LLM-based digital twins aim to predict how individuals would respond in new settings from representations of their prior responses. Existing evidence that compression of survey histories need not reduce predictive accuracy suggests that representation structure, rather than information volume alone, may be an important design choice. We study BDE, a fixed representation that organizes each respondent's survey history into Background, Decision procedure, and Evaluation. We evaluate it on Twin-2K-500 (Toubia et al., 2025) by predicting each respondent's held-out answers on 17 tasks. In a paired evaluation with 100 respondents, a fully inferred BDE profile improves overall accuracy over the raw survey transcript by 1.27 percentage points (pp) on gpt-5.4-nano (p < 0.01) and 1.19 pp on gpt-5.4-mini (p < 0.001). Three analyses then examine the schema, extraction depth, and component composition. Against a length-matched free-form profile written from the same transcript by the same extractor, BDE improves pricing accuracy on both simulators (2.15 pp on nano, p < 0.01; 1.38 pp on mini, p < 0.05), while its overall advantage is significant only on nano (1.05 pp, p < 0.05). Allowing deeper inference during extraction yields no statistically significant gain on either simulator. By contrast, adding Evaluation to a Background--Decision procedure profile improves overall accuracy by 1.44 pp on nano (p < 0.001) and 1.22 pp on mini (p < 0.001). These results indicate that the advantage over raw transcripts is not explained by compression or length alone, and attribute it primarily to profile composition rather than deeper extraction.

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