Movement and Uncertainty Resolution in Beliefs

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Date and Time: 
Monday, November 23, 2015
2:00 pm – 3:30 pm
Ned Augenblick
Haas School of Business University of California, Berkeley

This paper develops methods to assess whether belief changes are consistent with Bayesian updating, built from the intrinsic connection between movement of beliefs and the reduction of uncertainty: rationality dictates that people who's beliefs are changing are on average becoming more confident. Mathematically, the expected sum of squared changes of beliefs must equal the expected reduction of uncertainty. A set of well-known psychological biases are suggestive about ways that people form confident beliefs too quickly or too slowly and how changes in beliefs are variously too muted or volatile, meaning that they tend to generate biases in m and r. We show how patterns of violations of the equivalence of belief movement and uncertainty reduction might prove useful in categorizing, understanding, and empirically identifying systematic biases in statistical reasoning. From this psychology, some theoretical principles, and simulations we argue that this approach is at once less likely to falsely reject Bayesian beliefs as rational, but can often prove the presence of non-Bayesianness better than other potential tests, such as an unconditional-martingale, autocorrelation, and variance-ratio tests. The same principle can even be used to develop a test of whether an individual belief stream is likely too variable to be Bayesian. We then apply the large-data test to a variety of prediction markets. Analyzing 11 million transactions from 150,000 single-event prediction markets in the large British betting market Betfair, we show there is consistent excess belief movement, which arises from high-frequency changes. When these high-frequency changes are ignored, beliefs move too much at the beginning of sports events and too little towards the end relative to the uncertainty reduction.