Passing Coarse Marginal Checks Can Be Cheap: Persona Mixtures and Imprecise Treatment-Response Estimates in an LLM Persona Panel

Large language models are increasingly used as synthetic research participants and are often validated by whether their marginal responses resemble human data. We study a fixed panel of sixteen lightweight persona-conditioned GPT-4.1 configurations in repeated strategic games. The panel met preregistered broad-reference condition-mean criteria in three of four repeated-game cells; the sole miss was 0.011 below the lower reference bound. Variation was strongly prompt-indexed, but its share depended on uncertainty assumptions: fixed-panel symmetric-Dirichlet sensitivities produced median between-prompt shares of 63%-71% under Jeffreys alpha=0.5 and 47%-53% under alpha=1, while finite-opportunity plug-in estimates were 85%-96%. Aggregate continuation-probability contrasts were +0.083 and +0.078, with conservative simultaneous 95% intervals [-0.171, +0.330] and [-0.181, +0.330]. The treatment jointly changed the continuation process and its textual representation. A separate wording-and-position operation shifted cooperation from 0/40 to 37/40 in the bare configuration, and a label conflict also revealed representation control. The original persona-level p13 result was not prospectively family-controlled, while a post-adjudication exact gate was structurally underpowered; p13 is therefore a replication target rather than a finding. External review exposed family-error, dependence, construct, and boundary-uncertainty defects, and zero-call reanalysis changed the interpretation without rewriting the historical record. The registered marginal criteria could be passed without precisely estimating the treatment-response object. A public capsule verifies 4,916 confirmatory Phase 3-5 runs with no live model calls. The results concern one fixed model-prompt panel and do not establish human substitutability.