Voting on federations

In this paper, we study the problem faced by a set of sovereign countries deciding whether to form a federation. Incentives to merge stem from the externality of domestically produced international public goods. Each country's decision is taken by a domestic voting committee (parliament). If the federation forms, federal decisions are taken by a federal voting committee, made of the union of the national parliaments of federal members. We rely on results by [Kaneko, M., 1977a. The ratio equilibrium and a voting game in a public goods economy. Journal of Economic Theory 16, 123-136; Kaneko, M., 1997b. The ratio equilibria and the core of the voting game G(N,W) in a public goods economy. Econometrica 45, 1589-1594) and Hirokawa, M., 1992. The equivalence of the cost share equilibria and the core of a voting game in a public goods economy, Social Choice and Welfare 9, 63-72. International Journal of Game Theory 11, 385-393] to identify voting outcomes at both domestic and federal levels with ratio equilibrium allocations for the respective economies. We show that although the efficient full federation (encompassing all countries) might not form in general, it always does when federal voting bears on the variations of public goods production with respect to the status quo pre-federal equilibrium, and taxes are defined on individual incomes at the pre-federal equilibrium.