We study the problem of online dynamic pricing with two types of fairness constraints: a "procedural fairness" which requires the proposed prices to be equal in expectation among different groups, and a "substantive fairness" which requires the accepted prices to be equal in expectation among different groups. A policy that is simultaneously procedural and substantive fair is referred to as "doubly fair". We show that a doubly fair policy must be random to have higher revenue than the best trivial policy that assigns the same price to different groups. In a two-group setting, we propose an online learning algorithm for the 2-group pricing problems that achieves $\tilde{O}(\sqrt{T})$ regret, zero procedural unfairness and $\tilde{O}(\sqrt{T})$ substantive unfairness over $T$ rounds of learning. We also prove two lower bounds showing that these results on regret and unfairness are both information-theoretically optimal up to iterated logarithmic factors. To the best of our knowledge, this is the first dynamic pricing algorithm that learns to price while satisfying two fairness constraints at the same time.

Fixing algorithms may not be the best response to bias. Ethicist Tom Douglas offers a more radical approach to creating fairness, that aims for'substantive' rather than'procedural' fairness outside of design. Our lives are increasingly affected by algorithms. People may be denied loans, jobs, insurance policies, or even parole on the basis of risk scores that they produce. Yet algorithms are notoriously prone to biases.

Our lives are increasingly affected by algorithms. People may be denied loans, jobs, insurance policies, or even parole on the basis of risk scores that they produce. Yet algorithms are notoriously prone to biases. For example, algorithms used to assess the risk of criminal recidivism often have higher error rates in minority ethic groups. As ProPublica found, the COMPAS algorithm – widely used to predict re-offending in the US criminal justice system – had a higher false positive rate in black than in white people; black people were more likely to be wrongly predicted to re-offend.