Abstract
Liquid democracy is a collective decision making paradigm which lies between direct and representative democracy. One of its main features is that voters can delegate their votes in a transitive manner such that: A delegates to B and B delegates to C leads to A indirectly delegates to C. These delegations can be effectively empowered by implementing liquid democracy in a social network, so that voters can delegate their votes to any of their neighbors in the network. However, it is uncertain that such a delegation process will lead to a stable state where all voters are satisfied with the people representing them. We study the stability (w.r.t. voters preferences) of the delegation process in liquid democracy and model it as a game in which the players are the voters and the strategies are their possible delegations. We answer several questions on the equilibria of this process in any social network or in social networks that correspond to restricted types of graphs. We show that a Nash-equilibrium may not exist, and that it is even NP-complete to decide whether one exists or not. This holds even if the social network is a complete graph or a bounded degree graph. We further show that this existence problem is W[1]-hard w.r.t. the treewidth of the social network. Besides these hardness results, we demonstrate that an equilibrium always exists whatever the preferences of the voters iff the social network is a tree. We design a dynamic programming procedure to determine some desirable equilibria (e.g., minimizing the dissatisfaction of the voters) in polynomial time for tree social networks. Lastly, we study the convergence of delegation dynamics. Unfortunately, when an equilibrium exists, we show that a best response dynamics may not converge, even if the social network is a path or a complete graph.
Abstract (translated)
流动民主是介于直接民主和代表民主之间的集体决策范式。它的一个主要特点是选民可以以一种过渡的方式将选票委托给C：A代表B，B代表C，间接代表C。这些代表团可以通过在社会网络中实施流动民主而得到有效的授权，这样选民就可以将选票委托给他们的任何邻居。网络。然而，不确定的是，这样的授权过程将导致一个稳定的国家，所有的选民都对代表他们的人感到满意。我们研究了流动民主下代表团进程的稳定性（W.R.T.选民偏好），并将其模拟为一个博弈，其中参与者是选民，策略是他们可能的代表团。我们回答了几个关于这个过程在任何社会网络或社会网络中平衡的问题，这些社会网络对应于受限类型的图。
URL
https://arxiv.org/abs/1904.05775
