Subjective Expected Utility Theory SEU

1. (Subjective) Expected Utility Theory (SEU) Normative theory of decision making �how people SHOULD make decisions under uncertainty

2. Key concepts - DM underuncertainty Each ALTERNATIVE assigned a UTILE UTILE = numeric value or worth Each OUTCOME (O) assigned a PROBABILITY (P) How to choose? U X P = preferred O �Maximize Expected Utility�

3. Key concepts - DM underuncertainty �Maximize Expected Utility� A1�U X P�> .9 A2�U X P�> .01 O1 = �win� Modeling US decision Kosovo (2 alternatives generated) A1 (air strikes) (P of success) 5 .5 = 2.5 A2(troops + air) (P of success) 1 .9 = .9

4. ASSUMPTIONS ORDER Alternatives - compare & rank order 2 alternatives (prefer 1 or indifferent) TRANSITIVITY - consistent rank order preferences prefer A < B < C (NOT C more A) (UTILE) 

5. ASSUMPTIONS INVARIANCE Decision maker NOT affected by way alternatives presented I.e., 2-stage lottery with 50 % each stage $100 payoff 1 shot gamble with 25% chance win $100 (different FRAMING)

6. ASSUMPTIONS cont. DOMINANCE Pick strategy (OUTCOME) with greater UTILITY (I.E., no other strategy (weakly/strongly) dominates on any/all attributes)

7. ASSUMPTIONS cont. CANCELLATION If identical probabilities 2 outcomes ignore utility of outcomes Logic: Common factors cancel out��..> OPTIMAL CHICE - leave to chance!)

8. ASSUMPTIONS cont. CONTINUITY Always gamble rather than pick �sure thing� if odds high enough I.e... a person�s �risk calculus

9. General Assumptions Probabilities and Utiles can be calculated DM will have complete inforamtion about P and U DM WILL Use P * U = maximum expected value

10. Paradoxes of Rationality Bernoulli�s ST. PETERSBURG PARADOX if tail Outcome 1 $2 if tail Outcome 2 $ 8 if tail Outcome 3 $ 16 ��> Why most people unwilling to pay more than a few dollars to play game with infinite expected return?

11. �Subjective Utility� Daniel Bernoulli�> �solved paradox� value (utility) of money declines with amount won (or already possessed) Utility Wealth

12. Expected Utility Theory von Neumann and Morgenstern (1947) �classical probabilities� relative frequencies over time

13. �SUBJECTIVE Expected UTILITY theory Savage (1954) subjective probabilities (not based on relative frequency; Baysian)

14. Subjective Expected Utility - 1950s What�s probability of a �one-shot� unrepeatable event �What is likelihood of a nuclear war?�

15. �Expected Utility theory�, SEU,�Rational choice model� based on �image� of DM as rational chooser - seeks to �Maximize Expected Utility� U * P = optimal choice �the major paradigm of decision making since WWII� (Paul Schoemaker, 1982) (It�s WRONG!)

16. Paradoxes of Rationality cont. Cancellation Principle: choice on how 2 alternatives differ NOT on common factor(s) ALLAIS PARADOX Which would you choose? #1: 1,000,000 for sure #2: 10% chance $2.5m AND 1% chance of $0

17. ALLAIS PARADOX cont. Alternative A: An 11 % chance $1m & 89% chance $ 0 OR Alternative B: A 10 % chance $2.5 & 90% chance $0 (risk seeking choice preferred�.WHY?)

18. Paradox Alternative 1 first problem and Alternative 2 second violate Cancellation Principle Cancellation Principle �choice between 2 alternatives should depend only on how 2 differ� Ellsberg Paradox - similar results

19. People�s Intransivity TRANSITIVITY principle A < B < C decision rule: �if I.Q. differs 10+ pts for 2 applicants pick one with highest IQ. If less or = 10 pts, pick most experienced? I.Q. Experience Applicants #1 120 1 #2 110 2 #3 100 3

20. Application: Importance of who gets to �set the agenda� in a Committee Candidates Committee Members #1 #2 #3 #4 #5 Joe Schmoe 1 1 2 3 3 Jane Doe 2 3 3 1 1 Al Einstein 3 2 1 2 2

21. Preference Reversals(Lichtenstein and Slovic 1970s) If choice framed a gamble�s probabilities �..> CHOOSE between 2 bets people pay attention to probability of winning If choice framed bid�.>amounts to be won or lost SET a PRICE for how valuable a bet is�>look for large payoff