Encoded demographic information in internal model representations is a commonly assumed risk factor for algorithmic bias, with demographic representation invariance often being touted as the ideal state. However, while demographic shortcut learning is a genuine threat, some degree of encoding is necessary when demographics correlate with target labels. Here, we show, mathematically and empirically, that enforcing demographic invariance can actually hamper bias mitigation and even create new biases. We distinguish marginal from class-conditional representation invariance, and show that they imply the standard group fairness notions of demographic parity and equalized odds, respectively. We evaluate the effects on predictive performance and fairness of enforcing both invariance types, both theoretically and empirically across five tabular and two chest X-ray imaging datasets. Our findings support our mathematical argument that demographic representation invariance is neither desirable nor sufficient for fairness.

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