1. 1ESA 2007 World Meeting, Rome Partition Dependence in Prediction Markets - Evidence from the Lab and from the Field  Ulrich.Sonnemann@wiwi.uni-muenster.de  +49 (0) 251 83-22026 Titelfolie Ulrich Sonnemann Colin Camerer Craig Fox Thomas Langer Muenster CalTech 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

2. 2ESA 2007 World Meeting, Rome Prediction Markets and Partition Dependence 1. Motivation & Research Question Prediction Markets Markets where participants trade in contracts whose payoff depends on unknown future events. Iowa Electronic Markets TradeSports Siemens deadline (Ortner 98) „.. market forecasts are typically fairly accurate...“ HP printer sales (Chen, Plott 02) Survey: Wolfers, Zitzewitz JEP 04 Partition Dependence Different partitions of the event space can lead to different probability judgments for the same event Individual probability judgments depend on specific categorical „partition“, i.e. there is a bias towards the ignorance prior (bias toward 1/n). e.g. Fox, Clemen Mgt Sci 05: Subjective Probability Assessment in Decision Analysis: Partition Dependence and Bias Toward the Ignorance Prior

3. 3ESA 2007 World Meeting, Rome Research Question 1. Motivation & 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)?

4. 4ESA 2007 World Meeting, Rome 2. Experimental/Empirical Evidence Lab Study: DAX index, (temperature, sports) Study 1 Laboratory Study: DAX index, (temperature, sports)

5. 5ESA 2007 World Meeting, Rome Construction of the assets (for DAX index stimulus) 7328  DAX  7496.99 DAX  7327.99 7497  DAX Asset 2Asset 1Asset 3 DAX 7328 7497 7647 A claim will pay 100 cts if the DAX closes within the respective interval, otherwise the claim will pay nothing Lab Study: DAX index, (temperature, sports) 2. Experimental/Empirical Evidence Underlying event: „DAX close two weeks in the future“

6. 6ESA 2007 World Meeting, Rome Treatment 2 7497  DAX  7646.99 Asset 3Asset 1&2Asset 4 Treatment 1 7328  DAX  7496.99 DAX  7327.99 7497  DAX Asset 2Asset 1Asset 3&4 7328 7497 7647 DAX DAX  7496.99 7647  DAX Lab Study: DAX index, (temperature, sports) 2. Experimental/Empirical Evidence

7. 7ESA 2007 World Meeting, Rome Lab Study: Main Result 2. Experimental/Empirical Evidence 0.5610.1520.336 0.713 Treatment 1: 123&4 Treatment 2: intervals 341&2 p<0.0001 Wilcoxon p<0.0001 Wilcoxon N = 12 mean equil. prices 0.4040.4240.177 0.581 N = 12 mean equil. prices 0.289  12 0.245  34 Bias in Equilibrium Market Prices (DAX index stimulus)

8. 8ESA 2007 World Meeting, Rome 2. Experimental/Empirical Evidence Study 2 Field Experiment: NBA Playoffs, Soccer World Cup Field Experiment (NBA Playoffs, Soccer World Cup)

9. 9ESA 2007 World Meeting, Rome Field Experiment (NBA Playoffs, Soccer World Cup) 2. Experimental/Empirical Evidence  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!

10. 10ESA 2007 World Meeting, Rome 2. Experimental/Empirical Evidence Study 3 Field Data: Economic Derivatives Field Data (Economic Derivatives)

11. 11ESA 2007 World Meeting, Rome 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: 2. Experimental/Empirical Evidence Gürkaynak, Wolfers 06

12. 12ESA 2007 World Meeting, Rome  We assume the observed probability distribution to be actually a mixture between the true probability and an ignorance prior 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) Field Data (Economic Derivatives) 2. Experimental/Empirical Evidence = *+ (1- ) * Observed distribution True (i.e. unbiased) distribution Ignorance prior (1/n) distribution = *+ (1- ) * F(x)B(x)I(x)

13. 13ESA 2007 World Meeting, Rome 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! 3. Conclusions Thank you for your attention!