Multiple membership and federal structures

We consider a model of the 'world' with several regions that may create a unified entity or be partitioned into several unions (countries). The regions have distinct preferences over policies chosen in the country to which they belong and equally share the cost of public policies. It is known that stable \political maps' or country partitions, that do not admit a threat of secession by any group of regions, may fail to exist. To rectify this problem, in line with the recent trend for an increased autonomy and various regional arrangements, we consider federal structures, where a region can simultaneously be a part of several unions. We show that, under very general conditions, there always exists a stable federal structure.