There are circumstances in which the output is binary. Take for example, the output by bail decisions would be either ‘jail’ or ‘release’. This kind of algorithm falls into the category of classification. You may find a classification algorithm implementing the following measures on our GitHub repository. To be consistent with convention, positive outcome is considered as the desired one for a certain candidate in a group, e.g. being granted a loan given a certain credit score (target score).
The difference between the target score mean values of the protected vs. unprotected groups. No difference = no discrimination
The mean difference for binary classification normalized by the rate of positive outcomes. At a given positive outcome rate, maximum possible discrimination is taken into account
The ratio of positive outcomes for the protected group over the non-protected group.
The association between exposure and outcome
For a null hypothesis that the means of the two groups (protected and non-protected) are equal.
For a null hypothesis that the rates of positive outcomes within the two groups are equal.
Measures above can be found in the following paper: Žliobaitė, Indrė. “Measuring discrimination in algorithmic decision making” Data Mining and Knowledge Discovery 31, no. 4 (July 31, 2017): 1060-089. doi:10.1007/s10618-017-0506-1. bibtex