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A recent wave of research has attempted to define fairness quantitatively. In particular, this work has explored what fairness might mean in the context of decisions based on the predictions of statistical and machine learning models. The rapid growth of this new field has led to wildly inconsistent motivations, terminology, and notation, presenting a serious challenge for cataloging and comparing definitions. This article attempts to bring much-needed order. First, we explicate the various choices and assumptions made—often implicitly—to justify the use of prediction-based decision-making. Next, we show how such choices and assumptions can raise fairness concerns and we present a notationally consistent catalog of fairness definitions from the literature. In doing so, we offer a concise reference for thinking through the choices, assumptions, and fairness considerations of prediction-based decision-making. Expected final online publication date for the Annual Review of Statistics, Volume 8 is March 8, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

We survey 146 papers analyzing "bias" in NLP systems, fnding that their motivations are often vague, inconsistent, and lacking in normative reasoning, despite the fact that analyzing "bias" is an inherently normative process. We further fnd that these papers' proposed quantitative techniques for measuring or mitigating "bias" are poorly matched to their motivations and do not engage with the relevant literature outside of NLP. Based on these fndings, we describe the beginnings of a path forward by proposing three recommendations that should guide work analyzing "bias" in NLP systems. These recommendations rest on a greater recognition of the relationships between language and social hierarchies, encouraging researchers and practitioners to articulate their conceptualizations of "bias"-i.e., what kinds of system behaviors are harmful, in what ways, to whom, and why, as well as the normative reasoning underlying these statements-and to center work around the lived experiences of members of communities affected by NLP systems, while interrogating and reimagining the power relations between technologists and such communities.

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