Pirates in Wonderland: Liquid Democracy has Bicriteria Guarantees

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 $ϵ$-Nash equilibria is exactly $ϵ$ in the liquid democracy game.