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Debate about fairness in machine learning has largely centered aroundcompeting definitions of what fairness or nondiscrimination between groupsrequires. However, little attention has been paid to what precisely a group is.Many recent approaches to "fairness" require one to specify a causal model ofthe data generating process. These exercises make an implicit ontologicalassumption that a racial or sex group is simply a collection of individuals whoshare a given trait. We show this by exploring the formal assumption ofmodularity in causal models, which holds that the dependencies captured by onecausal pathway are invariant to interventions on any other pathways. Causalmodels of sex propose two substantive claims: 1) There exists a feature,sex-on-its-own, that is an inherent trait of an individual that causally bringsabout social phenomena external to it in the world; and 2) the relationsbetween sex and its effects can be modified in whichever ways and the formerfeature would still retain the meaning that sex has in our world. We argue thatthis ontological picture is false. Many of the "effects" that sex purportedly"causes" are in fact constitutive features of sex as a social status. They givethe social meaning of sex features, meanings that are precisely what make sexdiscrimination a distinctively morally problematic type of action. Correctingthis conceptual error has a number of implications for how models can be usedto detect discrimination. Formal diagrams of constitutive relations present anentirely different path toward reasoning about discrimination. Whereas causaldiagrams guide the construction of sophisticated modular counterfactuals,constitutive diagrams identify a different kind of counterfactual as central toan inquiry on discrimination: one that asks how the social meaning of a groupwould be changed if its non-modular features were altered.

What's Sex Got To Do With Fair Machine Learning?