Why the Variance of Beliefs Matters

When people flip coins, they usually believe that heads and tails are nearly equally likely. However, most potential events invite far more uncertainty, with sharply conflicting hypotheses competing for favor and people unclear about how to rate them. Looking at a single outcome, it is impossible to measure degrees of uncertainty; all one can ascertain is the mean. However, higher moments of uncertainty can be estimated from bets or scoring rules on multiple conditionally independent outcomes. The variance of beliefs is particularly important, for two reasons. First, it points to the expected wobble of future beliefs and thereby provides a rational explanation of the seemingly excess volatility of human decisions. Second, it is the best single indicator of the value of new information, which in turn can help guide research and experimentation