On efficiency and sustainability in a collective decision-making problem with heterogeneous agents

In this paper we examine a collective decision problem, where the set of heterogeneous individuals is partitioned into several groups, each choosing its own policy (e.g., location of a public project) from the given policy space. We first consider the notion of "efficient" partition that minimizes the total policy-related costs and aggregate personalized costs. We then examine 'sustainable' partitions, in which the policy-related costs can be distributed in a way that no subgroup (belonging to the partition or not) has an incentive to break away from the rest and to set its own policy. Our main result is that, with a unidimensional policy space and single-peaked personalized costs, every efficient partition is sustainable. We further describe some important features of efficiency by characterizing the efficient distribution (and number) of policies chosen from the policy space when their cost is small. It turns out that efficiency is achieved when the distribution of policies follows the square root of the density of individuals' ideal choices.