The Cost Perspective of Liquid Democracy: Feasibility and Control

TL;DR

The paper addresses cost-efficient representation in Liquid Democracy by modeling delegations on a graph with individual voting and delegating costs, and asking whether a budget-feasible set of casting voters can ensure full reachability for all voters. It introduces the Delegate Reachability problem and investigates stronger requirements like short delegation paths (Bounded Max Length) and bounded voting power (Bounded Power), showing polynomial-time solvability for certain simple topologies (e.g., small out-degree $"\Delta\

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.