The problem of induction is sometimes motivated via a comparison between rules of induction and rules of deduction. Valid deductive rules are necessarily truth preserving, while inductive rules are not.
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)
In this article, we provide a tutorial overview of some aspects of statistical learning theory, which also goes by other names such as statistical pattern recognition, nonparametric classification and estimation, and supervised learning. We focus on the problem of two-class pattern classification for various reasons. This problem is rich enough to capture many of the interesting aspects that are present in the cases of more than two classes and in the problem of estimation, and many of the results can be (...) extended to these cases. Focusing on two-class pattern classification simplifies our discussion, and yet it is directly applicable to a wide range of practical settings. (shrink)