Large Language Models, despite their power, have a fundamental architectural vulnerability stemming from their causal transformer design -- order sensitivity. This architectural constraint may distorts classification outcomes when prompt elements like label options are reordered, revealing a theoretical gap between accuracy metrics and true model reliability. The paper conceptualizes this vulnerability through the lens of survey methodology, where respondent biases parallel LLM positional dependencies. Empirical evidence using the F1000 biomedical dataset across three scales of LLaMA3.1 models (8B, 70B, 405B) demonstrates that these architectural constraints produce inconsistent annotations under controlled perturbations. The paper advances a practical solution for social science - Independent Probability Assessment - which decouples label evaluation to circumvent positional bias inherent in sequential processing. This approach yields an information-theoretic reliability measure (R-score) that quantifies annotation robustness at the case level. The findings establish that architectural vulnerabilities in causal transformers require methodological innovations beyond accuracy metrics to ensure valid social science inference, as demonstrated through downstream regression analyses where order-sensitive annotations significantly alter substantive conclusions about scientific impact.