Liquid democracy is a decision-making paradigm in which each agent can either vote directly for some alternative or (transitively) delegate its vote to another agent. To mitigate the issue of delegation cycles or the concentration of power, delegating agents might be allowed to specify multiple delegation options. Then, a (cycle-free) delegation is selected in which each delegating agent has exactly one representative. We study the winner determination problem for this setting, i.e., whether we can select a delegation such that a given alternative wins (or does not win). Moreover, we study the robustness of winning alternatives in two ways: First, we consider whether we can make a limited number of changes to the preferences cast by the agents such that a given alternative becomes a winner in one/in all delegations, and second, whether we can make a limited number of changes to a selected delegation to make a given alternative a winner.
翻译:液态民主是一种决策范式,每个代理人可以直接投票支持某种替代方案,或者(以透明方式)将其投票授权给另一代理人。为了缓解授权周期或权力集中的问题,授权代理人可以指定多个代表团选项。然后,选择一个(无周期的)代表团,每个授权代理人完全有一名代表。我们研究这一环境的赢家确定问题,即我们是否可以选择一个代表团,使某个替代方案获胜(或没有获胜)。此外,我们从两个方面研究赢得替代方案的稳健性:第一,我们考虑是否可以对代理人的偏好作有限的修改,使某个选择方案在同一个代表团中成为赢家;第二,我们是否可以对一个选定的代表团作有限的修改,使某个选择的代表团成为赢家。