From Proxy Voting to DeGroot Processes

Abstract

[[[THIS IS STILL THE OLD ABSTRACT!]]] This paper studies opinion diffusion in cases where each agent holds binary opinions and follows a unique influencer. This type of opinion diffusion, which we name ‘Boolean DeGroot process’, lies at the intersection of two more general frameworks for opinion diffusion: the seminal stochastic model proposed by DeGroot, and the more recent approach, stemming from the literature on judgment aggregation, of Propositional Opinion Diffusion. The paper provides three contributions. First, it establishes conditions for convergence of opinions in Boolean DeGroot processes and in a simple generalization of them. Second, it shows how these conditions can be captured by modal fixpoint logics, thereby enabling a rich toolbox for the study of opinion formation. Third, it applies the convergence results to gain a novel insight into a problematic aspect of the collective decision-making system known as ‘liquid democracy’.