While predictive models are a purely technological feat, they may operate in a social context in which benign engineering choices entail unexpected real-life consequences. Fairness -- pertaining both to individuals and groups -- is one of such considerations; it surfaces when data capture protected characteristics of people who may be discriminated upon these attributes. This notion has predominantly been studied for a fixed predictive model, sometimes under different classification thresholds, striving to identify and eradicate its undesirable behaviour. Here we backtrack on this assumption and explore a novel definition of fairness where individuals can be harmed when one predictor is chosen ad hoc from a group of equally well performing models, i.e., in view of model multiplicity. Since a person may be classified differently across models that are otherwise considered equivalent, this individual could argue for a model with a more favourable outcome, possibly causing others to be adversely affected. We introduce this scenario with a two-dimensional example based on linear classification; then investigate its analytical properties in a broader context; and finally present experimental results on data sets popular in fairness studies. Our findings suggest that such unfairness can be found in real-life situations and may be difficult to mitigate with technical measures alone, as doing so degrades certain metrics of predictive performance.
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