Probability weighting function for experience-based decisions

Katarzyna Domurat

Centre for Economic Psychology and Decision SciencesL. Kozminski Academy of Entrepreneurship and Management

Warsaw, Poland

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)

Experience-based Decision (ED)

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

Clicking paradigm

• In "experience-based" decisions (ED) people behave as if they underweight small probabilities [Hertwig et. al. (2004)]

• Explanation: sampling error [Fox&Hadar (2006)]

or something else?

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

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)

• Certainty equivalent (CE) method [Kahneman&Tversky, 1992; Wu&Gonzales, 1999]

• LabSee program (labsee.boby.pl)

The experiment design

First stage: sample a lottery (representive sample/without sampling error)

150

0

Second stage: choosing CE for observed lottery

OutcomeX (PLN)

Prefer SureOutcome X

Prefer Lottery

150 ο

120 ο

90 ο

60 ο

30 ο

0 ο

OutcomeX (PLN)

Prefer SureOutcome X

PreferLottery

60 ο

54 ο

48 ο

42 ο

36 ο

30ο

CE – approximated by the middle of final interval

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

.0),())(1()()()( 2121 xxwherexvpwxvpwCEv

)).())(1()()(( 211 xvpwxvpwvCE

Estimation procedure

• One functional form of v(x):

• And four parametric specifications of w(p):

(1) (3)

(2) (4)

.0,)( xdlaxxv

1

])1([

)(

pp

ppw

)1()(

pp

ppw

))ln(exp()( ppw

))ln(exp()( ppw

Results

• Estimations for two sets of median data:SET1 (N=15) and SET2 (N=7)

1

])1([

)(

pp

ppw

Model 1:

)1()(

pp

ppw

Model 2:

))ln(exp()( ppw Model 3:

))ln(exp()( ppw Model 4:

Conclusions

• The higher γ 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