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 proxy voting can be embedded into the framework of binary aggregation with abstentions, allowing known results about the latter to apply to the former. We then turn to an analysis of Boolean DeGroot processes, a special case of the DeGroot stochastic model of opinion diffusion, where each agent holds binary opinions and has a unique influencer. We establish the convergence conditions of such opinion dynamics, which in turn sheds novel light on the analysis of delegable proxy. The study is a first attempt to provide theoretical foundations to liquid democracy. Our analysis also leads to recommendations on how to modify the system to make it better behaved with respect to the handling of delegation cycles and of inconsistent majorities.
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