Continuous decisions by a committee: Median versus average mechanisms

A group of strategic agents with diverse private information and interdependent preferences has to take a continuous collective decision. I study the design of the decision-making procedure from the viewpoint of a utilitarian social planner. For uniformly distributed information, the implementation of the average report as decision dominates the implementation of the median report when the set of admissible reports is optimally designed. This is true for any number of agents and for any degree of interdependence. The result extends to a general class of distributions when the number of agents is large.