Power in Liquid Democracy: A Network Centrality Approach

2026-08-13

AI Summary

This study addresses the challenge of effectively measuring voters’ actual influence in liquid democracy systems that support transitive and revocable delegation. To this end, it introduces, for the first time, random-walk decay centrality into the analysis of power distribution in liquid democracy, establishing a computable framework that captures how influence propagates through delegation networks. This approach offers greater intuitiveness and theoretical advantages over PageRank, with its foundations rigorously justified through axiomatic analysis. Building on this framework, the paper further proposes an algorithm for selecting representative influencers, enabling efficient identification of pivotal participants and scalable construction of representative groups.

Abstract

This paper develops a computationally tractable framework for measuring voters' power in collective decision-making platforms that support transitive and suspendable delegations---commonly known as liquid democracy. We employ Random Walk Decay centrality to capture how influence propagates through delegation networks, argue for its intuitive appeal in this context and its advantages over alternatives such as PageRank, and derive a natural axiomatic characterization within the class of power metrics. Moreover, we conceptualize how the framework can be extended into a practical tool for analyzing power distributions in such platforms, and propose and study, both axiomatically and algorithmically, methods for selecting representative slates of influential participants.

Problem

• liquid democracy
• voter power
• delegation networks
• collective decision-making
• network centrality

Innovation

• liquid democracy
• Random Walk Decay centrality
• delegation networks
• power measurement
• axiomatic characterization