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Choice by Heuristics Eduard Brandstätter Johannes Kepler University of Linz Austria Conference of the Economic Science Association, Rome, June 30, 2007

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Overview Expectancy-value theories Problems Priority Heuristic Conclusion

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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

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Heuristics!

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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.

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What would you choose? A or B? O AO B A80% chance to win $5,000 20% chance to win $0 B2% chance to win $4,010 98% chance to win $4,000 Problem

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Priority Heuristic Three Reasons Minimum gains Chances of the minimum gains Maximum gains A80% chance to win $5,000 20% chance to win $0 B2% chance to win $4,010 98% chance to win $4,000

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Priority Heuristic Priority Rule 1) Do the minimum gains differ? STOP A80% chance to win $5,000 20% chance to win $0 B2% chance to win $4,010 98% chance to win $4,000

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Problem What would you choose? C or D? O CO D C40% chance to win $5,000 60% chance to win $0 D80% chance to win $2,500 20% chance to win $0

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Priority Heuristic C40% chance to win $5,000 60% chance to win $0 D80% chance to win $2,500 20% chance to win $0 Priority Rule 1) Do the minimum gains differ? 2) Do the chances of the minimum gains differ? STOP

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Problem E0.001% chance to win $5,000 99.999% chance to win $0 F0.002% chance to win $2,500 99.998% chance to win $0 What would you choose? E or F? O EO F

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Priority Heuristic E0.001% chance to win $5,000 99.999% chance to win $0 F0.002% chance to win $2,500 99.998% chance 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! Choose E!

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Questions When do the minimum gains differ? When do the chances differ?

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Aspiration Levels Minimum Gains10% of the highest gain of the decision problem Chances10% E0.001% chance to win $5,000 99.999% chance to win $0 F0.002% chance to win $2,500 99.998% chance to win $0 Aspiration Levels: $500, 10%

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Results (Kahneman & Tversky, 1979)

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Results BTA EQUI LL ML LEX MAXI EQW GUESS PROBMINI 0 10 20 30 40 50 60 70 80 90 100 0102030405060708090100 Information Ignored (%) C o r r e c t P r e d i c t i o n s ( % )

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Results

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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

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Choice by Heuristics Eduard Brandstätter Johannes Kepler University of Linz Austria Conference of the Economic Science Association, Rome, June 30, 2007

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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) 3 Reasons 1 Reason 2Consequences 5 Decision time (sec)

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Range of Application

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Results Mellers et al. (1992)

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Results Gambles with five consequences (Lopes & Oden, 1999)

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Results Choices between a gamble and a sure amount (Tversky & Kahneman, 1992)

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Results Randomly generated gambles (Erev et al., 2002)

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Results Priority Heuristic Correct Predictions Kahneman & Tversky (1979)100% Lopes & Oden (1999)87% Tversky & Kahneman (1992)89% Erev et al. (2002)85%

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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%

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Transitivity? Transitivity: If A > B and B > C then A > C

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Transitivity? A > B A29% chance to win $5.00 71% chance to win $0 B38% chance to win $4.50 62% chance to win $0 Choose A!

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Transitivity? A > B, B > C A29% chance to win $5.00 71% chance to win $0 B38% chance to win $4.50 62% chance to win $0 C46% chance to win $4.00 54% chance to win $0 Choose B!

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Transitivity? A > B, B > C, but C > A A29% chance to win $5.00 71% chance to win $0 B38% chance to win $4.50 62% chance to win $0 C46% chance to win $4.00 54% chance to win $0 STOP

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Transitivity? Empirical Pattern A-B: 68% A B-C:65% B A-C37% A Prioirty heuristic predicts intransitivies

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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.

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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. Losses 1) Do the minimum losses differ? AL: $42,000 STOP

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Decision Making In real life, many risky choice situations. Whether to approach an attractive boy/girl or not operate ones 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

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Outcome-Heuristics Maximax Select the gamble with the highest maximum outcome. A80% chance4 000 20% chance0 BFor sure3 000 Better-than-average Calculate the grand mean of all out- comes of all gambles. For each gamble calculate the number of out- comes equal or above the grand mean. Choose the gamble with the highest number of such outcomes.

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Least-Likely Identify each gambles worst payoff. Select the gamble with the lowest probability of the worst payoff. 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. A80% chance4 000 20% chance0 BFor sure3 000

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Most-likely Determine the most likely outcome of each gamble and their respective payoffs. Then select the gamble with the highest, most likely payoff. Dual-Heuristics 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. A80% chance4 000 20% chance0 BFor sure3 000

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A20% chance 5,000 80% chance 2,000 B50% chance 4,000 50% chance 1,200 AL = 500 p = 10 % C25% chance 4,000 75% chance 3,000 D20% chance 5,000 80% chance 2,800 AL = 500 p = 10 % Computerexperiment: Decision Time Prediction People need less time for choice between A and B than between C and D

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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?

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Datensatz Klassische Entscheidungsprobleme (14) (Kahneman & Tversky, 1979)

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Vier heterogene Datensätze 1) Klassische Entscheidungsprobleme (14) (Kahneman & Tversky, 1979)

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Vier heterogene Datensätze 1) Klassische Entscheidungsprobleme (14) (Kahneman & Tversky, 1979) 2) Spiele, mit fünf Ausgängen (90) (Lopes & Oden, 1999) AB 200mit p = 0.04200mit p = 0.04 150mit p = 0.21165mit p = 0.11 100mit p = 0.50130mit p = 0.19 50mit p = 0.21 95mit p = 0.28 0mit p = 0.04 60mit p = 0.38

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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) AB 50mit p = 0.195sicher 100mit p = 0.9

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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 = 0.49B 98 mit p = 0.17 0 mit p = 0.51 0 mit p = 0.83 EV = 37.7 EV = 16.7

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Prospekt-Theorie Kahneman & Tversky (1979) Wahrscheinlichkeits-Gewichtungs- Funktion Werte-Funktion U = (p i ) v(x i ) (p) ProblemMultiplikation

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Expectancy Value Theories Dependent Variable = Probability x Value

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Choice Difficulty A99% chance to win 5,000 1% chance to win 0 B100 % chance to win 3 C80% chance to win 5,000 20% chance to win 0 D2% chance to win 4,010 98% chance to win 4,000 EV 4,950 3 4,000

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Results

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GUESS 0 10 20 30 40 50 60 70 80 90 100 0102030405060708090100 Information Ignored (%) C o r r e c t P r e d i c t i o n s ( % )

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Results (Kahneman & Tversky, 1979) 0 10 20 30 40 50 60 70 80 90 100 C o r r e c t P r e d i c t i o n s ( % ) 100 50 40 30 20 10 0 60 80 90 70

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Results 0 10 20 30 40 50 60 70 80 90 100 0102030405060708090100 Information Ignored (%) C o r r e c t P r e d i c t i o n s ( % )

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Utility = Probability x Value

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What would you choose? A or B? O AO B A29% chance to win $3.00 71% chance to win $0 B17% chance to win $56.70 83% chance to win $0 Three Steps: Easy Choice

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Results

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