Optimal government under ideological diversity

We develop a theory of voluntary government formation under ideological heterogeneity. Individuals gain from the benefits of collective governance but incur psychological losses when laws diverge from their preferred rules. Despite these conflicts and competition over collective benefits from government, individual and social gains are aligned. This gives rise to a two-stage bargaining process that is an ordinal potential game yielding cooperative game solutions. In the first stage, citizens sort into ideologically compatible governments. In the second, each government adopts compromise laws that maximize collective value, leading to government decisions being affected by both intensities and preferences. Equilibrium allocations follow the Shapley value. The model addresses Sen’s paradox and explains why large governments do not socialize ideological costs. Under voluntary formation, multiple governments emerge naturally and constitutional constraints on majority rule become necessary to accommodate the impacts of ideological differences. The analysis serves as a baseline for traditional governments. It also provides a perspective on the classical welfare frameworks of Harsanyi and Rawls.