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).

翻译：考虑一个社会选择函数被选定用于正式系统中的投票决策，包括更换投票方法本身的投票。代理人根据其对现任SCF与建议替代方案的事前偏好进行投票。现有SCF随后汇总代理人的投票，并得出是否应被替换的决定。若一个SCF无法以这种方式被任何其他SCF替换，则称其为自维持的。我们的研究重点在于自维持性对集中化的影响。我们展示了关于代理人信念的乐观、悲观及独立同分布处理方式以及不同平局裁决规则的结果。为突出其中两项结果：(i) 对于具有任意平局裁决规则的独立同分布无偏情况，我们证明了一个"阿罗式"动态定理：证明仅有独裁制是自维持的，且任何其他SCF都存在一条最终通向独裁制的变更路径。(ii) 若考虑群体智慧效应，对于一个统治精英规模可变的社会，我们论证了稳定精英规模如何随经济榨取程度与个体决策质量的提升而递减。总体而言，我们为集中化动态与稳定性提供了一个基础框架和结果体系，适用于制度设计，特别是在诸如区块链去中心化自治组织等正式"法律上"的系统中。