Query Timing Produces Opposite Positional Biases Between LLMs and Humans

Large language models are routinely used as automated evaluators: to review code, moderate content, or score outputs, often with many items passing through one conversation. We ask whether the polarity of prior conversation history biases subsequent judgments, an effect we call the accumulated message effect on LLM judgments (AMEL). Across 84,088 API calls to 12 models from 5 providers (OpenAI, Anthropic, Google, DeepSeek, and four open-source models), we present identical test items in isolation or following histories saturated with predominantly positive or negative evaluations. Models shift toward the conversation's prevailing polarity (d = -0.17, p < 10^-53). The effect concentrates on items where the model is genuinely uncertain at baseline (d = -0.36 for high-entropy items, vs d = -0.15 when the baseline is deterministic). Bias does not grow with context length: 5 prior turns and 50 produce the same shift (Spearman |r| < 0.01; OLS slope p = 0.80). And there is a negativity asymmetry: paired per item, negative histories induce 1.52x more bias than positive (t = 13.03, p < 10^-36, n = 2,733). Scaling helps but does not solve it (Anthropic: Haiku -0.22 to Opus -0.17; OpenAI: Nano -0.34 to GPT-5.2 -0.17). Three follow-ups narrow the mechanism. The token probability distribution shifts continuously, not at a threshold. The negativity asymmetry has both token-level and semantic components, though attributing the balance is exploratory at our sample sizes. Position does not matter: five biased turns anywhere in a 50-turn history produce the same shift. The simplest fix for evaluation pipelines is a fresh context per item; when batching is unavoidable, balancing the history helps.

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.

Large language models (LLMs) increasingly issue judgments read as binary verdicts, and a growing literature reports such judgments shifting under logically irrelevant changes of wording - among them an amplified yes-no bias on moral dilemmas, absent in humans. A single framing cannot say what such a shift is: in a yes/no question the word "no" is at once logical verdict, lexical token, and last-printed option. We introduce a psychometric battery that separates these: crossed symmetrization - every logically irrelevant factor flipped in balanced pairs - across a corpus of question forms. A graded rating across logically equivalent forms recovers a coherent internal moral scale: frontier models' stance $θ$ is nearly format-invariant (cross-form incoherence 0.12-0.21 on a $\pm 1$ axis); small open-weight models fail in model-specific ways. Forcing the verdict through yes/no overlays a decomposable artifact: an order bias toward the last-printed option - opposite to classic human primacy - plus a lexical pull toward the word "no"; the artifact is substantial only in the Claude models (story-averaged -0.32 to -0.86), $\approx 0$ for GPT-5.5 and Gemini, and shrinks under extended reasoning. The word and the verdict share one token; swapping the words for arbitrary labels separates them, and the verdict-attached logical bias proves $\approx 0$ for every frontier model, while model-specific label and order attachments remain: the models are not drawn toward rejecting - the pull follows the printed surface, not the verdict it carries. A minimal model, $P = σ((θ\pm m)/s)$, summarizes any such artifact by a framing susceptibility m and a moral decisiveness s, measurably distinct from sampling temperature. The battery applies unchanged to any dilemma set and binary format: measuring what a model values requires crossing the frames of the question, not asking once.