Grounding Text Embeddings in Stakeholder Associations

Modern AI is opening the door to collective decision-making in which participants express their views as free-form text rather than voting on a fixed set of candidates. A natural idea is to embed these opinions in a vector space so that the substantial literature on facility location problems and fair clustering can be brought to bear. But standard text embeddings measure semantic similarity, whereas distances in facility location problems and fair clustering require what we call \textit{preferential similarity}: a participant's agreement with a piece of text should be inversely related to their distance from it. Off-the-shelf embeddings inherit a coarse preference signal through a correlation between semantic and preferential similarity, but fail to capture preferences when the correlation breaks. We formalize this as an invariance problem: text embedding models encode both a preference-relevant signal (stance and values) and semantic nuisance (style and wording), and the two are observationally correlated, so a geometry that relies on nuisance can appear preference-correct even when it is not. We show that synthetic training data designed to break this correlation provably shifts the optimal scorer away from nuisance-dominated cosine and significantly improves preference prediction across 11 online deliberation datasets.

Pretrained text embeddings are increasingly used as representational maps, yet high category separability does not imply that their geometry recovers expert-defined structure. We study this problem in mental-health-related language, where symptom relations provide an external reference and online communities introduce strong domain, affective, stylistic, and discourse confounds. Using 28 Reddit communities, we compare pretrained and supervised fine-tuned Qwen3 embedding spaces at two scales (0.6B and 4B). We construct category prototypes, evaluate their representational dissimilarity matrices against an expert symptom matrix with representational similarity analysis, and complement this global test with prototype-based typicality and multi-baseline confound controls. Pretrained embeddings show measurable alignment with expert structure within the mental-health subset; fine-tuning strengthens this alignment most at the finest category level; and larger scale improves both zero-shot alignment and supervision-induced gains. Residual alignment remains substantial after controlling for VAD, LIWC, lexical style, and topic-distribution structure. These results suggest that LLM embeddings can recover expert-relevant category geometry, but this recovery is level-dependent and should be tested against explicit confounds rather than inferred from classification alone.

When do text embeddings work as inputs to empirical analysis? Their use rests on an assumption: that we can trade text for its low-dimensional embedding, and lose little in doing so. I make that assumption precise under a generative model in which documents are mixtures of latent topics. I study two uses---clustering units in embedding space and controlling for high-dimensional text. A cluster of embeddings is a set of documents with similar topic mixtures; controlling for the embedding is equivalent to controlling for the topic mixture, so validity reduces to whether that mixture captures the confounding. In an application to 363 U.S. metropolitan areas, embedding-based clusters of LLM-generated economic descriptions recover interpretable economic archetypes and separate local employment dynamics more sharply than clustering on model residuals, or on a curated set of industry and demographic covariates.