Pirates in Wonderland: Liquid Democracy has Bicriteria Guarantees

TL;DR

This paper analyzes the strategic properties of liquid democracy using delegation graphs, proving bicriteria approximation guarantees for rationality and social welfare, including the price of stability for approximate equilibria.

Contribution

It introduces a game-theoretic framework for liquid democracy and establishes bicriteria approximation guarantees, a novel theoretical insight.

Findings

Price of stability for ε-Nash equilibria equals ε.

Liquid democracy game admits bicriteria approximation guarantees.

Strategic behavior in liquid democracy can be effectively bounded.

Abstract

Liquid democracy has a natural graphical representation, the delegation graph. Consequently, the strategic aspects of liquid democracy can be studied as a game over delegation graphs, called the liquid democracy game. Our main result is that this game has bicriteria approximation guarantees, in terms of both rationality and social welfare. Specifically, we prove the price of stability for $\epsilon$-Nash equilibria is exactly $\epsilon$ in the liquid democracy game.