We propose a framework for sequential decision-making aimed at dynamically influencing long-term societal fairness, illustrated via the problem of selecting applicants from a pool consisting of two groups, one of which is under-represented. We consider a dynamic model for the composition of the applicant pool, in which admission of more applicants from a group in a given selection round positively reinforces more candidates from the group to participate in future selection rounds. Under such a model, we show the efficacy of the proposed Fair-Greedy selection policy which systematically trades the sum of the scores of the selected applicants (greedy'') against the deviation of the proportion of selected applicants belonging to a given group from a target proportion (fair''). In addition to experimenting on synthetic data, we adapt static real-world datasets on law school candidates and credit lending to simulate the dynamics of the composition of the applicant pool. We prove that the applicant pool composition converges to a target proportion set by the decision-maker when score distributions across the groups are identical.