Choice by Heuristics

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