Generalizing liquid democracy to multi-agent delegation: a voting weight measure and equilibrium analysis

Francisco M. Bersetche ()
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Francisco M. Bersetche: FCEyN, Universidad de Buenos Aires

International Journal of Game Theory, 2025, vol. 54, issue 2, No 15, 35 pages

Abstract: 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 weight 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 Nash equilibria, contingent upon the imposition of a penalty on the length of delegation chains.

Keywords: Liquid democracy; Multi-agent delegation; Equilibrium analysis (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00182-025-00962-2

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