themis-ml defines discrimination as the preference (bias) for or against a set of social groups that result in the unfair treatment of its members with respect to some outcome.
It defines fairness as the inverse of discrimination, and in the context of a machine learning algorithm, this is measured by the degree to which the algorithm’s predictions favor one social group over another in relation to an outcome that holds socioeconomic, political, or legal importance, e.g. the denial/approval of a loan application.
A “fair” algorithm depends on how we define fairness. For example if we define fairness as statistical parity, a fair algorithm is one in which the proportion of approved loans among minorities is equal to the proportion of approved loans among white people.