Iterative Delegations in Liquid Democracy with Restricted Preferences

TL;DR

This paper explores the stability of vote delegation in liquid democracy under restricted preferences, demonstrating conditions for equilibrium existence and analyzing computational complexity of finding such states.

Contribution

It introduces preference restrictions that guarantee equilibrium existence and provides complexity results for computing equilibria in liquid democracy.

Findings

Preference restrictions ensure stable delegation equilibria.

Computational complexity results for equilibrium computation.

Conditions for guaranteed existence of stable states.

Abstract

In this paper, we study liquid democracy, a collective decision making paradigm which lies between direct and representative democracy. One main feature of liquid democracy is that voters can delegate their votes in a transitive manner so that: A delegates to B and B delegates to C leads to A delegates to C. Unfortunately, this process may not converge as there may not even exist a stable state (also called equilibrium). In this paper, we investigate the stability of the delegation process in liquid democracy when voters have restricted types of preference on the agent representing them (e.g., single-peaked preferences). We show that various natural structures of preferences guarantee the existence of an equilibrium and we obtain both tractability and hardness results for the problem of computing several equilibria with some desirable properties.