液态民主：二元聚集与扩散的分析
Liquid Democracy: An Analysis in Binary Aggregation and Diffusion
摘要：
本文从二元聚集模型和二元扩散模型的角度对流动民主（或委托代理投票）进行了分析。我们展示了如何在二元问题上的流动民主可以嵌入到二元聚集与弃权的框架中，使后者的已知结果-如不可能性定理-转移到前者。这种嵌入也揭示了流动民主中的委托周期与集体弃权概率之间的关系，以及可委托代理投票设置中的个人理性问题。然后，我们展示了如何流动的民主二元问题也可以建模和分析作为一个特定的过程中的动态二元网络上的意见。这些过程-被称为布尔DeGroot过程-是意见扩散的DeGroot随机模型的一个特例。我们建立了这种过程的收敛条件，并表明他们提供了一些新的见解，如何在流动民主的委托周期和个人理性的影响可以减轻。本研究首次尝试为流动民主投票制度的委托代理特征提供理论依据。我们的分析就如何修改该制度提出了建议，使其在处理授权周期和不一致的多数方面更具弹性。
英文摘要：
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.
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