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 belief over what decisions are considered, and whether they prefer them to be decided by the incumbent SCF or 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. For this purpose, unlike [Barbera and Jackson, 2004], we do not generally restrict attention to anonymous SCFs. We also do not restrict attention to neutral SCFs, unlike [Koray, 2000]. We present results considering optimistic, pessimistic and i.i.d. approaches with respect to agent beliefs, different tie-breaking rules, and different SCF domains. To highlight two of the results, (i) for the i.i.d. unbiased case with arbitrary tie-breaking and general Boolean functions, 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) With a pessimistic approach, tie-breaking that prefers the status quo, and WMGs, we provide a tight characterization of the self-maintaining rules, which are exactly all games with minimal winning coalitions of size at most 2. We then consider two extensions, (i) forward-looking voters, (ii) Where the voter utility depends on wisdom of the crowd effects. In both cases, less centralized SCFs become self-maintaining. 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：考虑一个在社会性投票系统中采用的社会选择函数（SCF），该系统包括对投票方法本身的替换投票。代理人根据其事前信念投票，该信念涉及哪些决策被考虑，以及他们是否更倾向于由现任SCF或提议的替代方案来做出决策。现有SCF随后汇总代理人投票，并决定是否应被自身替换。若某一SCF无法通过这种方式被任何其他SCF替换，则称该SCF是自我维持的。我们关注自我维持对集权的影响。为此，不同于[Barbera and Jackson, 2004]，我们一般不对匿名SCF加以限制。同时，也不同于[Koray, 2000]，我们不对中性SCF加以限制。我们呈现了考虑乐观、悲观及独立同分布（i.i.d.）三种代理人信念方法、不同平局打破规则及不同SCF域的结果。其中两项结果尤为突出：（i）对于任意平局打破规则与一般布尔函数的i.i.d.无偏情形，我们证明了动力学的阿罗式定理：仅独裁制是自我维持的，且任何其他SCF均存在可达独裁制的变更路径；（ii）在悲观方法、偏好现状的平局打破规则及加权多数博弈（WMG）下，我们给出了自我维持规则的严格刻画——这些规则恰好是最小获胜联盟规模不超过2的所有博弈。随后我们考虑两种扩展：（i）前瞻性投票者；（ii）投票者效用依赖于群体智慧效应。在这两种情形中，集权程度较低的SCF变得可自我维持。总之，我们为集权动力学与稳定性提供了基本框架和系列结果，适用于制度设计，特别是正式法定系统（如区块链去中心化自治组织DAO）。