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1 st lecture

1 st lecture. Probabilities and Prospect Theory. Probabilities. In a text over 10 standard novel-pages, how many 7-letter words are of the form: _ _ _ _ ing _ _ _ _ _ ly _ _ _ _ _n_. Linda and Bill.

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1 st lecture

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  1. 1st lecture Probabilities and Prospect Theory

  2. Probabilities • In a text over 10 standard novel-pages, how many 7-letter words are of the form: • _ _ _ _ ing • _ _ _ _ _ ly • _ _ _ _ _n_

  3. Linda and Bill • “Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.” • Linda is a teacher in elementary school • Linda is active in the feminist movement (F) • Linda is a bank teller (B) • Linda is an insurance sales person • Linda is a bank teller and is active in the feminist movement (B&F) • Probability rank: • Naïve: B&F – 3,3; B – 4,4 • Sophisticated: B&F – 3,2; B – 4,3.

  4. Indirect and Direct tests • Indirect versus direct • Are both A&B and A in same questionnaire? • Transparent • Argument 1: Linda is more likely to be a bank teller than she is to be a feminist bank teller, because every feminist bank teller is a bank teller, but some bank tellers are not feminists and Linda could be one of them (35%) • Argument 2: Linda is more likely to be a feminist bank teller than she is likely to be a bank teller, because she resembles an active feminist more than she resembles a bank teller (65%)

  5. Extensional versus intuitive • Extensional reasoning • Lists, inclusions, exclusions. Events • Formal statistics. • If , Pr(A) ≥ Pr (B) • Moreover: • Intuitive reasoning • Not extensional • Heuristic • Availability and Representativity. • _ _ _ _ ing

  6. Availability Heuristics • We assess the probability of an event by the ease with witch we can create a mental picture of it. • Works good most of the time. • Frequency of words • A: _ _ _ _ ing (13.4) • B: _ _ _ _ _ n _ ( 4.7) • Now, and hence Pr(B)≥Pr(A) • But ….ing words are easier to imagine • Watching TV affect our probability assessment of violent crimes, divorce and heroic doctors. (O’Guinn and Schrum)

  7. Expected utility • Preferences over lotteries • Notation • (x1,p1;…;xn,pn)= x1 with probability p1; … and xn with probability pn • Null outcomes not listed: • (x1,p1) means x1 with probability p1 and 0 with probability 1-p1 • (x) means x with certainty.

  8. Independence Axiom • If A ~ B, then (A,p;…)~ (B,p;…) • Add continuity: if b(est) > x > w(orst) then there is a p=u(x) such that (b,p;w,1-p)~ (x) • It follows that lotteries should be ranked according to Expected utility Max ∑ piu(xi)

  9. Proof • Start with (x1,p1;x2,p2 ) • Now • x1~ (b,f(x1);w,1-u(x1)) • x2~ (b,f(x2);w,1-u(x2)) • Replace x1 and x2 by the equally good lotteries and collect terms • (x1,p1;x2,p2 ) ~ (b,p1u(x1)+p2u(x2); w,1-p1u(x1)+p2u(x2)) • The latter is (b,Eu(x);w,1-Eu(x))

  10. Prospect theory • Loss and gains • Value v(x-r) rather than utility u(x) where r is a reference point. • Decisions weights replace probabilities Max ∑ piv(xi-r) ( Replaces Max ∑ piu(xi) )

  11. Evidence; Decision weights • Problem 3 • A: (4 000, 0.80) or B: (3 000) • N=95 [20] [80]* • Problem 4 • C: (4 000, 0.20) or D: (3 000, 0.25) • N=95 [65]* [35] • Violates expected utility • B better than A : u(3000) > 0.8 u(4000) • C better than D: 0.25u(3000) > 0.20 u(4000) • Perception is relative: • 100% is more different from 95% than 25% is from 20%

  12. Value functionReflection effect • Problem 3 • A: (4 000, 0.80) or B: (3 000) • N=95 [20] [80]* • Problem 3’ • A: (-4 000, 0.80) or B: (-3 000) • N=95 [92]* [8] • Ranking reverses with different sign (Table 1) • Concave (risk aversion) for gains and • Convex (risk lover) for losses

  13. The reference point • Problem 11: In addition to whatever you own, you have been given 1 000. You are now asked to choose between: • A: (1 000, 0.50) or B: (500) • N=95 [16] [84]* • Problem 12: In addition to whatever you own, you have been given 2 000. You are now asked to choose between: • A: (-1 000, 0.50) or B: (-500) • N=95 [69]* [31] • Both equivalent according to EU, but the initial instruction affect the reference point.

  14. Decision weights • Suggested by Allais (1953). • Originally a function of probability pi = f(pi) • This formulation violates stochastic dominance and are difficult to generalize to lotteries with many outcomes (pi→0) • The standard is thus to use cumulative prospect theory

  15. Rank dependent weights • Order the outcome such that x1>x2>…>xk>0>xk+1>…>xn • Decision weights for gains • Decision weights for losses

  16. Cumulative prospect theory • Value-function • Concave for gains • Convex for losses • Kink at 0 • Decision weights • Adjust cumulative distribution from above and below • Maximize

  17. Main difference between CPT and EU • Loss aversion • Marginal utility twice as large for losses compared to gains • Certainty effects • 100% is distinctively different from 99% • 49% is about the same as 50% • Reflection • Risk seeking for losses • Risk aversion form gains. • Most risk avers when both losses and gains.

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