Iterative Delegations in Liquid Democracy with Restricted Preferences
This work addresses stability issues in liquid democracy for collective decision-making systems, though it appears incremental as it builds on existing preference models.
The paper tackles the problem of ensuring stability in liquid democracy's delegation process by analyzing restricted preference types, such as single-peaked preferences, and shows that certain structures guarantee equilibrium existence while presenting mixed tractability and hardness results for computing desirable equilibria.
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.