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Combining multiple probability predictions using a simple logit model

Author

Listed:
  • Satopää, Ville A.
  • Baron, Jonathan
  • Foster, Dean P.
  • Mellers, Barbara A.
  • Tetlock, Philip E.
  • Ungar, Lyle H.

Abstract

This paper begins by presenting a simple model of the way in which experts estimate probabilities. The model is then used to construct a likelihood-based aggregation formula for combining multiple probability forecasts. The resulting aggregator has a simple analytical form that depends on a single, easily-interpretable parameter. This makes it computationally simple, attractive for further development, and robust against overfitting. Based on a large-scale dataset in which over 1300 experts tried to predict 69 geopolitical events, our aggregator is found to be superior to several widely-used aggregation algorithms.

Suggested Citation

  • Satopää, Ville A. & Baron, Jonathan & Foster, Dean P. & Mellers, Barbara A. & Tetlock, Philip E. & Ungar, Lyle H., 2014. "Combining multiple probability predictions using a simple logit model," International Journal of Forecasting, Elsevier, vol. 30(2), pages 344-356.
    • Handle: RePEc:eee:intfor:v:30:y:2014:i:2:p:344-356
    DOI: 10.1016/j.ijforecast.2013.09.009
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    References listed on IDEAS

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    7. Graefe, Andreas & Armstrong, J. Scott & Jones, Randall J. & Cuzán, Alfred G., 2014. "Combining forecasts: An application to elections," International Journal of Forecasting, Elsevier, vol. 30(1), pages 43-54.
    8. McKenzie, Craig R.M. & Liersch, Michael J. & Yaniv, Ilan, 2008. "Overconfidence in interval estimates: What does expertise buy you?," Organizational Behavior and Human Decision Processes, Elsevier, vol. 107(2), pages 179-191, November.
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    Citations

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    Cited by:

    1. Tao Lin & Yiling Chen, 2022. "Sample Complexity of Forecast Aggregation," Papers 2207.13126, arXiv.org, revised Oct 2023.
    2. Yakov Babichenko & Dan Garber, 2021. "Learning Optimal Forecast Aggregation in Partial Evidence Environments," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 628-641, May.
    3. repec:cup:judgdm:v:14:y:2019:i:4:p:395-411 is not listed on IDEAS
    4. Jonathan Baron & Barbara A. Mellers & Philip E. Tetlock & Eric Stone & Lyle H. Ungar, 2014. "Two Reasons to Make Aggregated Probability Forecasts More Extreme," Decision Analysis, INFORMS, vol. 11(2), pages 133-145, June.
    5. repec:cup:judgdm:v:14:y:2019:i:2:p:135-147 is not listed on IDEAS
    6. Hanea, Anca & Wilkinson, David Peter & McBride, Marissa & Lyon, Aidan & van Ravenzwaaij, Don & Singleton Thorn, Felix & Gray, Charles T. & Mandel, David R. & Willcox, Aaron & Gould, Elliot, 2021. "Mathematically aggregating experts' predictions of possible futures," MetaArXiv rxmh7, Center for Open Science.
    7. repec:cup:judgdm:v:13:y:2018:i:2:p:185-201 is not listed on IDEAS
    8. Jason Dana & Pavel Atanasov & Philip Tetlock & Barbara Mellers, 2019. "Are markets more accurate than polls? The surprising informational value of “just askingâ€," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 14(2), pages 135-147, March.
    9. Satopää, Ville A., 2021. "Improving the wisdom of crowds with analysis of variance of predictions of related outcomes," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1728-1747.
    10. Jared A. Beekman & Ronald F. A. Woodaman & Dennis M. Buede, 2020. "A Review of Probabilistic Opinion Pooling Algorithms with Application to Insider Threat Detection," Decision Analysis, INFORMS, vol. 17(1), pages 39-55, March.
    11. Ying Han & David Budescu, 2019. "A universal method for evaluating the quality of aggregators," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 14(4), pages 395-411, July.
    12. Satopää, Ville A. & Salikhov, Marat & Tetlock, Philip E. & Mellers, Barbara, 2023. "Decomposing the effects of crowd-wisdom aggregators: The bias–information–noise (BIN) model," International Journal of Forecasting, Elsevier, vol. 39(1), pages 470-485.
    13. Zanin, Luca, 2020. "Combining multiple probability predictions in the presence of class imbalance to discriminate between potential bad and good borrowers in the peer-to-peer lending market," Journal of Behavioral and Experimental Finance, Elsevier, vol. 25(C).
    14. Karvetski, Christopher W. & Meinel, Carolyn & Maxwell, Daniel T. & Lu, Yunzi & Mellers, Barbara A. & Tetlock, Philip E., 2022. "What do forecasting rationales reveal about thinking patterns of top geopolitical forecasters?," International Journal of Forecasting, Elsevier, vol. 38(2), pages 688-704.
    15. Ville A. Satopää & Robin Pemantle & Lyle H. Ungar, 2016. "Modeling Probability Forecasts via Information Diversity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1623-1633, October.
    16. Jens Witkowski & Rupert Freeman & Jennifer Wortman Vaughan & David M. Pennock & Andreas Krause, 2023. "Incentive-Compatible Forecasting Competitions," Management Science, INFORMS, vol. 69(3), pages 1354-1374, March.
    17. Niklas Valentin Lehmann, 2023. "Forecasting skill of a crowd-prediction platform: A comparison of exchange rate forecasts," Papers 2312.09081, arXiv.org.
    18. Ville A. Satopää & Marat Salikhov & Philip E. Tetlock & Barbara Mellers, 2021. "Bias, Information, Noise: The BIN Model of Forecasting," Management Science, INFORMS, vol. 67(12), pages 7599-7618, December.
    19. Edgar C. Merkle & Robert Hartman, 2018. "Weighted Brier score decompositions for topically heterogenous forecasting tournaments," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 13(2), pages 185-201, March.

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