Different base rates across groups make fairness definitions mathematically incompatible

Evidence

Our first definition of fairness is “group fairness.” We can say that a classifier satisfies this definition if both protected (e.g., Black defendants) and unprotected (White defendants) groups have equal probabilities of being assigned to the positive predicted class (Verma & Rubin, 2018). … 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. … 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. — Joseph Avery, Jim Sidanius, Joel Cooper, Gregory Davis, Amanda N., Bias in the Law, 1157 (#expands, via linked claim)

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 (#corroborates, via linked claim)

Categorization

• XREF: connects to: Mathematically distinct fairness definitions can directly conflict with one another — Joseph Avery, Jim Sidanius, Joel Cooper, Gregory Davis, Amanda N., Bias in the Law: A Definitive Look at…, 1158; Group fairness requires equal predicted outcomes across protected groups — Joseph Avery, Jim Sidanius, Joel Cooper, Gregory Davis, Amanda N., Bias in the Law: A Definitive Look at…, 1157; Competing statistical fairness definitions can conflict irreconcilably within one algorithm — Joseph Avery, Jim Sidanius, Joel Cooper, Gregory Davis, Amanda N., Bias in the Law: A Definitive Look at…, 1157 (+1 more)

Broader Connections

• Competing statistical fairness definitions can conflict irreconcilably within one algorithm #expands (0.95) — Joseph Avery, Jim Sidanius, Joel Cooper, Gregory Davis, Amanda N., Bias in the Law, 1157
• Mathematically distinct fairness definitions can directly conflict with one another #corroborates (0.93) — Joseph Avery, Jim Sidanius, Joel Cooper, Gregory Davis, Amanda N., Bias in the Law, 1158