  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.
