AnchorBench: A Multi-Pathway Benchmark for the Anchoring Effect in LLMs

AI summary

Overview

Research area: Evaluation of large language models — specifically cognitive bias (the anchoring effect) as a reliability failure in numeric judgment and decision-support tasks.

Technical level: Intermediate. The benchmark design and metrics are explained self-containedly, though familiarity with LLM evaluation terminology helps.

Scope: The paper introduces AnchorBench, a controlled multi-pathway benchmark that measures how, and how much, fourteen LLMs shift numeric estimates toward anchors delivered through five different context channels, while separating irrelevant from plausible anchors.

What This Paper Is About

The anchoring effect is the tendency for an initial reference value to pull a later judgment toward itself — a well-documented bias in human decision-making that recent work suggests also appears in LLMs. Prior LLM work typically tests only one or two anchor pathways (usually a value inserted into the prompt) and rarely distinguishes shifts toward anchors that carry no task-relevant information from shifts toward anchors that could plausibly be treated as evidence. AnchorBench addresses both gaps by evaluating five realistic anchor delivery pathways under an explicit control / irrelevant / plausible relevance axis, using tasks whose gold answer is fixed deterministically by visible numeric evidence.

Key Contributions

1. A multi-pathway diagnostic benchmark for LLMs. Five realistic anchor delivery pathways that mirror how context reaches a deployed model — External (the prompt), History (conversation), In-Context Learning / ICL (demonstrations), RAG (retrieved documents), and Tool (tool outputs) — evaluated under a shared framework, loosely informed by classic human anchoring theory.

2. A relevance-aware evaluation design. The benchmark separates control, irrelevant, and plausible anchor conditions. This distinguishes unambiguous bias (any shift toward an irrelevant anchor, which carries no task-relevant information) from sensitivity to plausible anchors, where a bounded shift can be consistent with rational evidence integration but a sufficiently large shift cannot.

3. A broad empirical comparison across model families and access regimes. Fourteen instruction-tuned models are evaluated — ten open-weight models from four families (Llama 3.1/3.2, Qwen2.5, Gemma 3, OLMo 2) and four frontier API models from OpenAI, Anthropic, Google, and xAI — across five suites and 9,000 condition-controlled prompts per model.

4. A public release. Code, benchmark data, and a Hugging Face dataset covering the five core suites and the partial-evidence variant — 14,400 prompts, each carrying its gold answer and its anchor value wherever the anchor is fixed in advance — plus separately distributed raw generations of approximately 520 MB.

Main Findings

• Anchoring is strongly pathway-dependent. External and RAG show the broadest positive effects; ICL (metadata) is uniformly near zero; History and Tool show substantial effects whose magnitudes are inflated by format confounds. No model is consistently best or worst across suites, and across the ten open-weight models the range of suite-mean Disc_Δ is 0.40 (bootstrap 95% CI [0.20, 0.60]).

• Plausible anchors usually induce larger shifts than irrelevant ones when the pathway is strong. Across the 69 model–suite cells with computable Disc_Δ, 55 (80%) show positive discrimination, rising to 48/55 (87%) once ICL is excluded. Wilcoxon signed-rank tests confirm the pattern on External, RAG, and Tool (p_BH < 0.01) and History (p_BH ≈ 0.02), but not ICL (p_BH = 0.81, n.s.).

• The ICL null result is a weak manipulation, not immunity. The standard ICL suite places anchors only in incidental demonstration metadata; a distribution-matching ICL-dist variant, which uses demonstration answers matching the anchor distribution, raises mean UAI_pls from approximately 0.03 to 0.16, with Disc_Δ > 0 for 8/10 open-weight models — comparable to RAG.

• Relevance is graded, not binary. On External, panel-mean UAI is +0.09 for a placebo framing, +0.05 for irrelevant, +0.27 for plausible, and +0.49 for authority. At matched mild/standard/strong intensity, RAG (0.05 → 0.08 → 0.18) sits one step below External (0.25 → 0.32 → 0.40) rather than differing in kind, with History non-monotone.

• Anchor influence generally decreases as the anchor moves farther from the evidence-supported answer. On External and RAG, mean UAI_pls decreases monotonically with offset δ ∈ {15, 25, 40}: open-weight External 0.32 → 0.26 → 0.18; RAG 0.23 → 0.15 → 0.06. API models show the same monotonic decrease on External at roughly 2× smaller magnitudes; on RAG, three of four API models peak at δ = 25 before decreasing. ICL stays near zero at all distances.

• High task accuracy does not guarantee robustness. Task accuracy and anchoring discrimination are only weakly correlated (r = −0.24, bootstrap 95% CI [−0.43, −0.00]); restricting to format-confound-free suites (External + RAG) gives r = −0.17 [−0.49, 0.16]. On External, OLMo-32B (53% accuracy) shows far higher discrimination (0.35) than OLMo-13B (89%; Disc_Δ = 0.17). All four API models reach at least 96% accuracy on External yet show positive Disc_Δ (0.05–0.16).

• Anchoring degrades prediction quality. Plausible anchors increase MAE by +3.6 (External) and +3.5 (Tool), while irrelevant anchors have near-zero impact. Error-increasing shifts outnumber error-reducing ones (29% vs. 23% overall), a gap driven by plausible anchors (37% vs. 20%) and largest on External and Tool (at least 22 percentage points).

• Some shifts exceed a rational integration ceiling. Treating the anchor as one extra piece of evidence among n = 5 ratings gives a rational UAI ceiling of w/(n+w) = 0.167 (w = 1); for irrelevant anchors w = 0, so any positive UAI_irr is bias. Of the 55 non-ICL plausible cells, 16 have a UAI_pls confidence interval entirely above 0.167 and 5 imply an implied weight w_imp > 5 — one anonymous number outweighing all five displayed ratings combined.

• The effect survives genuinely incomplete evidence. When only k of the five ratings are shown (k = 1, 2, 3), rational UAI_pls ceilings are 0.50, 0.33, and 0.25. Three of four tested models exceed the ceiling at some k: Llama-8B by +0.18 at k = 1 and +0.25 at k = 3, Qwen-7B at all three levels, and OLMo-13B at k = 2 and k = 3. Gemma-4B stays at or below the ceiling at every k.

• Prompt-level intervention has limited effect. Chain-of-thought attenuates UAI_pls without removing it (External: Gemma-4B 0.37 → 0.23, Llama-8B 0.39 → 0.37). An explicit averaging rule appended to the prompt collapses the panel mean from 0.33 to 0.06, but a prompt that instead invites the model to weigh sources by credibility brings it back to 0.26.

• Robustness checks. About 80% of cells keep the sign of Disc_Δ across ε ∈ {1, 3, 5}; bootstrap CIs on per-suite contrasts exclude zero outside ICL; harder items anchor more on External and RAG; stochastic decoding preserves the sign in 5 of 6 cells; and a weighted-mean gold moves UAI_pls by only +0.02. RAG influence survives rank changes and distractors (0.08 → 0.13) but collapses to 0.03 once documents carry relevance scores.

Methodology in Plain English

Every benchmark item is a numeric judgment task on a shared 0–100 scale across six domains: pricing, operations, logistics, resource consumption, market adoption, and compliance. The model receives a set of numeric evidence ratings and must return a single integer estimate. The gold answer is the rounded arithmetic mean of the visible ratings, which makes the task a deterministic aggregation problem — a model that correctly averages the given numbers matches gold exactly. A latent center θ drawn uniformly from [30, 70] sets the evidence range, and ratings are sampled from a normal distribution around θ with clipping to [0, 100]. Easy items present all five ratings with low noise (σ = 8); hard items hide two of five ratings, add a conflicting value, and raise noise (σ = 15). Items come from author-designed templates; the numeric evidence, anchor values, and gold answers are produced by seeded sampling, never by a model.

Each item is presented under five matched conditions: a control with no anchor, and four anchored conditions crossing two relevance levels (irrelevant and plausible) with a low and a high anchor direction. The critical design feature is that an irrelevant and a plausible condition in the same direction use an identical numeric anchor value; only the surrounding sentence differs. An irrelevant framing presents the value as incidental metadata (for example, an assessment case number), while a plausible framing presents it as a substantive prior estimate (for example, an industry report suggesting that value). Low and high anchors are placed symmetrically around the evidence center with offsets δ ∈ {15, 25, 40}. The History suite is the exception: its anchor is the model's own Stage-1 response rather than a designer-specified value, so its offset varies by item.

The five suites hold the numeric task fixed and vary only the pathway. External places an anchor sentence directly in the user prompt. History uses a two-stage conversation where Stage 1 shows partial evidence and Stage 2 reveals the full evidence. ICL places anchors in demonstration metadata (the main benchmark) or, in the ICL-dist variant, in demonstration answers. RAG embeds the anchor in one document of a frozen three-document mini-corpus, with the other two documents containing evidence consistent with the gold answer. Tool returns the anchor in a tool-call response, natively for models supporting structured tool messages (Qwen, Llama) and in an equivalent plaintext rendering for others (Gemma, OLMo, and APIs). External and RAG have no format confounds and provide the strongest cross-model evidence; History and Tool have format-related confounds, so their magnitudes are read qualitatively.

Each suite contains 360 items (6 domains × 60 items) in five conditions, giving 1,800 prompts per model per suite. Metrics cover three dimensions. Task accuracy is measured only on control responses via mean absolute error and Acc_10, the fraction of control responses within 10 points of gold. Anchor susceptibility is measured by Unified Anchor Influence (UAI), the fraction of the anchor–control gap closed by the anchored response, where 0 indicates no shift and 1 indicates full movement to the anchor; items where the control response already falls within ε = 3 points of the anchor are excluded. The denominator-free Toward-Anchor Rate (TAR) covers all items by recording whether the response moved toward rather than away from the anchor. Relevance discrimination is the difference Disc_Δ = UAI_pls − UAI_irr.

All fourteen models use greedy decoding (temperature 0), with answers extracted by deterministic hierarchical parsing (median parse rate 99.9%). Open-weight models were served locally on H100 GPUs using vLLM; API models were queried through OpenRouter with max tokens of 512.

Why This Matters

The paper argues that average task accuracy is not enough to certify reliable LLM judgment. In decision-support settings, a model may give a reasonable answer but still be pulled by a value that merely appears in the surrounding context — an earlier guess in a conversation, a value in a provided example, a retrieved document, or a tool output. The finding that highly accurate frontier models remain susceptible means robustness must be evaluated separately from accuracy, and along the specific pathways through which numeric context actually reaches a model.

Real-world applications:

• Medical question answering, where a model that gives sensible answers could still be shifted by a loosely related number in the clinical context.
• Time-series forecasting, where retrieved documents, prior conversation turns, or tool outputs may carry values that pull a forecast away from the evidence.
• LLM-as-a-judge and model-based evaluation pipelines, where position and related judging biases are already documented, and evaluators show anchoring in multi-attribute scoring — so the effect reaches the evaluation machinery itself, not only end-user tasks.
• Multi-turn price negotiation, where anchoring is known to persist and reasoning models are reported to be less susceptible.

Industry relevance: Any deployment that mixes retrieval, tool calls, and conversation history with quantitative reasoning — pricing, operations, logistics, compliance, resource planning — is exposed to the pathway-dependent effects documented here. The practical threshold the authors propose (a rational UAI ceiling of about 0.167 for a five-rating task) gives teams a concrete reference for when a shift is defensible versus when it indicates bias.

Future Directions

• Fully agentic loops. The suites stop short of a setting in which an agent plans its own retrieval and tool calls; testing whether the pathway effects persist there is described as a natural next step.

• Stronger or more realistic mitigations. Prompt-based mitigations weaken but do not remove anchoring — an explicit averaging rule collapsed the panel mean from 0.33 to 0.06, but a credibility-weighting prompt brought it back to 0.26. Methods beyond prompt engineering remain open.

• Extending beyond the six core domains. A pilot adding medical, legal, and consumer domains shows the same UAI_pls > UAI_irr > 0 pattern, suggesting broader domain coverage is feasible and worth pursuing.

• Resolving the known confounds. History uses a different interaction structure from its control (a matched-format analysis reduces Disc_Δ by up to 70% for some models) and Tool mixes structured and plaintext tool messages across model families, so cleaner operationalizations of those two pathways would sharpen cross-suite comparisons.

Target Audience

Researchers and practitioners working on LLM reliability, evaluation design, and decision-support deployment. The paper is most useful to those who need to test whether a model's numeric judgments are stable under realistic context injection — including teams building RAG pipelines, tool-using agents, and model-based evaluation systems — as well as to cognitive-bias researchers interested in comparing LLM behavior against human anchoring findings. Readers looking for training-time or architectural solutions will not find them here; the focus is measurement and diagnosis.

Authors’ abstract

The anchoring effect is a cognitive bias in which an initial reference value shifts a later judgment toward itself. This effect is well established in human judgment and decision-making, and recent work suggests that large language models (LLMs) exhibit similar behavior. However, existing work on anchoring in LLMs typically evaluates only a narrow set of anchor pathways and rarely distinguishes irrelevant from plausible anchors. We introduce AnchorBench, a benchmark for the anchoring effect in LLMs that evaluates multiple anchor pathways under an explicit anchor relevance axis. Across fourteen models, including ten open-weight models and four frontier API models, and a large set of controlled prompts, we find that (1) anchoring is strongly pathway-dependent, (2) plausible anchors usually induce larger shifts than irrelevant ones when introduced through stronger pathways, (3) anchor influence generally weakens as the anchor moves farther from the evidence-supported answer, most clearly on External and RAG, and (4) high task accuracy on the anchor-free control condition (Acc$_{10}$: answers within 10 points of gold) does not guarantee robustness: even frontier API models above 95% control accuracy remain susceptible to plausible anchors.