Probability weighting function for experience-based decisions

1
Probability weighting function for
experience-based decisions

• Katarzyna Domurat
• Centre for Economic Psychology and Decision
  SciencesL. Kozminski Academy of Entrepreneurship
  and Management
• Warsaw, Poland

2
Prospect Theory

• when making decisions under risk people use
  decision weights in such a way that they
  overweight low probability events and underweight
  high probability events
• supported in several experiments when people were
  provided with probabilities of potential outcomes
  (DD)

3
Experience-based Decision (ED)

• DM samples information about risky options
  (sample the payoff distributions) and then makes
  a choice

Clicking paradigm
4

• In "experience-based" decisions (ED) people
  behave as if they underweight small probabilities
  Hertwig et. al. (2004)
• Explanation sampling error FoxHadar (2006)
• or something else?

5
The goal of research

• Estimate probability weighting function under
  experience condition without sampling error

• The probability weighting function will be
  more linear for ED than for DD

6
The experiment design

• 54 two-outcome lotteries
• ? with six different pairs of outcomes
• (150-0, 300-0, 600-0, 300-150, 450-150, 600-300)
• ? and nine levels of probability associated with
  maximum outcome in lottery
• (0.01, 0.05, 0.1, 0.25, 0.5, 0.75, 0.0, 0.95,
  0.99)
• 3 computerized sessions (about 20 gambles per
  session)

7
The experiment design

• Certainty equivalent (CE) method
• KahnemanTversky, 1992 WuGonzales, 1999
• LabSee program (labsee.boby.pl)

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First stage sample a lottery (representive
sample/without sampling error)
150
0
9
Second stage choosing CE for observed lottery
Outcome X (PLN) Prefer Sure Outcome X Prefer Lottery
150 ?
120 ?
90 ?
60 ?
30 ?
0 ?
Outcome X (PLN) Prefer Sure Outcome X Prefer Lottery
60 ?
54 ?
48 ?
42 ?
36 ?
30 ?
?
CE approximated by the middle of final interval
10
Estimation procedure

• Standard parametric fit of the weighting function
  w(p) and the value function v(x)
• Cumulative Prospect Theory
• Nonlinear least square regression
• CE-median certainty equivalent

11
Estimation procedure

• One functional form of v(x)
• And four parametric specifications of w(p)
• (1) (3)
• (2) (4)

12
Results

• Estimations for two sets of median data
• SET1 (N15) and SET2 (N7)

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Model 1
14
Model 2
15
Model 3
16
Model 4
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Conclusions

• The higher ? obtained under experience condition
  means that w(p) is more linear for ED than for DD
  
• the effect of overweighting small probabilities
  is weaker
• Greater sensitivity to changes in probability in
  ED