  Liquid democracy is a form of transitive delegative democracy that has
received a flurry of scholarly attention from the computer science community in
recent years. In its simplest form, every agent starts with one vote and may
have other votes assigned to them via delegation from other agents. They can
choose to delegate all votes assigned to them to another agent or vote directly
with all votes assigned to them. However, many proposed realizations of liquid
democracy allow for agents to express their delegation/voting preferences in
more complex ways (e.g., a ranked list of potential delegates) and employ a
centralized delegation mechanism to compute the final vote tally. In doing so,
centralized delegation mechanisms can make decisions that affect the outcome of
a vote and where/whether agents are able to delegate their votes. Much of the
analysis thus far has focused on the ability of these mechanisms to make a
correct choice. We extend this analysis by introducing and formalizing other
important properties of a centralized delegation mechanism in liquid democracy
with respect to crucial features such as accountability, transparency,
explainability, fairness, and user agency. In addition, we evaluate existing
methods in terms of these properties, show how some prior work can be augmented
to achieve desirable properties, prove impossibility results for achieving
certain sets of properties simultaneously, and highlight directions for future
work.
