Self-financed wagering mechanisms for forecasting

ABSTRACT

We examine a class of wagering mechanisms designed to elicit truthful predictions from a group of people without requiring any outside subsidy. We propose a number of desirable properties for wagering mechanisms, identifying one mechanism - weighted-score wagering - that satisfies all of the properties. Moreover, we show that a single-parameter generalization of weighted-score wagering is the only mechanism that satisfies these properties. We explore some variants of the core mechanism based on practical considerations.

REFERENCES

• 1: M. Ali. Probability and Utility Estimates for Racetrack Bettors. The Journal of Political Economy, 85(4):803--815, 1977.
• 2: Yiling Chen , Lance Fortnow , Evdokia Nikolova , David M. Pennock, Betting on permutations, Proceedings of the 8th ACM conference on Electronic commerce, June 11-15, 2007, San Diego, California, USA [doi>10.1145/1250910.1250957]
• 3: Y. Chen, D. Reeves, D. Pennock, R. Hanson, L. Fortnow, and R. Gonen. Bluffing and strategic reticence in prediction markets. In WINE, pages 70--81, 2007.
• 4: N. Economides and J. Lange. A Parimutuel Market Microstructure for Contingent Claims Trading. European Financial Management, 11(1):25--49, 2005.
• 5: Lance Fortnow , Joe Kilian , David M. Pennock , Michael P. Wellman, Betting Boolean-style: a framework for trading in securities based on logical formulas, Decision Support Systems, v.39 n.1, p.87-104, March 2005 [doi>10.1016/j.dss.2004.08.010]
• 6: T. Gneiting and A. Raftery. Strictly proper scoring rules, prediction and estimation. Journal of the American Statistical Association, 102(477):359--378, 2007.
• 7: Robin Hanson, Combinatorial Information Market Design, Information Systems Frontiers, v.5 n.1, p.107-119, January 2003 [doi>10.1023/A:1022058209073]
• 8: D. Johnstone. The Parimutuel Kelly Probability Scoring Rule. Decision Analysis, 4(2):66, 2007.
• 9: C. H. Kehr, J. P. Krahnen, and E. Theissen. The anatomy of a call market. Journal of Financial Intermediation, 10(3-4):249--270, 2001.
• 10: D. Marc Kilgour , Yigal Gerchak, Elicitation of Probabilities Using Competitive Scoring Rules, Decision Analysis, v.1 n.2, p.108-113, June 2004 [doi>10.1287/deca.1030.0003]
• 11: Nicolas S. Lambert , David M. Pennock , Yoav Shoham, Eliciting properties of probability distributions, Proceedings of the 9th ACM conference on Electronic commerce, July 08-12, 2008, Chicago, Il, USA [doi>10.1145/1386790.1386813]
• 12: P. Milgrom and N. Stokey. Information, trade, and common knowledge. Journal of Economic Theory, 1982.
• 13: M. Peters, A. Man-Cho So, and Y. Ye. Pari-mutuel markets: Mechanisms and performance. In WINE, pages 82--95, 2007.
• 14: L. Savage. Elicitation of Personal Probabilities and Expectations. Journal of the American Statistical Association, 66(336):783--801, 1971.
• 15: R. H. Thaler and W. T. Ziemba. Anomalies: Parimutuel betting markets: Racetracks and lotteries. Journal of Economic Perspectives, 2(2):161--174, 1988.
• 16: R. Winkler, J.Munoz, J. Cervera, J. Bernardo, G. Blattenberger, J. Kadane, D. Lindley, A. Murphy, R. Oliver, and D. Rios-Insua. Scoring rules and the evaluation of probabilities. TEST, 5(1):1--60, 1996.
• 17: J. Wolfers and E. Zitzewitz. Prediction Markets. The Journal of Economic Perspectives, 18(2):107--126, 2004.
• 18: J. Wolfers and E. Zitzewitz. Prediction Markets in Theory and Practice. Working paper, 2006.

INDEX TERMS

Primary Classification:
  J. Computer Applications
  J.4 SOCIAL AND BEHAVIORAL SCIENCES
      Subjects: Economics

General Terms:
Economics, Theory

Keywords:
group forecasting, mechanism design, prediction market