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Rankings are ubiquitous in the online world today. As we have transitionedfrom finding books in libraries to ranking products, jobs, job applicants,opinions and potential romantic partners, there is a substantial precedent thatranking systems have a responsibility not only to their users but also to theitems being ranked. To address these often conflicting responsibilities, wepropose a conceptual and computational framework that allows the formulation offairness constraints on rankings in terms of exposure allocation. As part ofthis framework, we develop efficient algorithms for finding rankings thatmaximize the utility for the user while provably satisfying a specifiablenotion of fairness. Since fairness goals can be application specific, we showhow a broad range of fairness constraints can be implemented using ourframework, including forms of demographic parity, disparate treatment, anddisparate impact constraints. We illustrate the effect of these constraints byproviding empirical results on two ranking problems.

Fairness of Exposure in Rankings