Collective Decisions with Interdependent Valuations

Many collective decision problems have the common feature that individuals' desired outcomes are correlated but not identical. This Paper studies collective decisions with private information about these desired policies. Each agent holds private information that mainly concerns their own bliss point, but this private information also affects all other agents' bliss points. We concentrate on two specific mechanisms, the mean and the median mechanism. We establish existence of two symmetric Bayesian Nash equilibria of the corresponding game and compare the performance of the mechanisms for different degrees of interdependencies. Applications of our framework include the assignment of voting rights in the council of the European Central Bank, the design of decision processes in teams, firms and international organizations.