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.

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When selecting a subset of candidates (a so-called committee) based on the preferences of voters, proportional representation is often a major desideratum. When going beyond simplistic models such as party-list or district-based elections, it is surprisingly challenging to capture proportionality formally. As a consequence, the literature has produced numerous competing criteria of when a selected committee qualifies as proportional. Two of the most prominent notions are Dummett's proportionality for solid coalitions (PSC) and Aziz et al. 's extended justified representation (EJR). Both definitions guarantee proportional representation to groups of voters who have very similar preferences; such groups are referred to as solid coalitions by Dummett and as cohesive groups by Aziz et al. However, these notions lose their bite when groups are only almost solid or almost cohesive. In this paper, we propose proportionality axioms that are more robust than their existing counterparts, in the sense that they guarantee representation also to groups that do not qualify as solid or cohesive. Importantly, we show that these stronger proportionality requirements are always satisfiable. Another important advantage of our novel axioms is that their satisfaction can be easily verified: Given a committee, we can check in polynomial time whether it satisfies the axiom or not. This is in contrast to many established notions like EJR, for which the corresponding verification problem is known to be intractable.In the setting with approval preferences, we propose a robust and verifiable variant of EJR and a simply greedy procedure to compute committees satisfying it. We show that our axiom is considerably more discriminating in randomly generated instances compared to EJR and other existing axioms. In the setting with ranked preferences, we propose a robust variant of Dummett's PSC. In contrast to earlier strengthenings of PSC, our axiom can be efficiently verified even for general weak preferences. In the special case of strict preferences, our notion is the first known satisfiable proportionality axiom that is violated by the Single Tranferable Vote (STV). In order to prove that our axiom can always be satisfied, we extend the notion of priceability to the ranked preferences setting. We also discuss implications of our results for participatory budgeting, querying procedures, and to the notion of proportionality degree.