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Subjective Expected Utility Theory SEU

Key concepts - DM under uncertainty. Each ALTERNATIVE assigned a UTILE UTILE = numeric value or worthEach OUTCOME (O) assigned a PROBABILITY (P). How to choose?U X P = preferred O Maximize Expected Utility" . Key concepts - DM under uncertain

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Subjective Expected Utility Theory SEU

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

    2. Key concepts - DM under uncertainty 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 under uncertainty “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

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