When algorithms cannot be fair: constitutive and contingent discrimination and the limits of less-discriminatory alternatives

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The literature on algorithmic fairness has concentrated on the choice amongst fairness metrics, a choice constrained by well-known impossibility results (Chouldechova 2017; Kleinberg et al. 2017). This paper argues that a prior question deserves equal attention: how the categories, variables, and objective functions that constitute an algorithmic system’s representation of its domain are chosen, and when those choices themselves discriminate? We propose a criterion for distinguishing two kinds of algorithmic discrimination. A disparity is contingent, relative to a legitimate purpose and a class of admissible designs, when an alternative design within that class serves the purpose whilst reducing the disparity; it is constitutive, relative to the same parameters, when no such alternative is available. Because contingency is an existential claim and constitutivity a negative existential over a class of designs, the two carry asymmetric obligations: contingency is shown by exhibit, constitutivity by documented exhaustion, and neither is discharged by assertion. Every constitutivity claim therefore states in advance the exhibit that would refute it, which is what makes the distinction actionable in design review, audit, and litigation rather than merely classificatory. The criterion adapts the comparative logic of the less-discriminatory alternative from disparate-impact doctrine (Laufer et al. 2025) and shifts it from the level of models and outcomes to the level of representational choices, whose distinctive rigidity we analyse through the notion of open texture (Waismann 1945; Hart 1961): computational systems fix ex ante the precisifications that human decision-makers perform case by case. Three case studies (the ImageNet person categories, tokeniser-level disparities in large language models, and automated hiring together with clinical risk scoring) are used to test, not merely to illustrate, the criterion. We conclude by proposing ontological auditing, an upstream evaluation of representational choices articulated through an Ontological Impact Statement, and by locating it within the risk management and data governance provisions of the EU AI Act.