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REVIEW 4 major objections 5 minor 2 cited by

Anchoring Bias in Large Language Models: An Experimental Study

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read LLMs let a planted number steer their numerical guesses.

desk verdict Useful empirical study of hint sensitivity in LLMs with a promising mitigation idea, but the main test does not separate anchoring bias from rational use of informative hints. read the letter →

arxiv 2412.06593 v2 pith:XI2U5GOU submitted 2024-12-09 cs.CL

Jiaxu Lou , Yifan Sun This is my paper · ORCID
classification cs.CL
keywords anchoringbiaslargelanguagemodelscognitivepromptmitigationstrategiesGPT-4GPT-4oGPT-3.5numericalprediction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether large language models fall for anchoring bias—the tendency to let the first number they see drag their estimate toward it. On 62 everyday prediction questions taken from a human behavioral study, the authors compare each model's numerical answers when given a low anchor versus a high anchor alongside the question. They find that GPT-4, GPT-4o, and GPT-3.5 answer higher when the hint number is higher, with same-signed differences in 151 of 162 model-question comparisons, and that the effect is especially strong for 'expert' hints. They also test four common prompt-level fixes—chain-of-thought, principles-first reasoning, explicit instructions to ignore the anchor, and reflection—and find none of them removes the bias. The only partial remedy is to give the model both anchors at once, which pulls answers back toward the unbiased benchmark when the two anchors bracket it.

What carries the argument

The operative measure is a sign-match test. For each question, the model answers 30 times with the low anchor H2 (treatment A) and 30 times with the high anchor H3 (treatment B); the paper computes the mean difference (B − A) and compares its sign with the sign of (H3 − H2), using a two-sample t-test for significance. A same-signed, statistically significant difference is taken as evidence of anchoring. Supporting this test are a CO-STAR-based prompt template that asks for an 'educated guess' in JSON format, and the anchoring index AI = (median_high − median_low)/(high anchor − low anchor), borrowed from the human anchoring literature to compare LLM and human susceptibility.

What would settle it

Give the same prompts to a model with the hint labels swapped (high anchor presented where the low anchor was, and vice versa) and check whether the answer difference flips sign exactly as a function of the presented values; if it tracks the presented values symmetrically, the sign-match test cannot distinguish anchoring from arithmetic averaging. A cleaner check would add a per-question no-anchor condition and require answers to move toward the anchor beyond the no-anchor baseline.

Watch

Extended reading notes

Core claim

The paper's central discovery is that GPT-family models exhibit anchoring bias in numeric prediction tasks: answers under a high hint are significantly higher than answers under a low hint, and the sign of the answer difference matches the sign of the hint difference in the large majority of cases. This holds across fact-based and expert-opinion anchors, with expert hints producing the strongest and most consistent effect—none of the 12 expert-hint questions produced a sign mismatch for any model. The bias survives four prompting strategies designed to reduce it, and only the Both-Anchor condition, where both the low and high hints are included in the prompt, moves answers close to the no-anchor baseline, and only when the two hints lie on opposite sides of that baseline. The authors also report an anchoring index near 0.45 for GPT-4, lower than the 0.61 observed in the human study on the same questions, indicating LLMs are influenced by anchors but less so than humans.

Load-bearing premise

The paper counts an answer as anchored when the difference between answers under the high and low hints has the same sign as the difference between the two hints; that test would also fire for a model that simply averaged the two hints, because no no-anchor baseline is built into the main comparison.

Editorial extensions

If this is right

  • Numerical answers from GPT-4, GPT-4o, and GPT-3.5 move in the direction of an anchoring hint, and the effect is strongest for 'expert' opinions, where all 12 test questions showed same-signed differences.
  • Prompting strategies that work for reasoning tasks in general—Chain-of-Thought, Thoughts of Principles, explicit ignore-anchor instructions, and Reflection—do not remove or significantly reduce the anchoring effect.
  • Presenting both a low and a high anchor together moves GPT-4's answers close to the no-anchor value when the two anchors lie on opposite sides of that value, suggesting a practical mitigation path.
  • Stronger models (GPT-4, GPT-4o) are more consistently biased than GPT-3.5, which the authors attribute to lower answer variance in stronger models.
  • Anchoring effects were not statistically significant for time-period answers and for questions whose first hint was irrelevant to the question.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The sign-match test would classify a rational interpolator—a model that simply averages the two hint values—as 'anchored,' so the true effect size is likely overstated until a no-anchor baseline is subtracted.
  • A direct prediction from the paper: reordering hints or placing a neutral number before the anchor should change the strength of the effect if anchoring is about the first salient number; this ordering test is not run and would separate anchoring from generic numeric context sensitivity.
  • The Both-Anchor result suggests a cheap deployment rule: when eliciting numeric estimates from LLMs, prompt with several bracket-style estimates rather than a single reference value, since the paper shows this reduces anchor pull even though it does not eliminate it.
  • If stronger models are more consistently anchored, calibration efforts that reduce output variance may inadvertently amplify the appearance of bias in sign-match tests; reporting absolute deviations from a no-anchor baseline would clarify whether variance or true pull drives the result.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper reports an empirical study of anchoring bias in large language models (GPT-4, GPT-4o, GPT-3.5) using 62 numerical-prediction questions taken from a human behavioral experiment by Yasseri and Reher. For each question, the model is given a contextual hint H1 plus either a low anchor H2 or a high anchor H3, and the distribution of model answers under the two treatments is compared with t-tests. The authors define evidence of anchoring as a statistically significant difference between Treatment A and Treatment B whose sign matches the sign of H3−H2. They report that most differences are sign-consistent, that stronger models are more consistently influenced, that expert-opinion anchors are particularly effective, and that simple prompting mitigations (Chain-of-Thought, Principles of Thought, Ignore, Reflection) do not reduce the effect, whereas providing both H2 and H3 sometimes brings answers close to a no-anchor benchmark. The paper concludes that LLMs exhibit anchoring bias and that collecting hints from multiple angles is a partially effective mitigation.

Significance. If the central claim were established, the study would provide a useful quantitative demonstration of a cognitive bias in LLMs, extending prior work beyond financial questions and offering practical guidance for prompt design. The use of a diverse 62-item human dataset, repeated sampling of 30 responses per condition, and the comparison with human anchoring indices are strengths, and the authors make their prompts and answers publicly available. However, the experimental design conflates anchoring bias with rational sensitivity to informative hints: because H2 and H3 are factual or expert opinions about the target quantity, a model that simply weights all provided evidence would also produce sign-consistent differences. The paper therefore measures sensitivity to hints, not bias. The mitigation claims rest on a small, selected subset of questions and lack formal comparisons. The result is of interest as a descriptive measurement, but the central inference to 'anchoring bias' is not yet supported.

major comments (4)
  1. [Section 4.2] The operational definition of anchoring bias is a sign-concordant difference between Treatment A (H1+H2) and Treatment B (H1+H3). This criterion cannot distinguish anchoring bias from rational integration of informative hints. For the fact-anchoring and expert-opinion conditions, H2 and H3 carry genuine information about the target quantity (e.g., last week's stock price range, another forecaster's estimate). A model that forms a posterior estimate as a weighted average of H1 and the provided hint will also produce A<B whenever H2<H3, and may do so with very small p-values. The t-test only rejects equality of the two treatment distributions; it does not reject the null hypothesis that the model uses the hints in an unbiased way. The No_anchor condition already present in Figure 9 should be used in the main analysis as a baseline, or the paper should specify a normative model for the unbiased answer and show that the model's answers are pulled toward the anchor beyond that benchmark.
  2. [Section 4.2.1] The claim that 151 of 162 sign-consistent differences provide 'strong evidence' for anchoring is overstated because sign consistency is counted regardless of statistical significance. Many of the differences in Figures 4 and 5 have p-values well above 0.05 (e.g., question 3 with p=1.00, question 21 with p=0.163, question 22 with p=0.813 for GPT-3.5), yet they are apparently treated as non-exceptions if the sign matches. The paper should report the number of sign-consistent differences that are also statistically significant at a pre-specified level, and ideally account for multiple comparisons across the 54 tests per model. As presented, the evidence is weaker than the text suggests.
  3. [Section 4.3] The anchoring index AI = (median_high − median_low)/(high − low) is a measure of response sensitivity to the hint values, not a measure of bias. An unbiased rational integrator can produce any intermediate AI depending on the relative reliability it assigns to H1 versus the hint, so the value 0.45 for GPT-4 does not indicate that the model is 'biased' or that its bias is smaller than the human value of 0.61. The comparison to the human anchoring index also lacks confidence intervals and a formal statistical test. The claims about human–LLM differences in anchoring strength are therefore not supported by the reported data.
  4. [Section 5] The mitigation experiments are run only on the 12 'expert' questions, which are the questions with the strongest anchoring effects, and the paper provides no formal comparison between the mitigation conditions and the no-mitigation baseline. For example, Figures 7 and 8 should be tested against the corresponding differences in Figure 5 to determine whether the absolute bias magnitude is significantly reduced by CoT, PoT, Ignore, or Reflection; the current narrative relies on visual inspection. The Both-Anchor evaluation in Figure 9 reports only mean answers for one model (GPT-4), without standard deviations, error bars, or a significance test against the No_anchor condition. The conclusion that Both-Anchor partially mitigates anchoring bias is therefore not quantitatively established.
minor comments (5)
  1. [Section 3.2] The text refers to 'Control and Treatment B & C' but only Treatments A and B are defined; the Control condition is denoted C in Section 3.2. This is likely a typo and should be corrected.
  2. [Section 4.2 / Figures 4–6] Many p-values are reported as 0.00E+00 or with excessive precision. The actual floating-point values should be reported, and the threshold of 0.05 should be stated in the text; the authors should also address the multiple-comparisons issue arising from running many t-tests.
  3. [Section 5] The sentence 'We use the "expert" anchoring questions because the anchoring effects are very significant for these questions. [19]' cites a reference about human anchoring and adjustment (Simmons et al.) rather than the authors' own analysis. The citation is misplaced; the authors should either cite their own Figures 4–5 or provide a different rationale.
  4. [Section 3.2 / Appendix A] The prompt template explicitly instructs the model to make an 'educated guess based on the provided information.' This instruction likely encourages the model to incorporate the hints, making it difficult to attribute the observed sensitivity to an automatic cognitive bias. The paper should discuss this potential confound or include a control prompt that does not instruct the model to use the hints.
  5. [Figure 9] The column labeled 'No_anchor' is not defined in the body text. It should be explained how this condition was constructed (e.g., whether it is the Control condition from Section 3.2, or a separate no-hint condition) and why it is used only in the mitigation section.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper is a self-contained experimental measurement against an external human dataset.

full rationale

The paper does not derive any quantity from itself. It takes an external experimental dataset of 62 questions with pre-specified hints (H1, H2, H3), prompts LLMs under control and treatment conditions, and compares the resulting answer distributions. The anchoring index and the sign-match t-test are operational definitions applied directly to the measured answers and hint values, not parameters fitted to data and then renamed as predictions. No load-bearing self-citation appears: the cited prior work, including the human study in [10], is external to the authors and serves as an independent benchmark rather than as justification for the paper's own claims. The comparison to human anchoring results is a comparison against outside data, not a restatement of the paper's inputs. Even if the sign-match test could be questioned on construct-validity grounds—because informative hints might move answers in the same direction under rational weighting—that concern is about experimental interpretation, not circularity. The central claim, that LLM answers are sensitive to biased hints, is directly measured rather than assumed. Therefore no circular step is present.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claims rest on experimental design choices and operational definitions, not on fitted parameters. The paper introduces no new theoretical entities; the both-anchor strategy is a prompting method, not an entity.

free parameters (3)
  • Sampling temperature = 0.8
    Chosen by the authors for all LLM runs; affects response variability and thus the t-test results, though the core bias direction is likely robust.
  • Number of repetitions per condition = 30
    Chosen to have enough samples for t-tests; no power analysis is reported.
  • p-value threshold for significance = 0.05
    Used to call differences 'significant', but sign consistency is counted even when p > 0.05.
assumptions (4)
  • domain assumption The PTF human-anchoring dataset (62 questions with H1, H2, H3 hints) is a valid instrument for probing anchoring bias in LLMs.
    The paper adopts the dataset from [10] without validating that the questions are meaningful for models trained on internet text; e.g., events are dated (2018), which may cause temporal confusion.
  • ad hoc to paper Sign consistency between the answer difference and the hint difference is evidence of anchoring bias.
    The paper's operational definition in Section 4.2; rational averaging of the two hints would also produce sign consistency, so this does not isolate bias.
  • domain assumption LLM responses across 30 runs at temperature 0.8 are independent and identically distributed samples.
    Needed for the t-test; API sampling is stochastic, but the near-zero standard deviations on many questions suggest near-deterministic behavior.
  • standard math The t-test is an appropriate significance test for the difference between two answer distributions.
    Used throughout Section 4; distributions are not shown to be normal or equal variance.

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Cite this review

Pith. "Pith review of Anchoring Bias in Large Language Models: An Experimental Study." pith.science (2026). https://pith.science/paper/XI2U5GOU

@misc{pith2026241206593,
  author       = {Pith},
  title        = {Pith review of: Anchoring Bias in Large Language Models: An Experimental Study},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XI2U5GOU}},
  note         = {Machine review of arXiv:2412.06593}
}
read the original abstract

Large Language Models (LLMs) like GPT-4 and Gemini have significantly advanced artificial intelligence by enabling machines to generate and comprehend human-like text. Despite their impressive capabilities, LLMs are not immune to limitations, including various biases. While much research has explored demographic biases, the cognitive biases in LLMs have not been equally scrutinized. This study delves into anchoring bias, a cognitive bias where initial information disproportionately influences judgment. Utilizing an experimental dataset, we examine how anchoring bias manifests in LLMs and verify the effectiveness of various mitigation strategies. Our findings highlight the sensitivity of LLM responses to biased hints. At the same time, our experiments show that, to mitigate anchoring bias, one needs to collect hints from comprehensive angles to prevent the LLMs from being anchored to individual pieces of information, while simple algorithms such as Chain-of-Thought, Thoughts of Principles, Ignoring Anchor Hints, and Reflection are not sufficient.

Figures

Figures reproduced from arXiv: 2412.06593 by the authors.

Figure 1
Figure 1. Question Examples 4 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Standard deviations of answers from different mod [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Standard deviations of answers from different mod [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: T-test results of biased answers on fact hints [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: T-test results of biased answers on expert hints [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: T-test results of biased answers when H1 is irrelevant to the question p-values show that the corresponding differences are not statistically significant enough. It also shows that the answers from stronger models (i.e., GPT-4 and GPT-4o) are more consistently influenc…
Figure 7
Figure 7. Figure 7: T-test results of biased answers under different m [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: T-test results of biased answers under different m [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: The average answer values obtained from GPT-4 from [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

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Reviewed August 11, 2026 · model on record in the stance chip above.