Abstract We study fairness in sequential decision making environments, where at each time step a learning algorithm receives data corresponding to a new individual (e.g. a new job application) and must make an irrevocable decision about him/her (e.g. whether to hire the applicant) based on observations made so far. In order to prevent cases of disparate treatment, our time-dependent notion of fairness requires algorithmic decisions to be consistent: if two individuals are similar in the feature space and arrive during the same time epoch, the algorithm must assign them to similar outcomes. We propose a general framework for post-processing predictions made by a black-box learning model, that guarantees the resulting sequence of outcomes is consistent. We show theoretically that imposing consistency will not significantly slow down learning. Our experiments on two real-world data sets illustrate and confirm this finding in practice.