The Vocabulary Gap Is an Equity Gap: Register Mismatch in Retrieval Systems for Public-Benefits Access

Retrieval-augmented question answering is increasingly used to help people navigate public-benefits eligibility, yet the documents these systems retrieve from are written in agency register while intended users often ask questions in plain, informal, or non-native English. We show that this register mismatch can turn a high-performing retrieval system into an inequitable one. We construct a controlled benchmark of 51 publicly documented federal benefit-eligibility rules and 25 information needs, each phrased in both agency register and plain user register while keeping the gold passage fixed. Across BM25, TF-IDF, and a term-graph retriever, formal-register evaluation is nearly perfect (Recall@5 96-100%), but plain-register retrieval collapses (Recall@5 36-44%). For BM25, Recall@1 falls from 84% to 16% and Recall@5 from 100% to 44%, a 56-point equity gap on identical information needs. We trace the mechanism to a measurable vocabulary gap: formal queries share 0.63 of their content terms with the gold passage, while plain queries share only 0.11, a 5.9x reduction. A deliberately simple, auditable plain-to-formal lexicon bridge recovers much of the failure, lifting plain-query BM25 Recall@5 from 44% to 80%. The contribution is not a new retriever; it is an evaluation protocol, benchmark, mechanistic diagnosis, and transparent mitigation for a high-stakes social-impact failure mode that standard retrieval evaluation hides.