Machine learning tasks may admit multiple competing models that achieve similar performance yet produce conflicting outputs for individual samples -- a phenomenon known as predictive multiplicity. We demonstrate that fairness interventions in machine learning optimized solely for group fairness and accuracy can exacerbate predictive multiplicity. Consequently, state-of-the-art fairness interventions can mask high predictive multiplicity behind favorable group fairness and accuracy metrics. We argue that a third axis of ``arbitrariness'' should be considered when deploying models to aid decision-making in applications of individual-level impact. To address this challenge, we propose an ensemble algorithm applicable to any fairness intervention that provably ensures more consistent predictions.

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