Centralization and Stability in Formal Constitutions

Consider a social-choice function (SCF) is chosen to decide votes in a formal system, including votes to replace the voting method itself. Agents vote according to their ex-ante preference between the incumbent SCF and the suggested replacement. The existing SCF then aggregates the agents' votes and arrives at a decision of whether it should itself be replaced. An SCF is self-maintaining if it can not be replaced in such fashion by any other SCF. Our focus is on the implications of self-maintenance for centralization. We present results considering optimistic, pessimistic and i.i.d. approaches w.r.t. agent beliefs, and different tie-breaking rules. To highlight two of the results, (i) for the i.i.d. unbiased case with arbitrary tie-breaking, we prove an ``Arrow-Style'' Theorem for Dynamics: We show that only a dictatorship is self-maintaining, and any other SCF has a path of changes that arrives at a dictatorship. (ii) If we take into account wisdom of the crowd effects, for a society with a variable size of ruling elite, we demonstrate how the stable elite size is decreasing in both how extractive the economy is, and the quality of individual decision-making. All in all we provide a basic framework and body of results for centralization dynamics and stability, applicable for institution design, especially in formal ``De-Jure'' systems, such as Blockchain Decentralized Autonomous Organizations (DAOs).