Stochastic forecasts in complex environments can benefit from combining the estimates of large groups of forecasters (“judges”). But aggregating multiple opinions faces several challenges. First, human judges are notoriously incoherent when their forecasts involve logically complex events. Second, individual judges may have specialized knowledge, so different judges may produce forecasts for different events. Third, the credibility of individual judges might vary, and one would like to pay greater attention to more trustworthy forecasts. These considerations limit the value of simple aggregation (...) methods like linear averaging. In this paper, a new algorithm is proposed for combining probabilistic assessments from a large pool of judges. Two measures of a judge’s likely credibility are introduced and used in the algorithm to determine the judge’s weight in aggregation. The algorithm was tested on a data set of nearly half a million probability estimates of events related to the 2008 U.S. presidential election (∼ 16000 judges). (shrink)

This paper analyzes individual probabilistic predictions of state outcomes in the 2008 U.S. presidential election. Employing an original survey of more than 19,000 respondents, ours is the first study of electoral forecasting to involve multiple subnational predictions and to incorporate the influence of respondents’ home states. We relate a range of demographic, political, and cognitive variables to individual accuracy and predictions, as well as to how accuracy improved over time. We find strong support for wishful thinking bias in expectations, as (...) Republicans gave higher probabilities to McCain victories and were worse at overall prediction. In addition, we find that respondents living in states with higher vote shares for Obama performed better at prediction and displayed less wishful thinking bias. We conclude by showing that suitable aggregations of our respondents’ predictions outperformed Intrade (a prediction market) and fivethirtyeight.com (a poll-based forecast) at most points in time. (shrink)

��The Coherent Approximation Principle (CAP) is a method for aggregating forecasts of probability from a group of judges by enforcing coherence with minimal adjustment. This paper explores two methods to further improve the forecasting accuracy within the CAP framework and proposes practical algorithms that implement them. These methods allow flexibility to add fixed constraints to the coherentization process and compensate for the psychological bias present in probability estimates from human judges. The algorithms were tested on a data set of nearly (...) half a million probability estimates of events related to the 2008 U.S. presidential election (from about 16000 judges). The results show that both methods improve the stochastic accuracy of the aggregated forecasts compared to using simple CAP. (shrink)