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Abstract: This experiment explored various methods for modeling and aggregating continuous probability distributions from relatively few discrete judgments by individual forecasters. Our results provide compelling evidence that accurate continuous subjective probability forecasts can be modeled from a small set of discrete ordinal forecasts, and that these continuous distributions can be aggregated to yield consensus distributions that consistently outperform the average forecaster. At the forecaster level, modeled distributions performed equivalently to explicit forecasts, implying that with no additional effort on the part of the forecaster, we can derive accurate continuous forecasts from just a few discrete judgments, and then estimate probabilistic forecasts for any value of the forecasted variable. We evaluated two continuous aggregation methods, one taken from the existing literature and one newly developed hereone. They achieve increases in performance accuracy similar to the known benefits of aggregating discrete forecasts. This result suggests the potential to apply many of the known techniques for aggregating and weighting discrete forecasts to the continuous domain. While there is still much research to do regarding which particular families of distributions perform best under what conditions, this experiment clearly demonstrates that even with forecast sets that vary widely in terms of response quality, consensus methods can efficiently aggregate signal from the crowd noise in the context of continuous probability forecasting, even when eliciting only a small set of discrete judgments from forecasters.
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