Consistent Judgment Aggregation in Liquid Democracy: Utilizing Delegation Structure in the Ranked Agenda Rule
Pelle Nelissen

Abstract:
Liquid democracy is a collective decision-making process in which voters are allowed to delegate their vote to any peer. We consider a liquid version of judgment aggregation – a setting in which the collective decision concerns multiple interdependent issues. We translate a number of well-known normative requirements on aggregation mechanisms from the literature to our setting, and reproduce two famous impossibility theorems. One such mechanism is the ranked agenda rule, which efficiently computes a collective judgment by prioritizing issues that receive strong support from the voters. To arrive at satisfactory and logically consistent collective judgments in liquid democracy, we propose a refinement of the ranked agenda rule that breaks ties between issues with an equal number of supporters by the underlying delegation structure.
We motivate the rule formally by axiomatically characterizing the ranked agenda rule, and numerically by studying its behavior on a computational model of voter behavior. The computational model probabilistically simulates boundedly rational voters translating their uncertain preferences to liquid ballots. We study the correlation between delegation structure and epistemic performance of the profiles generated, and find that deeper delegation structures tend to approximate voters’ true preferences less accurately. When we numerically compare our structural ranked agenda rule with Kemeny’s rule, the original ranked agenda rule and viscous democracy, we conclude that all rules approximate the optimal collective decision equally accurately, but that our structural rule returns fewer possible collective judgments per input profile, i.e., is more resolute.