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Is It Better to Average Probabilities or Quantiles?

Author

Listed:
  • Kenneth C. Lichtendahl

    (Darden School of Business, University of Virginia, Charlottesville, Virginia 22906)

  • Yael Grushka-Cockayne

    (Darden School of Business, University of Virginia, Charlottesville, Virginia 22906)

  • Robert L. Winkler

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

Abstract

We consider two ways to aggregate expert opinions using simple averages: averaging probabilities and averaging quantiles. We examine analytical properties of these forecasts and compare their ability to harness the wisdom of the crowd. In terms of location, the two average forecasts have the same mean. The average quantile forecast is always sharper: it has lower variance than the average probability forecast. Even when the average probability forecast is overconfident, the shape of the average quantile forecast still offers the possibility of a better forecast. Using probability forecasts for gross domestic product growth and inflation from the Survey of Professional Forecasters, we present evidence that both when the average probability forecast is overconfident and when it is underconfident, it is outperformed by the average quantile forecast. Our results show that averaging quantiles is a viable alternative and indicate some conditions under which it is likely to be more useful than averaging probabilities. This paper was accepted by Peter Wakker, decision analysis.

Suggested Citation

  • Kenneth C. Lichtendahl & Yael Grushka-Cockayne & Robert L. Winkler, 2013. "Is It Better to Average Probabilities or Quantiles?," Management Science, INFORMS, vol. 59(7), pages 1594-1611, July.
  • Handle: RePEc:inm:ormnsc:v:59:y:2013:i:7:p:1594-1611
    DOI: 10.1287/mnsc.1120.1667
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    References listed on IDEAS

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