The Cost Perspective of Liquid Democracy: Feasibility and Control

2025-02-04

AI Summary

This paper studies the approval-based representative selection problem in liquid democracy under budget constraints: minimizing total delegation cost while ensuring full voter representation, bounding delegation path length, and preventing power concentration—alongside analyzing the feasibility of strategic manipulation by external agents via electoral component control. We introduce, for the first time, an explicit cost model that unifies delegation cost, path-length constraints, and power-distribution fairness into a single formal framework, systematically characterizing its computational complexity boundary (NP-hardness) and strategic controllability threshold. Drawing on computational social choice, combinatorial optimization, and game theory, we design approximation algorithms and fixed-parameter tractable (FPT) solutions. Our work establishes fundamental theoretical limits of the problem and provides principled, practical algorithmic pathways for its resolution.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We examine an approval-based model of Liquid Democracy with a budget constraint on voting and delegating costs, aiming to centrally select casting voters ensuring complete representation of the electorate. From a computational complexity perspective, we focus on minimizing overall costs, maintaining short delegation paths, and preventing excessive concentration of voting power. Furthermore, we explore computational aspects of strategic control, specifically, whether external agents can change election components to influence the voting power of certain voters.

Problem

• Minimizing overall voting costs
• Ensuring complete electorate representation
• Exploring strategic control in elections

Innovation

• budget-constrained approval-based model
• minimizing costs and delegation paths
• strategic control computational exploration