Delegations as Adaptive Representation Patterns: Rethinking Influence in Liquid Democracy

In this study, we propose a generalization of the classic model of liquid democracy that allows fractional delegation of voting weight, while simultaneously allowing for the existence of equilibrium states. Our approach empowers agents to partition and delegate their votes to multiple representatives, all while retaining a fraction of the voting power for themselves. We introduce a penalty mechanism for the length of delegation chains. We discuss the desirable properties of a reasonable generalization of the classic model, and prove that smaller penalty factors bring the model closer to satisfying these properties. In the subsequent section, we explore the presence of equilibrium states in a general delegation game utilizing the proposed voting measure. In contrast to the classical model, we demonstrate that this game exhibits pure strategy Nash equilibria, contingent upon the imposition of a penalty on the length of delegation chains.

Democracy is not a single mechanism. It is a space of possible configurations -- a spectrum stretching from pure direct participation to full delegation of authority. The systems we live under today occupy a narrow band of that spectrum, chosen centuries ago under constraints that no longer apply, and rarely questioned since. Votiverse is a platform for exploring the rest of that space. It provides organizations, communities, and institutions of any size with a configurable governance engine. Participants can vote directly, delegate their vote to trusted individuals by topic, or operate under any hybrid arrangement their group defines. Delegations are revocable, topic-specific, and transitive. A direct vote always overrides a delegation. In this model, traditional representative democracy is not the norm -- it is an edge case: the configuration you get when delegation is forced, universal, non-specific, and irrevocable for a fixed term. Votiverse introduces two structural innovations. First, a governance awareness layer -- a built-in system that monitors the delegation network and delivers contextual, progressive-disclosure reporting to participants at the point of decision. Second, a prediction-tracking accountability layer. Proposals carry falsifiable predictions. Outcomes are recorded. Over time, the platform builds a collective memory of what was decided, what was promised, and what actually happened. Together, these layers transform voting from a momentary act into an ongoing process of collective learning. This paper formalizes the governance model, situates it within existing work on liquid democracy and participatory decision-making, addresses known failure modes, and describes the architecture of the platform. The core platform has been implemented and released as open-source software.

Many collective-action systems are neither fully decentralized nor fully centralized: agents voluntarily organize into institutions that share organizational costs and delegate decisions to representatives. Delegation can reduce individual costs, but it also transfers control to representatives whose private objectives need not align with those of their constituents. We study this tension in a repeated game with endogenous delegation to self-interested centers. A simple reduced-form model yields a scale--accountability tradeoff: larger constituencies offer greater cost-sharing benefits to members, yet the marginal value to a center of retaining any one constituent decreases as group size grows. Consequently, the prospect of individual exit can sustain non-exploitative delegation only up to an endogenous accountable constituency size. Additionally, we identify parameter regions in which fully delegated, accountable governance, when feasible, must be polycentric. We investigate these predictions through simulations with large language model (LLM) agents. Across five matched pairs of 30-agent simulations, polycentric structures repeatedly emerge but remain fluid, exhibiting cycles of concentration, exploitation, exit, and re-formation. We further find that models of different capacity exhibit similar willingness to assume leadership but differ substantially in their exercise of authority, with Sol initiating exploitation more frequently than Luna in matched decision states.