Optimal Response Formats for AI Brand Perception Measurement: Evidence for a J-Shaped Rate-Distortion Curve

This study applies Shannon rate-distortion theory to measure how response-format constraints affect the fidelity of AI-generated brand perception profiles. Seventeen large language model architectures from distinct training lineages are prompted to evaluate five canonical reference brands under five response formats spanning 3 to 26 bits of information rate. Distortion is measured as total variation distance between each model’s normalized output and a canonical eight-dimensional brand profile. The resulting rate-distortion curve is J-shaped: minimum distortion occurs not at the highest-rate format (100-point allocation, 26 bits) but at an intermediate bounded format (1-5 ordinal scale, 19 bits), corresponding to a 49.4% reduction in mean distortion (R1 = .172 → R2 = .087). All 17 models exhibit this pattern (paired t(16) = 11.92, p < .001, Cohen’s d_(z) = 2.89 for R1 vs R2). Cross-model coefficient of variation averages .140 across all five rate conditions (CV = .171 excluding the structurally degenerate R5 single-dimension condition), indicating codebook convergence across architectures. These findings demonstrate that structured response formats suppress encoder bias and yield higher-fidelity brand perception measurements than unconstrained elicitation, with direct implications for AI-mediated brand research instrument design. Includes zharnikov-2026aa-r19.yaml (Paper Spec v0.1.0) – a machine-readable specification of the paper's claims, assumptions, and dependencies. The paper's full machine-first bundle (the SPINE claim/dependency graph and the ONTOLOGY term module) lives in the public repository; see https://github.com/spectralbranding/paper-spec for the standard. This PDF is generated programmatically from that machine-first source under a research-as-repository model.