Cycles in Liquid Democracy: A Game-Theoretic Justification

2026-07-14

AI Summary

This study addresses the prevalent yet often criticized phenomenon of delegation cycles in liquid democracy, traditionally viewed as a flaw causing wasted voting power. The authors propose the first non-cooperative game-theoretic model in which agents strategically form delegation relationships under uncertainty. They analyze the existence, structure, and social welfare properties of Nash equilibria within this framework and computationally verify their findings using best-response dynamics. The results demonstrate that delegation cycles can naturally emerge in equilibrium and exhibit favorable performance, suggesting that such cycles are not merely institutional defects but functional features of the system. This work thus provides a theoretical foundation and justification for the observed prevalence of cycles in real-world liquid democratic systems.

Abstract

A common criticism of liquid democracy within the relevant academic literature is that delegation cycles can occur, seemingly resulting in unused voting power. Yet, practitioners argue that delegation cycles are not only unproblematic but are even formed intentionally by participants. To bring theory closer to reality, we introduce a model that captures this strategic behavior under uncertainty. We study the existence, structure and quality of Nash equilibria, revealing that delegation cycles naturally emerge. To complement these findings, we perform computational experiments using best-response dynamics.

Problem

• liquid democracy
• delegation cycles
• voting power
• strategic behavior
• Nash equilibria

Innovation

• liquid democracy
• delegation cycles
• game-theoretic model
• Nash equilibrium
• best-response dynamics