cs.AIMay 9, 2026

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

Authors: Jikun WuDongxin GuoSiu-Ming Yiu

Organizations: 1Stellaris AI Limited, Hong Kong, China · 3The University of Hong Kong, Hong Kong, China

Abstract

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=0.89R^2 = 0.89; ΔΔBIC =16.6= 16.6 vs. next-best alternative). We then derive quantitative predictions from the framework and test them in two pre-registered human experiments (N=464N = 464 analyzed). Study 1 confirms anchor position modulates anchoring magnitude (d=0.52d = 0.52, BF10=847_{10} = 847). Study 2 shows working memory load amplifies primacy bias (d=0.41d = 0.41, BF10=156_{10} = 156), with WM capacity predicting bias reduction (r=.38r = -.38). These convergent findings reframe cognitive biases as resource-rational responses to sequential processing.

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