Quantitative Economics: Jul, 2010, Volume 1, Issue 1

When consensus choice dominates individualism: Jensen’s inequality and collective decisions under uncertainty

Charles F Manski

Research on collective provision of private goods has focused on distributional considerations. This paper studies a class of problems of decision under uncertainty in which an efficiency argument for collective choice emerges from the mathematics of aggregating individual payoffs. Consider decision making when each member of a population has the same objective function, which depends on an unknown state of nature. If agents knew the state of nature, they would make the same decision. However, they may have different beliefs or may use different decision criteria to cope with their incomplete knowledge. Hence, they may choose different actions even though they share the same objective. Let the set of feasible actions be convex and the objective function be concave in actions, for all states of nature. Then Jensen’s inequality implies that consensus choice of the mean privately chosen action yields a larger mean payoff than does individualistic decision making, in all states of nature. If payoffs are transferable, the mean payoff from consensus choice may be allocated to Pareto dominate individualistic decision making. I develop these ideas. I also use Jensen’s inequality to show that a planner with the power to assign actions to the members of the population should not diversify. Finally, I give a version of the collective-choice result that holds with consensus choice of the median rather than mean action.

Keywords. Collective choice of private goods, social choice, mechanism design, ambiguity, heterogeneous beliefs.

JEL classification. D7, D81, H42.

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