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

2026-05-09

AI Summary

This study investigates whether cognitive biases—such as the primacy and anchoring effects—arise from the mathematical structure of sequential information processing. By introducing three impossibility theorems, it theoretically demonstrates for the first time that such biases are mathematically inevitable under the causal masking constraints inherent to autoregressive architectures, thereby establishing a unified framework that explains both artificial and human cognitive biases. The theoretical predictions are empirically validated across twelve state-of-the-art large language models (R² = 0.89) through attention analysis, information-theoretic boundary derivations, approximate inference, and Monte Carlo simulations. Furthermore, two preregistered human experiments (N = 464) confirm the modulatory roles of anchor position and working memory load on bias magnitude.

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 ($R^2 = 0.89$; $Δ$BIC $= 16.6$ 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 ($d = 0.52$, BF$_{10} = 847$). Study 2 shows working memory load amplifies primacy bias ($d = 0.41$, BF$_{10} = 156$), with WM capacity predicting bias reduction ($r = -.38$). These convergent findings reframe cognitive biases as resource-rational responses to sequential processing.

Problem

• cognitive biases
• sequential processing
• primacy effect
• anchoring
• impossibility theorems

Innovation

• impossibility theorems
• sequential processing
• cognitive biases
• autoregressive language models
• causal masking