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：在基于代理人的批准偏好选择多位候选人时，代理人意见的比例代表性是一个重要且被深入研究的理想特性。现有评估结果代表性的标准主要关注代理人群体，要求足够大规模且具有凝聚力的群体以"被代表"的形式体现，即选择该群体部分成员所批准的候选人。关键的是，这些标准并未涉及个体代理人的代表性，即使这些代理人是应被代表群体的成员。本文形式化了个体代表性（IR）的概念，并探讨其在何种程度及何种条件下能够实现。我们证明检查是否存在满足IR的结果在计算上是难解的，并验证了所有常见的基于批准的投票规则即使在可能实现IR的情况下也可能无法提供IR。随后我们聚焦于定义域限制，在"投票者区间"偏好与"候选人区间"偏好之间建立了有趣的对比关系。这种对比同样体现在我们的实验结果中，我们在此分析了现实偏好配置下IR的可实现性。