  Representativeness is a foundational yet slippery concept. Though familiar at
first blush, it lacks a single precise meaning. Instead, meanings range from
typical or characteristic, to a proportionate match between sample and
population, to a more general sense of accuracy, generalizability, coverage, or
inclusiveness. Moreover, the concept has long been contested. In statistics,
debates about the merits and methods of selecting a representative sample date
back to the late 19th century; in politics, debates about the value of likeness
as a logic of political representation are older still. Today, as the concept
crops up in the study of fairness and accountability in machine learning, we
need to carefully consider the term's meanings in order to communicate clearly
and account for their normative implications. In this paper, we ask what
representativeness means, how it is mobilized socially, and what values and
ideals it communicates or confronts. We trace the concept's history in
statistics and discuss normative tensions concerning its relationship to
likeness, exclusion, authority, and aspiration. We draw on these analyses to
think through how representativeness is used in FAccT debates, with emphasis on
data, shift, participation, and power.
