Retrieval-Augmented Generation (RAG) grounds large language models (LLMs) in external knowledge, but the retrieved documents can systematically skew generated answers toward one group. This effect is difficult to analyze and control in top-k settings, where several documents at different context positions jointly shape the output. We present a three-stage framework for fairness-aware retrieval in top-k RAG. First, a probabilistic reranker sets the group composition of the retrieved context at each position, enabling controlled perturbation of retrieval bias without modifying the retriever. Second, we show that output bias is well approximated by a position-weighted linear function of position-wise retrieval bias, revealing model-specific positional sensitivities. Third, we use this model to formulate retrieval as an optimization problem that trades off relevance against predicted output bias, and propose FARO, a scalable solution to that problem which decomposes the globally coupled quadratic objective into independent per-query assignment problems through a Fenchel--Legendre dual reformulation. Experiments with four open LLMs, and political and gender bias as use cases show that the linear model predicts output bias on unseen configurations in 17 of 24 settings. FARO substantially reduces output bias in most settings, while, compared with a linear-programming baseline, FARO achieves similar relevance, remains feasible where the baseline does not, and scales better to larger query sets and candidate pools.

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