As AI-based decision-making becomes increasingly impactful on human society, the study of the influence of fairness-aware policies on the population becomes important. In this work, 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, where the admission of more applicants from a particular group positively reinforces more such candidates to participate in the selection process. Under such a model, we show the efficacy of the proposed Fair-Greedy selection policy which systematically trades greedy score maximization against fairness objectives. 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.