Titelfolie
Partition Dependence in Prediction Markets Evidence from the Lab and from the Field
Ulrich Sonnemann
Muenster
Colin Camerer
CalTech
Craig Fox
Thomas Langer
UCLA
Muenster
Outline
1. Motivation & Research Question
2. Experimental/Empirical Evidence
• Lab Study: DAX index, (temperature, sports)
• Field Experiment (NBA Playoffs, Soccer World Cup)
• Field Data (Economic Derivatives)
3. Conclusions
 [email protected]
 +49 (0) 251 83-22026
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1. Motivation & Research Question
Prediction Markets and Partition Dependence
Prediction Markets
Markets where participants trade in
contracts whose payoff depends on
unknown future events.
Iowa Electronic Markets
TradeSports
HP printer sales (Chen, Plott 02)
Siemens deadline (Ortner 98)
Partition Dependence
Individual probability judgments
depend on specific categorical
„partition“, i.e. there is a bias
towards the ignorance prior
(bias toward 1/n).
Different partitions of the
event space can lead to
different probability
judgments for the same event
e.g. Fox, Clemen Mgt Sci 05:
Survey: Wolfers, Zitzewitz JEP 04
„.. market forecasts are
typically fairly accurate...“
Subjective Probability Assessment in
Decision Analysis: Partition
Dependence and Bias Toward the
Ignorance Prior
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1. Motivation & Research Question
Research Question
 Are prices in prediction markets
(and therefrom inferred probabilities)
influenced by the partition of the event space?
 Do markets eliminate (or at least mitigate) the
partition dependence bias which is observed in
individual judgment (and under what circumstances)?
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2. Experimental/Empirical Evidence
Lab Study: DAX index, (temperature, sports)
Study 1
Laboratory Study:
DAX index, (temperature, sports)
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2. Experimental/Empirical Evidence
Lab Study: DAX index, (temperature, sports)
Construction of the assets (for DAX index stimulus)
Underlying event:
A claim will pay 100 cts if the DAX
closes within the respective interval,
otherwise the claim will pay nothing
„DAX close two
weeks in the future“
DAX
7497
7328
Asset 1
DAX  7327.99
Asset 2
7328  DAX  7496.99
7647
Asset 3
7497  DAX
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2. Experimental/Empirical Evidence
Lab Study: DAX index, (temperature, sports)
DAX
7497
7328
7647
Treatment 1
Asset 1
DAX  7327.99
Asset 2
7328  DAX  7496.99
Asset 3&4
7497  DAX
Treatment 2
Asset 1&2
DAX  7496.99
Asset 3
7497  DAX  7646.99
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Asset 4
7647  DAX
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2. Experimental/Empirical Evidence
Lab Study: Main Result
Bias in Equilibrium Market Prices (DAX index stimulus)
intervals
Treatment 1:
N = 12
mean equil.
prices
1
2
3&4
0.152
0.561
0.336
0.713
p<0.0001
Wilcoxon
N = 12
mean equil.
prices
Treatment 2:
12
34
0.245
p<0.0001
Wilcoxon
0.581
0.289
0.424
0.404
0.177
1&2
3
4
intervals
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2. Experimental/Empirical Evidence
Field Experiment (NBA Playoffs, Soccer World Cup)
Study 2
Field Experiment:
NBA Playoffs, Soccer World Cup
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2. Experimental/Empirical Evidence
Field Experiment (NBA Playoffs, Soccer World Cup)
 Engaging events!


NBA Basketball Playoffs 2006
FIFA Soccer World Cup 2006
 Large scale study: N = 317 (Germany) + 139 (UCLA) = 456

Max. 20 traders per single market
 Long span of continuous open markets (24/7)


Playoffs April 22 through June 22, 2006 (~9 weeks)
World Cup May 24 through July 9, 2006 (~6½ weeks)
 Main Finding:

Evidence for Partition Dependence!
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2. Experimental/Empirical Evidence
Field Data (Economic Derivatives)
Study 3
Field Data:
Economic Derivatives
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2. Experimental/Empirical Evidence
Field Data (Economic Derivatives)
 Economic Derivatives (by Goldman Sachs and Deutsche Bank)

Field Prediction Markets for macroeconomic derivatives such like
 growth in non-farm payrolls,
 retail sales,
 etc.


Highly professional traders / High stakes ($)
Allows derivation of probability density function from prices of digital
options:
Gürkaynak, Wolfers 06
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2. Experimental/Empirical Evidence
Field Data (Economic Derivatives)
 We assume the observed probability distribution to be actually
a mixture between
•
•
the true probability and
an ignorance prior distribution
0.1
0.1
0.1
0.09
0.08
0.09
0.09
0.07
0.08
0.07
0.08
0.07
0.06
0.06
0.06
0.05
0.04
0.05
0.05
F(x)
B(x)
Observed
distribution
=*
0.04
0.03
0.02
0.01
1.
35
1.
15
0.
95
0.
75
0.
55
0.
35
0.
15
-0
.0
5
0
-0
.3
60
69
02
1.
35
1.
15
0.
95
0.
75
0.
55
0.
35
0
0.
15
1.
35
1.
15
0.
95
0.
75
0.
55
0.
35
0.
15
-0
.0
5
-0
.3
60
69
02
0
+ (1- ) *
0.01
-0
.0
5
0.02
0.01
0.03
0.02
-0
.3
60
69
02
=*
0.03
0.04
I(x)
True
(i.e. unbiased) + (1- ) *
distribution
Ignorance
prior (1/n)
distribution
 Are bias-corrected B(x) more accurate than observed F(x)?



Yes:  =.6  mean abs error .673
( =1  .680)
Slight correction w/  =.99 improves forecasts (mean forecast error)
53%, 56%, 70%, 54% in four markets (overall n=153, p<.01)
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3. Conclusions
Conclusions
 Partition-dependence exists in prediction markets
 Evidence from:



Lab: Around 25% in judgment and equilibrium prices
Field experiments: Virtual arbitrage 1-6%
Field markets: 40% weight on (1/n)?
 Market forces seem not to be able to mitigate the systematic distortion in
individual judgment!
Thank you for
your attention!
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