Coalition-proof jurisdiction structures under monotone housing density

Abstract

What size of a group (club, party, jurisdiction etc.) is optimal when a large society partitions itself into smaller entities? On the one hand, in a large group fixed cost is split among greater number of agents. On the other hand, small groups are more homogeneous. Do these forces always balance each other? Our paper studies unidimensional model with median public good location and individual transportation costs. Unlike the general case, under monotonically and “smoothly” decreasing population density on a half-line a stable partition does always exist. Moreover, one such partition is constructed explicitly. The condition of “smooth” decreasing implies a single-crossing condition that guarantees the stability of our construction. However, the question about monotone density on a segment or “non-smoothly” decreasing density on a half-line is open. There are counterexamples to the current construction, but there is no general refutation.