What is fair? Proxy discrimination vs. demographic disparities in insurance pricing

Discrimination and fairness are major concerns in algorithmic models. This is particularly true in insurance, where protected policyholder attributes are not allowed to be used for insurance pricing. Simply disregarding protected policyholder attributes is not an appropriate solution as this still allows for the possibility of inferring protected attributes from non-protected covariates, leading to the phenomenon of proxy discrimination. Although proxy discrimination is qualitatively different from the group fairness concepts discussed in the machine learning and actuarial literature, group fairness criteria have been proposed to control the impact of protected attributes on the calculation of insurance prices. The purpose of this paper is to discuss the relationship between direct and proxy discrimination in insurance and the most popular group fairness axioms. We provide a technical definition of proxy discrimination and derive incompatibility results, showing that avoiding proxy discrimination does not imply satisfying group fairness and vice versa. This shows that the two concepts are materially different. Furthermore, we discuss input data pre-processing and model post-processing methods that achieve group fairness in the sense of demographic parity. As these methods induce transformations that explicitly depend on policyholders' protected attributes, it becomes ambiguous whether direct and proxy discrimination is, in fact, avoided.