Social Sciences Brown Bag Seminar

Instead of simply looking for an average expert answer to a particular question, an ignorant planner wants to rank  experts according to the quality of their knowledge.  She knows nothing about the experts, and she has to design an universal mechanism, that would work for all possible  distributions of expert  types and the possible states of nature.

We prove that, if a given such mechanism  results in an equilibrium in which it is optimal for all the experts to truthfully reveal their type,  then, in that equilibrium they are necessarily ranked according to their posterior probabilities of the states of nature.

We identify  natural conditions under which payoffs in equilibrium must be logarithmic functions of the posterior probabilities, even when those probabilities are not explicitly elicited by the mechanism. This provides a novel game-theoretic axiomatization of entropy. Logarithmic scoring can be implemented  by the ignorant planner  via the Bayesian Truth Serum algorithm of Prelec (2004), using simple inputs.