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

TL;DR

This paper proves that certain cognitive biases are mathematically unavoidable in sequential AI and human processing, supported by theoretical impossibility results, empirical validation across language models, and human experiments.

Contribution

It introduces three impossibility theorems explaining biases like primacy and anchoring as necessary in autoregressive models and validates these with extensive experiments.

Findings

Biases are architecturally necessary due to causal masking constraints.

Empirical validation across 12 frontier LLMs supports theoretical bounds.

Human experiments confirm the influence of position and working memory on biases.

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 ($R^2 = 0.89$; $\Delta$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.