When selecting multiple candidates based on approval preferences of agents, the proportional representation of agents' opinions is an important and well-studied desideratum. Existing criteria for evaluating the representativeness of outcomes focus on groups of agents and demand that sufficiently large and cohesive groups are ''represented'' in the sense that candidates approved by some group members are selected. Crucially, these criteria say nothing about the representation of individual agents, even if these agents are members of groups that deserve representation. In this paper, we formalize the concept of individual representation (IR) and explore to which extent, and under which circumstances, it can be achieved. We show that checking whether an IR outcome exists is computationally intractable, and we verify that all common approval-based voting rules may fail to provide IR even in cases where this is possible. We then focus on domain restrictions and establish an interesting contrast between ''voter interval'' and ''candidate interval'' preferences. This contrast can also be observed in our experimental results, where we analyze the attainability of IR for realistic preference profiles.
翻译:在根据代理人的核准偏好选择多个候选人时,代理人意见的成比例代表是一个重要且经过深思熟虑的德席拉图姆。 评估结果代表性的现有标准侧重于代理人群体,要求足够大和有凝聚力的集团在某个集团成员核准的候选人被选中的意义上是“有代表性”的。 至关重要的是,这些标准丝毫不提及个别代理人的代表性,即使这些代理人是值得代表的集团的成员。 在本文中,我们正式确定个人代表的概念,并探索在何种程度和在何种情况下可以实现。 我们表明,检查IR结果是否存在是计算上难以实现的,我们核实所有共同的基于批准的选举规则即使在可能的情况下也可能无法提供IR。 我们然后侧重于领域限制,并在“ 投票间隔” 和“ 日期间隔” 的偏好之间确立一个有趣的对比。 在我们的实验结果中,我们也可以看到这种对比,我们在这里分析IR能否实现现实的优惠概况。