  Increasingly, discrimination by algorithms is perceived as a societal and
legal problem. As a response, a number of criteria for implementing algorithmic
fairness in machine learning have been developed in the literature. This paper
proposes the Continuous Fairness Algorithm (CFA$\theta$) which enables a
continuous interpolation between different fairness definitions. More
specifically, we make three main contributions to the existing literature.
First, our approach allows the decision maker to continuously vary between
specific concepts of individual and group fairness. As a consequence, the
algorithm enables the decision maker to adopt intermediate ``worldviews'' on
the degree of discrimination encoded in algorithmic processes, adding nuance to
the extreme cases of ``we're all equal'' (WAE) and ``what you see is what you
get'' (WYSIWYG) proposed so far in the literature. Second, we use optimal
transport theory, and specifically the concept of the barycenter, to maximize
decision maker utility under the chosen fairness constraints. Third, the
algorithm is able to handle cases of intersectionality, i.e., of
multi-dimensional discrimination of certain groups on grounds of several
criteria. We discuss three main examples (credit applications; college
admissions; insurance contracts) and map out the legal and policy implications
of our approach. The explicit formalization of the trade-off between individual
and group fairness allows this post-processing approach to be tailored to
different situational contexts in which one or the other fairness criterion may
take precedence. Finally, we evaluate our model experimentally.
