WARP: Wasserstein-Aligned RAG for Population Opinions

RAG systems are increasingly used to summarize what large collections of documents say. A user asks "What do people think about X?" and receives an answer that reads as consensus. But standard top-k retrieval ranks documents by query similarity, not by how faithfully they represent the population, so minority views quietly disappear. Existing fixes fall short. Diversity re-rankers like MMR and DPP spread retrieved documents apart, but with no target distribution to aim for. Calibration methods based on KL or JS divergence do target one, yet treat opinion bins as unordered: confusing strong positive with strong negative costs no more than an adjacent-bin miss. We introduce WARP, a family of post-retrieval algorithms that calibrate retrieved evidence to the population's opinion distribution. WARP first recovers underrepresented opinions that cosine ranking may bury, then uses Wasserstein-1 distance to select documents whose sentiment-intensity distribution matches the population target, capturing the ordinal structure ignored by KL and JS divergence. We develop three variants for dense, sparse, and variable candidate pools, trading off calibration quality and speed. Across three review domains spanning 35K documents, 156 queries, and 26 entities, WARP's domain-matched variants reduce distributional error by at least 43% with sub-second latency. These gains carry through to generation: a five-judge LLM panel prefers WARP-generated answers in 86% of decided comparisons at k <= 5.

Normative Alignment of Recommender Systems via Internal Label Shift

We introduce NAILS (Normative Alignment of Recommender Systems via Internal Label Shift), a simple and scalable method for aligning recommendation outputs with target distributions over item-level attributes, such as categories. Recommender systems optimized solely for user engagement often fail to satisfy broader normative objectives, including fairness, diversity, and editorial values. NAILS modifies the user-conditional item distribution to induce a specified marginal distribution over attributes while preserving the preferences learned by an existing recommender system and requiring no model retraining. We formulate this problem as a form of label shift applied internally within a hierarchical classification framework. By adopting a stakeholder-centric perspective, NAILS enables recommendation outputs to be aligned with global normative objectives. Empirically, we show that NAILS consistently improves attribute-level alignment with minimal impact on user engagement, providing a practical mechanism for value-driven recommendation.