  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.
