The Geometry of Power: Political Path Integrals and Their Properties

This paper, "The Geometry of Power," presents a path-integral framework for studying the geometry of political regimes, by considering both the static, kinematic and dynamic aspects of the landscape. Instead of focusing on optimal paths, the present approach replaces single optimal paths with ensembles of permissible political histories, each weighted by an action functional. We then introduce the concepts of path entropy, state entropy, free action, survival probability, entropy flux (hazard rate), survival entropy, and first passage time to describe the structures of political accessibility, strength, fragility, deformation and transformation (arising from phase transition). We used Monte Carlo simulations, calibrated with political, economic, and conflict indicators, to test the validity of the framework on six East African countries: Ethiopia, Kenya, Rwanda, South Sudan, Tanzania, and Uganda. The aim of the analysis is to evaluate the relative accessibility, stability, survival time, and transformation risk of democratic, authoritarian, military, and collapsed regime endpoints. The results show that the stability, survival of regimes and shifts is governed not only by minimizing costs but also by the “entropy of the geometry” that shapes rational political behavior under uncertainty. Authoritarian regimes are found to be structurally strong under prevailing regional constraints. However, democratic transitions are restricted to narrow and fragile pathways.