Algorithms are increasingly being used to help automate and improve data-driven decisions, but care must be taken to prevent such algorithms from learning discriminatory patterns from historical data and perpetuating their biases. Statistical notions of fairness aim to mitigate either a model's disparate impact on disadvantaged groups (thus ensuring group fairness) or the resulting disparate treatment of individuals with similar features (thus ensuring individual fairness). Simultaneously mitigating disparate impact and disparate treatment is generally impossible for non-trivial models, necessitating a compromise. In this paper, we introduce the Fair Lasso and Fair Posterior as methods for selecting fair covariates in generalised linear models. By targeting variables that are simultaneously strong predictors of the response and weakly dependent on the sensitive group memberships, we aim to achieve favourable trade-offs between disparate treatment and disparate impact. Additionally, our selected set of fair features can be used as the conditioning set of legitimate features in the paradigm of Conditional Demographic parity (CDP) when no prescriptive legal framework exists.

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