This paper defines a family of functions that measure the distance between opinions. I introduce six axioms that a measure of disagreement should satisfy, and characterize the functions that satisfy them. The disagreement measures we characterize generalize the Renyi divergences, and include the Kullback-Leibler divergence and the Bhattacharyya distance.
I analyze two applications. In the first, I find a necessary and sufficient condition under which public information reduces expected disagreement between Bayesian agents. In the second, I show that our measures of disagreement are useful to understand trading under heterogeneous beliefs. Trade volume and gains from trade are increasing in some of our measures disagreement.
Department of Economics
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