The paper provides an analysis of the voting method known as delegable proxy
voting, or liquid democracy. The analysis first positions liquid democracy
within the theory of binary aggregation. It then focuses on two issues of the
system: the occurrence of delegation cycles; and the effect of delegations on
individual rationality when voting on logically interdependent propositions. It
finally points to proposals on how the system may be modified in order to
address the above issues.Comment: In Proceedings TARK 2017, arXiv:1707.0825
We take a logical approach to threshold models, used to study the diffusion of opinions, new technologies, infections, or behaviors in social networks. Threshold models consist of a network graph of agents connected by a social relationship and a threshold value which regulates the diffusion process. Agents adopt a new behavior/product/opinion when the proportion of their neighbors who have already adopted it meets the threshold. Under this diffusion policy, threshold models develop dynamically towards a guaranteed fixed point. We construct a minimal dynamic propositional logic to describe the threshold dynamics and show that the logic is sound and complete. We then extend this framework with an epistemic dimension and investigate how information about more distant neighbors' behavior allows agents to anticipate changes in behavior of their closer neighbors. Overall, our logical formalism captures the interplay between the epistemic and social dimensions in social networks.
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