Mathematically distinct fairness definitions can directly conflict with one another

Evidence

But group fairness considers only predicted outcomes; it fails to include a consideration of actual outcomes. Our second definition of fairness is “predictive parity” that considers both predicted and actual outcomes. A classifier would satisfy this definition if both Black and White defendants have equal positive predictive value (PPV); that is, for both Black and White defendants, the probability that a defendant who received a good score will actually refrain from additional crimes and show up for subsequent court dates should be the same. This is an intuitively appealing definition of fairness: the percentage of correct positive predictions should be the same across race/ethnicity, or else it would seem that one group was receiving preferential treatment. While this definition is appealing, the problem is that it may be in conflict with the group fairness definition. It is possible to have predictive parity but fail to satisfy group fairness—and vice versa. And these are just two of the fairness definitions; there are many more equally intuitive definitions of fairness, and they also might conflict with each other (see Verma & Rubin, 2018). — Joseph Avery, Jim Sidanius, Joel Cooper, Gregory Davis, Amanda N., Bias in the Law, 1158

Categorization

• DEFINE: Defines predictive parity and explains its formal incompatibility with group fairness.
• SEED: An angle on how competing mathematical notions of fairness make ‘fair algorithm’ essentially contestable — relevant to any debate over AI risk assessment in courts.
• XREF: connects to: Quantification always depends on contested conventions, not neutral measurement. — Ève Chiapello, Financialisation of Valuation, 10