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Robust Forecast Aggregation

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  • Itai Areili
  • Yakov Babichenko
  • Rann Smorodinsky

Abstract

Bayesian experts who are exposed to different evidence often make contradictory probabilistic forecasts. An aggregator, ignorant of the underlying model, uses this to calculate her own forecast. We use the notions of scoring rules and regret to propose a natural way to evaluate an aggregation scheme. We focus on a binary state space and construct low regret aggregation schemes whenever there are only two experts which are either Blackwell-ordered or receive conditionally i.i.d. signals. In contrast, if there are many experts with conditionally i.i.d. signals, then no scheme performs (asymptotically) better than a $(0.5,0.5)$ forecast.

Suggested Citation

  • Itai Areili & Yakov Babichenko & Rann Smorodinsky, 2017. "Robust Forecast Aggregation," Papers 1710.02838, arXiv.org, revised Feb 2018.
    • Handle: RePEc:arx:papers:1710.02838
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    References listed on IDEAS

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    1. Nabil I. Al-Najjar & Jonathan Weinstein, 2008. "Comparative Testing of Experts," Econometrica, Econometric Society, vol. 76(3), pages 541-559, May.
    2. 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.
    3. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    4. Colin Bermingham & Antonello D’Agostino, 2014. "Understanding and forecasting aggregate and disaggregate price dynamics," Empirical Economics, Springer, vol. 46(2), pages 765-788, March.
    5. Ernst, Philip & Pemantle, Robin & Satopää, Ville & Ungar, Lyle, 2016. "Bayesian aggregation of two forecasts in the partial information framework," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 170-180.
    6. Alvaro Sandroni, 2000. "Do Markets Favor Agents Able to Make Accurate Predicitions?," Econometrica, Econometric Society, vol. 68(6), pages 1303-1342, November.
    7. Yossi Feinberg & Colin Stewart, 2008. "Testing Multiple Forecasters," Econometrica, Econometric Society, vol. 76(3), pages 561-582, May.
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    Cited by:

    1. 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.
    2. Henrique de Oliveira & Yuhta Ishii & Xiao Lin, 2021. "Robust Merging of Information," Papers 2106.00088, arXiv.org.
    3. Babichenko, Yakov & Talgam-Cohen, Inbal & Xu, Haifeng & Zabarnyi, Konstantin, 2022. "Regret-minimizing Bayesian persuasion," Games and Economic Behavior, Elsevier, vol. 136(C), pages 226-248.
    4. Arieli, Itai & Babichenko, Yakov & Smorodinsky, Rann, 2020. "Identifiable information structures," Games and Economic Behavior, Elsevier, vol. 120(C), pages 16-27.
    5. 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.
    6. Itay Kavaler & Rann Smorodinsky, 2019. "A Cardinal Comparison of Experts," Papers 1908.10649, arXiv.org, revised Feb 2020.

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