Hybrid Search: Fusing Two Ranked Lists with RRF

Your RAG system runs both a dense (embedding) retriever and a BM25 lexical retriever against the query "invoice PDF export fails with error 500". The two ranked lists (best first) are:

Dense: [doc_X, doc_Y, doc_Z] BM25: [doc_W, doc_X, doc_Y]

1. Write the Reciprocal Rank Fusion formula and explain what each term represents.
2. Compute the RRF score for every document that appears in either list, using k = 60, and give the final fused ranking.
3. Explain, using this example, why RRF is preferred over directly averaging or summing the dense cosine-similarity score and the BM25 score.