Bias by Necessity: Impossibility Theorems for Sequential Processing with Convergent AI and Human Validation

Are certain cognitive biases mathematically inevitable consequences of sequential information processing? We prove that primacy effects, anchoring, and order-dependence are architecturally necessary in autoregressive language models due to causal masking constraints. Our three impossibility theorems establish: (1) primacy bias arises from asymmetric attention accumulation; (2) anchoring emerges from sequential conditioning with provable information bounds; and (3) exact debiasing by permutation marginalization requires factorial-time computation, with Monte Carlo approximation feasible at constant per-tolerance overhead. We validate these bounds across 12 frontier LLMs (R2 = 0.89; DeltaBIC = 16.6 vs. next-best alternative). We then derive quantitative predictions from the framework and test them in two pre-registered human experiments (N = 464 analyzed). Study 1 confirms anchor position modulates anchoring magnitude (d = 0.52, BF10 = 847). Study 2 shows working memory load amplifies primacy bias (d = 0.41, BF10 = 156), with WM capacity predicting bias reduction (r = -.38). These convergent findings reframe cognitive biases as resource-rational responses to sequential processing.