Sharing Statistical Strength Across Personas: Sample-Efficient Preference Learning and Aggregate Intransitivity

A user's preferences may reflect multiple semantic personas rather than a single profile. We study the sample-efficient learning of persona-conditioned choice probabilities from sparse persona-specific supervision. When user context is available, it can determine which persona probabilities to use or how to combine them; in the context-agnostic setting studied here, we use their uniform average. This average can be cyclic even when each persona's preferences are transitive. A natural approach fits each persona independently and aggregates the predictions, but it cannot exploit structure shared across personas. To address this, we introduce Persona Variation Subspace (PVS), which constrains persona parameters to an affine low-rank family, sharing statistical strength without forcing personas to agree. We establish prediction error rates governed by the intrinsic dimension of this family, with matching minimax lower bounds up to logarithmic factors. These rates support scaling to large pairwise comparison spaces under sparse supervision. We also characterize exact aggregate cycle recovery in terms of cycle margin and sampling coverage. On the Amazon--Walmart product benchmark annotated by LLMs under five personas, two centered components of independent persona fits explain about 93% of inter-persona variation. In the sparsest evaluated setting, PVS reduces persona-level Brier score by about 16% relative to independent per-persona Bradley--Terry models, with its largest gains on comparisons where personas disagree. PVS consistently recovers more aggregate cycles than baselines.