% chance to win $0
B 38% chance to win $4.5062% chance to win $0
Choose A!
Transitivity?
A > B, B > C
A 29% chance to win $5.0071% chance to win $0
B 38% chance to win $4.5062% chance to win $0
C 46% chance to win $4.0054% chance to win $0
Choose B!
Transitivity?
A > B, B > C, but C > A
A 29% chance to win $5.0071% chance to win $0
B 38% chance to win $4.5062% chance to win $0
C 46% chance to win $4.0054% chance to win $0
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 orface a trial with a 50% chance of winning €420,000,otherwise nothing.
A defendant can either pay for a €200,000 settlement orface a trial with a 50% chance of losing €420,000,otherwise nothing.
Example
A defendant can either pay for a $200,000 settlement orface a trial with a 50% chance of losing $420,000,or a 50% chance of losing nothing.
Losses1) Do the minimum losses differ? AL: $42,000
STOP
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.
A 80% chance 4 00020% chance 0
B For sure 3 000
• Better-than-average Calculate the grand mean of all out-comes of all gambles. For eachgamble calculate the number of
out-comes equal or above
the grand mean.Choose the gamble
with the highestnumber of such
outcomes.
• Least-Likely Identify each gamble‘s worst payoff. Select thegamble with the lowest
probability of the worstpayoff.
Dual-Heuristics
• 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 4 00020% chance 0
B For sure 3 000
• Most-likely Determine the most likely outcome of eachgamble and their respective payoffs. Then select the gamble with the highest, most
likelypayoff.
Dual-Heuristics
• Lexikographic Like most-likely. If two outcomes are equal,determine the second most likely outcome ofeach gamble and select the gamble with the(second most likely) payoff. Proceed, until a decision is reached.
A 80% chance 4 00020% chance 0
B For sure 3 000
A 20% chance 5,00080% chance 2,000
B 50% chance 4,00050% chance 1,200
AL € = 500p = 10%
C 25% chance 4,00075% chance 3,000
D 20% chance 5,00080% chance 2,800
AL € = 500p = 10%
Computerexperiment: Decision Time
PredictionPeople 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 Entscheidungstheoriena) Kumulative Prospekt-Theorie (CPT)b) Security-Potential/Aspiration Theorie (SPA) abc) 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 B
200 mit p = 0.04 200 mit p = 0.04
150 mit p = 0.21 165 mit p = 0.11
100 mit p = 0.50 130 mit p = 0.19
50 mit p = 0.21 95 mit p = 0.28
0 mit p = 0.04 60 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 B
50 mit p = 0.1 95 sicher
100 mit p = 0.9
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 B 98 mit p = 0.17 0 mit p = 0.51 0 mit p = 0.83
EV = 37.7 EV = 16.7
Prospekt-TheorieKahneman & Tversky (1979)
Wahrscheinlichkeits-Gewichtungs-Funktion
Werte-Funktion
v x( )
x(-x)
U = (pi) v(xi)
Probability ( )p0 1
1
(p)
Problem Multiplikation
Expectancy Value Theories
Dependent Variable = Probability x Value
Choice Difficulty
A 99% chance to win €5,0001% chance to win €0
B 100 % chance to win €3
C 80% chance to win €5,00020% chance to win €0
D 2% chance to win €4,01098% chance to win €4,000
EV
€4,950
€3
€4,000
€4,000
Results
TAX
TALL
PRIORITY
BTA
EQ UI
LL
M LLEX
M AXI
EQ W
G UESSPROB M INI
SPACPT
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
In form a tion Igno red (% )
Co
rrec
t Pre
dict
ions
(%
)
Results
GUESS
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Information Ignored (%)
Co
rrec
t Pre
dic t
ions
(%
)
Results
(Kahneman & Tversky, 1979)
0
10
20
30
40
50
60
70
80
90
100
Cor
rect
Pre
dict
ions
(%)
100
50
40
30
20
10
0
60
80
90
70
Results
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
Information Ignored (%)
Co
rrec
t Pre
dic t
ions
(%
)
Utility = ∑ Probability x Value
What would you choose? A or B?
O A O B
A 29% chance to win $3.0071% chance to win $0
B 17% chance to win $56.7083% chance to win $0
Three Steps: Easy Choice
Results
0
10
20
30
40
50
60
70
80
90
100
Equi-probable
Equal-weight
Minimax Maximax Betterthan
average
Tallying Mostlikely
Lexico-graphic
Leastlikely
Probable
Cor
rect
Pre
dict
ions
(%)
50
60
70
80
90
100
10
0
20
30
40
Results
0
10
20
30
40
50
60
70
80
90
100
CPT SPA Equi-probable
Equal-weight
Minimax Maximax Betterthan
average
Tallying Mostlikely
Lexico-graphic
Leastlikely
Probable
Co
rre
ctP
red
ictio
ns(%
)
50
60
70
80
90
100
10
0
20
30
40
Results
0
10
20
30
40
50
60
70
80
90
100
Priority CPT SPA Equi-probable
Equal-weight
Minimax Maximax Betterthan
average
Tallying Mostlikely
Lexico-graphic
Leastlikely
Probable
Cor
rect
Pre
dict
ions
(%)
50
60
70
80
90
100
10
0
20
30
40