  The paper proposes an analysis of liquid democracy (or, delegable proxy
voting) from the perspective of binary aggregation and of binary diffusion
models. We show how liquid democracy on binary issues can be embedded into the
framework of binary aggregation with abstentions, enabling the transfer of
known results about the latter---such as impossibility theorems---to the
former. This embedding also sheds light on the relation between delegation
cycles in liquid democracy and the probability of collective abstentions, as
well as the issue of individual rationality in a delegable proxy voting
setting. We then show how liquid democracy on binary issues can be modeled and
analyzed also as a specific process of dynamics of binary opinions on networks.
These processes---called Boolean DeGroot processes---are a special case of the
DeGroot stochastic model of opinion diffusion. We establish the convergence
conditions of such processes and show they provide some novel insights on how
the effects of delegation cycles and individual rationality could be mitigated
within liquid democracy.
  The study is a first attempt to provide theoretical foundations to the
delgable proxy features of the liquid democracy voting system. Our analysis
suggests recommendations on how the system may be modified to make it more
resilient with respect to the handling of delegation cycles and of inconsistent
majorities.
