The Stability Threshold and Two Facts of Polarization

In this paper we introduce the notion of stability threshold that quantifies the minimal returns to size sufficient to prevent credible secession threats by regions of the country. Severity of internal tension has been linked to degree of polarization of citizens' preferences and characteristics. We show that the increasing degree of polarization does not, in general, raise the stability threshold, even though this hypothesis holds in some asymptotic sense. Thus, somewhat counter-intuitively, the relation between polarization and the stability threshold is ambiguous. We also examine the question of the number of smaller countries to be created if the unity of the large country is not sustainable, and investigate the link between this number and the degree of the country polarization. We find that the stable number of countries also behaves non-monotonically with respect to polarization indices. However, monotonicity does emerge when the stable number is large, and the stable number decreases when polarization rises.