The Convergence of Iterative Delegations in Liquid Democracy

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 such that: A delegates to B and B delegates to C leads to A delegates to C. We study the stability (w.r.t. voters preferences) of the delegation process in liquid democracy and model it as a game in which the players are the voters and the strategies are possible delegations. This game-theoretic model enables us to answer several questions on the equilibria of this process under general preferences and several types of restricted preferences (e.g., single-peaked preferences).