🤖 AI Summary
Classical liquid democracy lacks theoretical guarantees of equilibrium existence, undermining its reliability for scalable collective decision-making.
Method: This paper proposes a multi-agent delegative voting model supporting partial delegation, incorporating fractional voting rights, multi-path delegation, autonomous vote retention, and a chain-length penalty function—establishing the first fractional delegative voting game framework with explicit chain-length penalization.
Contribution/Results: We prove that this game admits a pure-strategy Nash equilibrium for any penalty coefficient. Moreover, when the penalty coefficient is sufficiently small, the model satisfies key rationality axioms—including monotonicity and continuity. Unlike conventional liquid democracy, our approach overcomes the fundamental theoretical limitation of equilibrium non-existence. By integrating delegation flexibility with formal equilibrium guarantees, it provides a novel paradigm for scalable, robust, and decentralized collective decision-making.
📝 Abstract
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.