Can every mathematical fairness condition usually be satisfied at once?

No. Important fairness conditions can be mathematically incompatible.

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  1. Yes, with enough data
  2. Yes, with a larger model
  3. No, some conditions conflict ✔

Why: Fairness has multiple definitions. Except in special cases, a classifier cannot simultaneously satisfy every desirable group fairness constraint, so the choice must fit the real context.

Huh, didn't know that: Calibration can conflict with balancing errors across positive and negative classes.

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The fairness metrics agreed to disagree, very evenly.
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References

Answer: No, some conditions conflict. Fairness has multiple definitions. Except in special cases, a classifier cannot simultaneously satisfy every desirable group fairness constraint, so the choice must fit the real context.

  1. NIST SP 1270: Identifying and Managing Bias in AI nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.1270.pdf
    there is an inherent incompatibility between two conditions: calibration and balancing the positive and negative classes.
    Checked 2026-10-10.

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