Anchoring Bias in Language Models

Search can help LLM agents correct mistakes, but their starting conditions may shape which evidence they find and use. Drawing on cognitive-bias paradigms, we develop a controlled search harness to examine result order, records of prior work, and initial hypotheses while holding each question and document collection fixed. Matched controls distinguish order effects from differences in document composition and the effects of failed work from context length. Across 10 models and 1,000 synthetic search worlds, we track queries, retrieved documents, document openings, and final answers. Our comparisons suggest that final answers are more sensitive to initial evidence order during active search than when all evidence is supplied in full. Dead-end histories can reduce strategy switching relative to matched neutral histories, indicating an effect beyond context length. Under wrong hypotheses, stage measurements distinguish reduced retrieval or opening from errors that persist after counter-evidence is opened. Exploratory interventions show that opening counter-evidence more often can coincide with lower accuracy, while accuracy can improve with little change in opening.

Does eliciting five weighted estimates within a single response consistently improve numerical judgments? We compare direct and multi-estimate elicitation across anchoring, hindsight, base-rate, conjunction, and status-quo/default tasks in six frozen configurations. Each configuration contributes 618 admitted development units and 3,702 admitted formal units; the six-configuration formal cohort contains 22,212 units, including 21 missing outcomes. Of 45 preregistered confirmatory tests across five configurations, 12 reject on complete cases and 11 retain directional confirmation after the prespecified missingness-protection rule. Only one adjusted bound exceeds its smallest effect size of interest: gpt-oss-120b shows a 10.68-percentage-point increase in post-outcome confirmation error under multi-estimate elicitation (worst-case estimate 10.04 points). The remaining ten retained effects have sub-threshold point estimates; non-rejection does not establish equivalence. Joint presentation lowers signed conjunction excess in four confirmatory configurations, but this comparison changes both constraint visibility and call structure. Flash-high combines two disjoint execution-window batches under an approved continuation protocol, preserving their identities and non-causal interpretation. Post-hoc candidate-spread associations across all six configurations remain in-sample and require independent predictive validation. The completed cohort provides no evidence for uniform debiasing by multi-estimate elicitation. Materials: https://github.com/asj252/llm-judgment-studies

Triage in the emergency department (ED) is a sequential decision process that unfolds turn by turn. Existing evaluations of large language models (LLMs) for triage use completed retrospective records and report performance close to that of physicians. We implement a methodology for evaluating LLMs on sequential triage, the task of predicting a triage acuity label from a growing prefix of a nurse-patient conversation. We evaluate six LLMs at five sequential checkpoints on two corpora: 425 LLM-generated (SIMULATED) and 50 physician-authored (CLINICIAN) conversations, both labelled under the Emergency Severity Index (ESI). Every model, measured by quadratic weighted kappa (QWK), degrades from moderate-to-substantial agreement on completed records to fair-to-moderate agreement at every sequential checkpoint. Controlled perturbations show that the label at every checkpoint is anchored on the chief complaint exchanges, and prompting interventions fail to lift this plateau. Models extract clinically relevant content from later turns, yet the surprisal of the true label rises across the checkpoints. So the model fails to integrate the evidence. Three expert clinicians on the same conversations reach a QWK of 0.887-0.929, while the best model reaches 0.295. Predictions concentrate at ESI-2 and ESI-3, and models agree with each other more than with the ground truth, so ensembling worsens the failure. Deploying LLMs for ED triage based on offline benchmarks alone misses this sequential failure.

Irrelevant numbers in a prompt can shift language model judgments, producing anchoring effects in numerical reasoning. We study where this anchor-sensitive signal is carried inside language models using a controlled multiple-choice setup with shared answer options. We define a logit-difference metric comparing the correct answer option with the answer option corresponding to the anchor, and validate that it tracks behavioral anchoring. Using attribution-based circuit localization on 7B--8B Qwen and Llama base and instruction-tuned models, we find that edge-level methods recover this signal more faithfully than node-level methods. Low- and high-anchor circuits transfer strongly within a model, suggesting shared pathway structure across anchor direction. However, sparse transfer across base and instruction-tuned variants is less reliable, indicating that post-training changes which pathways matter most. Overall, our results provide a mechanistic account of how anchoring-related decision signals are carried inside language models.

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.

What if the twelve jurors of Sidney Lumet's 12 Angry Men (1957) were not men, but large language models? Would the one juror who disagrees still be able to change everyone's mind? This paper instantiates that scenario as a multi-agent benchmark for LLM deliberation: twelve agents, each conditioned on a film-faithful persona, debate the film's murder case using multi-agent framework. Two models representing opposite ends of the RLHF spectrum are tested: GPT-4o (closed-source, heavy alignment) and Llama-4-Scout (open-weight, lighter alignment), across three conditions (baseline, open-minded prompt, no initial vote), with N = 3 replications per cell (18 runs total). Three findings emerge. (i) Seventeen of eighteen runs end in a hung jury (a state where the jury fails to reach a unanimous verdict); the film's central event, gradual minority-to-majority persuasion, almost never occurs, indicating that anchoring is the dominant failure mode of current LLMs in this setting. (ii) The two models exhibit sharply different internal dynamics: GPT-4o produces a mean of 1.0 vote changes per run across all conditions, while Llama-4-Scout ranges from 2.0 (baseline) to 6.0 (open-minded prompt), and is the only model to reach a NOT_GUILTY verdict (1 of 3 runs in the no-initial-vote condition). The same ``open-minded'' instruction is internalized by Llama and ignored by GPT-4o. (iii) This asymmetry suggests that the intensity of RLHF alignment training, not model capability, is the primary determinant of deliberative flexibility in multi-agent settings. Flexibility, not capability, tracks human deliberation. The work is framed as an exploratory study and discusses implications for jury-of-LLMs evaluation and multi-agent debate.

Count-based F1 is widely used as a proxy for LLM error-detection quality, but this paper shows that it can rise dramatically without a corresponding improvement in span localization, a gap termed F1 Inflation. The paper introduces ErrorBench, a controlled stress-test protocol for prompt-induced count distortion. ErrorBench evaluates six contemporary LLMs under five prompt conditions over 4,290 responses from 143 CoNLL-2014 passages. Under CoNLL-2014 M2-style scoring, anchored prompts produce up to 0.79 points of F1 Inflation, and up to 0.96 under strict matching. A 100-passage replication using the official ERRANT 3.0.0 pipeline and multi-reference scoring reproduces the pattern: averaged over six models, the Blind-to-Anchored prompt shift raises Count-F1 by +0.21 while raising multi-reference ERRANT F0.5 by only +0.04. The study finds larger count responses in highly instruction-compliant GPT/Claude systems and smaller responses in the Gemini family under this stress-test protocol. The findings suggest that LLM proofreading and document-review evaluations should avoid pre-populated error counts and should report span-aware metrics alongside count-based metrics.

We observe that LLM cascading and routing implicitly solves an anytime computation problem -- a class of algorithms, well-studied in classical AI, that improve solutions as additional computation is allocated. We formalize this connection and propose Pyramid MoA, a hierarchical Mixture-of-Agents architecture governed by a decision-theoretic router that escalates queries only when necessary. We establish a Probabilistic Anytime Property with provable monotonicity guarantees and derive a generalized escalation rule from Value of Computation theory that accounts for imperfect oracles, extending the Hansen-Zilberstein monitoring framework to stochastic LLM inference. On MBPP, the router intercepts 81.6% of bugs; on GSM8K/MMLU, the system nearly matches the 68.1% Oracle baseline while achieving up to 42.9% compute savings. The router transfers zero-shot to unseen benchmarks: matching Oracle accuracy on HumanEval (81.1%) and MATH 500 (58.0%) with significant cost reductions. We further discover a context-conditioned anchoring effect across four benchmarks: passing correct SLM reasoning improves Oracle accuracy by up to +19.2pp, while incorrect reasoning degrades it by up to -18.0pp, revealing a fundamental tension in hierarchical MoA architectures.