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Expected Utility with Random Optimism and Pessimism EUROPE

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Expected Utility with Random Optimism and Pessimism EUROPE Powered By Docstoc
					   Expected Utility with Random
    Optimism and Pessimism
           (EUROPE)


Pavlo Blavatskyy        Ulrich Schmidt
 University of Zurich   University of Kiel &
                        Kiel Institute for the
                         World Economy
                Motivation
• Evidence on errors in risky choice [Harless
  and Camerer (1994), Hey and Orme
  (1994)]
• Expected utility plus noise
          Vc(p) = i u(xi)pi+ 
                 = i [u(xi) + ]pi
• Noise is added to the utility scale, i.e. the
  evaluation of outcomes is noisy
                   Motivation
• Our model: evaluation of probabilities is noisy:
   – People are less familiar with probabilities than with
     monetary amounts
   – Psychological studies: people in good mood are
     optimistic while people in bad mood are pessimistic
     [Johnson and Tversky (1983), Wright and Bower
     (1992), Mayer and Hanson (1995)]
   – Optimism and pessimism influence perception of
     probabilities
   – If moods are not modelled endogenously they can be
     taken as random
                  Motivation
• Vc(p) = i u(xi)[pi+ i]
• p i = pi + i is perceived probability of xi
    *


• Our goal:
   – Analyze this model as simple as possible
   – Take some basic requirements of rationalitiy
     into account:
                      (i) 0  pi + i  1,
                      (ii) i (pi + i) = 1,
                      (iii) i = 0 if pi = 0
               The Model
• X = (x1, x2, ..., xn)
• p = (p1, p2, ..., pn)
• True preferences satisfy axioms of EU
• (u1, u2, ..., un) such that V(p) = i uipi
• Choice is subject to noise in the probability
  perception
• (1, 2, ..., n)
• V c(p) =  u p *    with p i = [pi+ i]
                             *
               i i i
                      The Model
• What is the simplest formulation of the
  model such that the three rationality
  requirements are satisfied?
• Errors i cannot be independently drawn if
  they should always sum up to zero
• Independently drawn primary distortions:
  (´1, ´2, ..., ´n)
           p i  ε
• p 
   *              i

        1   j1 ε j
   i            n
                The Model
• Each ´i is drawn from a symmetric
  distribution with zero mean and support
  [-, ]
• 0 ≤  < 0.5
• Lemma 1:
  If perceived probabilities should satisfy
  0  p i  1, we must have pi + ´i  0 for all
        *

  i.
                  The Model
• What happens if pi < ?
• Realizations of ´i which lead to pi + ´i < 0 have
  to be ruled out
• Distribution of primary distortions has to be
  truncated
• Lemma 2:
  (i) E(´i) = 0 if pi  
  (ii) E(´i) > 0 if pi < 
  (iii) E(´i) > E(´j) if pi < pj and pi < .
                  The Model
• Proposition 1:
  (i) E(p i ) > pi if pi < pj for all j  i.
          *


  (ii) E(p i ) < pi if pi >  and there exists an
            *

  outcome xj with pj < .

          p*  p i
  (iii) E *  
            i
         p  p     for all pi < pj with pi < .
          j     j
     Behavioral Implications
• Common consequence and common ratio
  effect
• Reflection effect
• Fourfold pattern of risk attitudes
• Event-splitting effects
• Violations of betweenness
             Conclusions
• Simple model of probability distortions
  leads to overweighting of small and
  underweighting of large probabilities
• Psychological foundation for weighting
  function in OPT
• Extensions to uncertainty and cumulative
  probabilities

				
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