Aggregating experts’ opinions to select the winner of a competition

The honest opinions of a group of experts must be aggregated to determine the deserving winner of a competition. The aggregation procedure is majoritarian if, whenever a majority of experts honestly believe that a contestant is the best one, then that contestant is considered the deserving winner. The fact that an expert believes that a contestant is the best one does not necessarily imply that she wants this contestant to win as, for example, she might be biased in favor of some other contestant. Then, we have to design a mechanism that implements the deserving winner. We show that, if the aggregation procedure is majoritarian, such a mechanism exists only if the experts are totally impartial. This impossibility result is very strong as it does not depend on the equilibrium concept considered. Moreover, the result still holds if we replace majoritarianism by anonymity and other reasonable property called respect for the jury. The impossibility result is even stronger if we focus on Nash implementation: no majoritarian aggregation procedure can be Nash implemented even if the experts are totally impartial.