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Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation

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  • Robin Hanson

Abstract

In practice, scoring rules elicit good probability estimates from individuals, while betting markets elicit good consensus estimates from groups. Market scoring rules combine these features, eliciting estimates from individuals or groups, with groups costing no more than individuals. Regarding a bet on one event given another event, only logarithmic versions preserve the probability of the given event. Logarithmic versions also preserve the conditional probabilities of other events, and so preserve conditional independence relations. Given logarithmic rules that elicit relative probabilities of base event pairs, it costs no more to elicit estimates on all combinations of these base events.

Suggested Citation

  • Robin Hanson, 2007. "Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation," Journal of Prediction Markets, University of Buckingham Press, vol. 1(1), pages 3-15, February.
  • Handle: RePEc:buc:jpredm:v:1:y:2007:i:1:p:3-15
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    Cited by:

    1. Snowberg, Erik & Wolfers, Justin & Zitzewitz, Eric, 2013. "Prediction Markets for Economic Forecasting," Handbook of Economic Forecasting, Elsevier.
    2. Papakonstantinou, A. & Rogers, A & Gerding, E. H. & Jennings, N. R., 2010. "Mechanism Design for the truthful elicitation of costly probabilistic estimates in Distributed Information Systems," MPRA Paper 43324, University Library of Munich, Germany.
    3. Florian Teschner & David Rothschild & Henner Gimpel, 2017. "Manipulation in Conditional Decision Markets," Group Decision and Negotiation, Springer, vol. 26(5), pages 953-971, September.
    4. Mueller-Frank, Manuel, 2014. "Does one Bayesian make a difference?," Journal of Economic Theory, Elsevier, vol. 154(C), pages 423-452.
    5. Patrick Buckley & Fergal O’Brien, 0. "The effect of malicious manipulations on prediction market accuracy," Information Systems Frontiers, Springer, vol. 0, pages 1-13.
    6. Hanea, A.M. & McBride, M.F. & Burgman, M.A. & Wintle, B.C. & Fidler, F. & Flander, L. & Twardy, C.R. & Manning, B. & Mascaro, S., 2017. "I nvestigate D iscuss E stimate A ggregate for structured expert judgement," International Journal of Forecasting, Elsevier, vol. 33(1), pages 267-279.
    7. Abraham Othman & Tuomas Sandholm, 2013. "The Gates Hillman prediction market," Review of Economic Design, Springer;Society for Economic Design, vol. 17(2), pages 95-128, June.
    8. Mikuláš Gangur & Miroslav Plevný, 2014. "Tools for Consumer Rights Protection in the Prediction of Electronic Virtual Market and Technological Changes," The AMFITEATRU ECONOMIC journal, Academy of Economic Studies - Bucharest, Romania, vol. 16(36), pages 578-578, May.
    9. Ledyard, John & Hanson, Robin & Ishikida, Takashi, 2009. "An experimental test of combinatorial information markets," Journal of Economic Behavior & Organization, Elsevier, vol. 69(2), pages 182-189, February.
    10. Jinli Hu, 2012. "Combinatorial Modelling and Learning with Prediction Markets," Papers 1201.3851, arXiv.org.
    11. Yiling Chen & David M Pennock, 2012. "A Utility Framework for Bounded-Loss Market Makers," Papers 1206.5252, arXiv.org.
    12. Yiling Chen & Mike Ruberry & Jennifer Wortman Vaughan, 2012. "Designing Informative Securities," Papers 1210.4837, arXiv.org.
    13. Kelly, David L. & Letson, David & Nelson, Forrest & Nolan, David S. & Solís, Daniel, 2012. "Evolution of subjective hurricane risk perceptions: A Bayesian approach," Journal of Economic Behavior & Organization, Elsevier, vol. 81(2), pages 644-663.
    14. Lambert, Nicolas S. & Langford, John & Wortman Vaughan, Jennifer & Chen, Yiling & Reeves, Daniel M. & Shoham, Yoav & Pennock, David M., 2015. "An axiomatic characterization of wagering mechanisms," Journal of Economic Theory, Elsevier, vol. 156(C), pages 389-416.
    15. Buckley, Patrick, 2016. "Harnessing the wisdom of crowds: Decision spaces for prediction markets," Business Horizons, Elsevier, vol. 59(1), pages 85-94.
    16. Wei Sun & Robin Hanson & Kathryn Blackmond Laskey & Charles Twardy, 2012. "Probability and Asset Updating using Bayesian Networks for Combinatorial Prediction Markets," Papers 1210.4900, arXiv.org.
    17. Riekhof, Hans-Christian & Riekhof, Marie-Catherine & Brinkhoff, Stefan, 2012. "Predictive Markets: Ein vielversprechender Weg zur Verbesserung der Prognosequalität im Unternehmen?," PFH Forschungspapiere/Research Papers 2012/07, PFH Private University of Applied Sciences, Göttingen.
    18. Rajiv Sethi & Jennifer Wortman Vaughan, 2016. "Belief Aggregation with Automated Market Makers," Computational Economics, Springer;Society for Computational Economics, vol. 48(1), pages 155-178, June.
    19. Nicolas Della Penna & Mark D. Reid, 2011. "Bandit Market Makers," Papers 1112.0076, arXiv.org, revised Aug 2013.
    20. Camerer, Colin & Dreber, Anna & Forsell, Eskil & Ho, Teck-Hua & Huber, Jurgen & Johannesson, Magnus & Kirchler, Michael & Almenberg, Johan & Altmejd, Adam & Chan, Taizan & Heikensten, Emma & Holzmeist, 2016. "Evaluating replicability of laboratory experiments in Economics," MPRA Paper 75461, University Library of Munich, Germany.
    21. repec:spr:infosf:v:19:y:2017:i:3:d:10.1007_s10796-015-9617-7 is not listed on IDEAS

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