Anchoring Bias Sensitivity Score (ABSS)

• ABSS is a quantitative metric that defines and measures anchoring bias by comparing baseline responses with those under anchored conditions.
• It employs statistical methods such as regression slopes, normalized bias calculations, and attributional frameworks to aggregate deviations into a single score.
• Applications include human behavioral experiments, log-based user analyses, and large language model evaluations, enabling robust cross-domain comparisons and bias mitigation.

The Anchoring Bias Sensitivity Score (ABSS) is a quantitative metric designed to assess the degree to which an individual, agent, or model exhibits susceptibility to anchoring bias—the cognitive tendency to over-rely on initial cues or “anchors” when making judgments. ABSS has been operationalized across human behavioral experiments, log-based user-action analyses, and LLM evaluations, employing rigorous statistical, probabilistic, and attributional frameworks. It unifies previously fragmented methodologies into a scalar index, permitting robust comparison, risk assessment, and mitigation of anchoring bias across different domains.

1. Cognitive and Methodological Foundations

Anchoring bias is characterized as a systematic and predictable deviation from a normative reference (PN1), with deviation patterns that must persistently recur, rather than arise by chance (PN2) (Sinha et al., 2022, Yasseri et al., 2019). In quantifying bias sensitivity, ABSS formalizes (a) the detection of systematic deviations in behavioral responses or model outputs as a function of exogenous anchor values and (b) the consolidation of these deviations into a single per-entity metric following established principles from cognitive psychology and behavioral economics.

For human-centric settings, baseline responses are empirically determined from unanchored (control) groups, anchors are introduced under randomized controlled protocols, and the magnitude of bias is calculated relative to individual or population-level shifts in predictions (Yasseri et al., 2019). In log-based or model-centric contexts, the “norm” is inferred from aggregate behavior or model outputs absent anchors, and deviation patterns are quantified via statistical modeling, differentiating true susceptibility from spurious fluctuations (Sinha et al., 2022, Valencia-Clavijo, 7 Nov 2025).

2. Mathematical Formalizations and Core Components

The ABSS is constructed from domain-specific definitions, always adhering to the principle that it must (i) be responsive to systematic shifts induced by anchors and (ii) lie on a normalized or bounded scale.

In human behavioral tasks, two standard operationalizations are prominent (Yasseri et al., 2019):

• Regression Slope: For user $i$, ABSS is the slope $\beta_{i,1}$ in $$P_{ij} = \beta_{i,0} + \beta_{i,1}A_{ij} + \varepsilon_{ij}$$, expressing the linear response of predictions $P_{ij}$ to anchor values $A_{ij}$. $\mathrm{ABSS}_i = \beta_{i,1}$.
• Normalized Bias: Relative displacement toward the anchor, $\alpha_{ij} = (P_{ij}-M_j^0)/(A_{ij}-M_j^0)$, aggregated as $$\mathrm{ABSS}_i = \operatorname{median}_j \alpha_{ij}$$.

For user logs and clickstreams, the deviation vector $\delta_{k,i}$ of individual attention weights from a learned norm is modeled across prediction windows, with linear fitting $$\delta_{k,i} = \beta_{k,1}\,i + \beta_{k,2}\,w + \varepsilon_{k,i}$$. The score is $\mathrm{ABSS}_k = -\beta_{k,1}$, where $i$ is visit position and $w$ indexes windows. Significance is established via statistical testing on $\beta_{k,1}$ (Sinha et al., 2022).

In LLMs, ABSS is typically the aggregation of multiple submetrics—measuring behavioral distributional shifts (e.g., in log-probabilities of outputs), attributional contributions (e.g., via Shapley values assigned to anchor fields), and their robustness (Valencia-Clavijo, 7 Nov 2025, Huang et al., 21 May 2025). For price negotiation, ABSS averages normalized objective susceptibility (utility drop) and subjective satisfaction change, both mapped to 0,1. In generalized LLM scoring:

• Behavioral: $S_B$ rescales the expected value shift ($\Delta \mathrm{EV}$) in output distributions, using e.g., a softmax-weighted mean.
• Attributional: $S_A$ is the sign and scaled magnitude of Shapley-value shifts associated with anchors in prompt fields.
• Statistical weighting: $w(p)$ functions reweight contributions by significance; additional robustness and concordance terms modulate the final score.
• Combined ABSS: For prompt variation $v$, $$\mathrm{ABSS}_v = \rho[S_B\,w(p_\mathrm{log}) + S_A\,w(p_\mathrm{shap})] + \lambda_{\mathrm{conc}}c$$ (Valencia-Clavijo, 7 Nov 2025).

3. Representative Empirical Frameworks

Human Behavioral and Decision Tasks

Large-scale studies administer anchoring experiments with random anchor assignment, control conditions, and population stratification. ABSS is computed as either the individual's anchor-response regression slope or as the median shift normalized to the anchor–control gap (Yasseri et al., 2019). Across 62 real-world forecasting questions, the mean anchoring index $\mathrm{AI}_j$ is approximately 0.61, and population-level regression yields $\beta_1 \approx 0.6$, with negligible modulation by engagement, prior accuracy, or gender.

User Log Analytics

Using Hierarchical Attention Networks (HANs), attention weights over user actions in visits to analytic UIs are interpreted as reflecting information reliance. Personalized models yield per-user deviations from the common attention norm; ABSS is derived from the slope of deviation with respect to visit position, after significance testing. Approximately 79% of users show statistically significant anchoring patterns ($\mathrm{ABSS}_k > 0$) (Sinha et al., 2022).

LLMs

LLM-centric ABSS frameworks (Valencia-Clavijo, 7 Nov 2025, Huang et al., 21 May 2025) distinguish:

• Log-probability distributional shifts between high-anchor and low-anchor prompts, captured in paired differences and softmax-based "expected value" metrics.
• Shapley-value attribution quantifying anchor contribution to answer log-probs across marginal prompt subsets.
• Aggregation over controlled prompt families and anchor pairs, with strict statistical controls and robustness metrics.
• Example ABSS values: high for Gemma-2B (~6.8) and Phi-2 (~6.2), intermediate for GPT-2 (~2.1), and negative for GPT-Neo-125M (~–0.9) (Valencia-Clavijo, 7 Nov 2025). In semantic/numeric priming tasks, ABSS via averaged A-Index and R-Error ranges from ~60% (small models) to ~22% (reasoning-tuned models) (Huang et al., 21 May 2025).

Multi-metric Negotiation Simulations

In LLM-driven price negotiation, ABSS synthesizes:

• Objective susceptibility: the difference in buyer utility between baseline and anchor conditions.
• Subjective susceptibility: mean drop in satisfaction across outcome, self, process, and relationship dimensions, scaled to [0,1].
• Joint ABSS: weighted mean of normalized objective and subjective susceptibilities (Takenami et al., 28 Aug 2025).

Context	ABSS Core Formula	Typical Range/Interpretation
Human forecasts	Regression slope ($\beta_{i,1}$), normalized bias	0: anchor-immune, 1: fully anchored
User logs (HAN)	$\mathrm{ABSS}_k = -\beta_{k,1}$	>0: anchoring, 0: neutral, <0: recency
LLMs (joint metrics)	See above (behavioral + attribution)	~–1 … 7 absolute or [0,1] normalized
Negotiation (multi)	Mean of normalized utility and satisfaction drops	0: robust, 1: maximally susceptible

4. Statistical Foundations, Controls, and Thresholds

Computation of ABSS requires rigorous statistical safeguards:

• Significance of response shifts is assessed via t-tests, Wilcoxon signed-rank, and sign-flip permutation tests, with weights reflecting confidence (Valencia-Clavijo, 7 Nov 2025, Yasseri et al., 2019).
• For per-user or per-model ABSS, only statistically significant effects are reported; otherwise, scores are set to zero or flagged as inconclusive (Sinha et al., 2022).
• All normalization steps—removal of outliers (e.g., median ± 2.5 MAD), adjustment to baseline medians, field-based prompt enumeration—are strictly defined to prevent scale artifacts or spurious detection.

Robustness across window sizes, anchor ranges, and prompt templates is empirically validated: HAN-based user log ABSS produces concordance 0.79–0.94 across window sizes; LLM ABSS is resilient under moderate anchor variation but can show attributional fragility when prompt design changes (Sinha et al., 2022, Valencia-Clavijo, 7 Nov 2025).

5. Empirical Findings and Model Comparisons

Human experimental ABSS consistently shows strong and pervasive anchoring effects, largely invariant to external covariates (e.g., engagement, gender, prior performance) (Yasseri et al., 2019).

HAN methods reveal that conventional frequency-based metrics are underpowered (~70% inconclusive), while attention-based ABSS yields high detection rates of anchoring or recency in real interaction logs (Sinha et al., 2022).

In LLM benchmarking, model scale and training regime correlate with ABSS magnitude and coherence. Larger models (Gemma-2B, Phi-2, Llama-2-7B) manifest highly positive ABSS scores, indicating robust, attributionally coherent anchoring effects; smaller models display mixed behavioral/attributional alignment or even negative ABSS. Reasoning-tuned LLMs and explicit "anti–dual-process" prompts can reduce—though not eliminate—ABSS (Valencia-Clavijo, 7 Nov 2025, Huang et al., 21 May 2025).

In negotiation simulations, both objective (utility) and subjective (satisfaction) ABSS components are significant under anchoring interventions. Reasoning models show reduced ABSS, and individual-level susceptibility is uncorrelated with Big Five personality dimensions (Takenami et al., 28 Aug 2025).

6. Domain-Specific Construction and Interpretation

ABSS construction is adapted to domain requirements:

• Human studies: Baseline responses are directly measured. ABSS reflects either direct regression-derived anchor sensitivity or normalized median bias.
• User-action logs: ABSS is based on deviation slopes of personalized attention weights against a global norm, providing individualized detection (Sinha et al., 2022).
• LLMs: ABSS merges behavioral log-prob shifts and attributional causality from anchor tokens, with statistical weighting and concordance checks. In some cases, semantic and numerical priming submetrics are averaged (Valencia-Clavijo, 7 Nov 2025, Huang et al., 21 May 2025).
• Multi-metric (negotiation): ABSS is the (possibly weighted) mean of normalized objective and subjective drops under anchoring, extending beyond accuracy to experiential impact (Takenami et al., 28 Aug 2025).

ABSS values are bounded (e.g., [0,1] or defined by regression limits), fully interpretable, and permit robust cross-system or cross-individual comparison.

7. Limitations, Extensions, and Future Directions

The ABSS construct is bounded by several analytical and practical constraints:

• Inference of “norms” is only as strong as the baseline or control data employed; poor controls can miscalibrate sensitivity.
• Noise and small samples particularly affect per-individual or per-user ABSS—regularization or mixed-effects modeling is necessary for stability in sparse contexts (Yasseri et al., 2019).
• Attributional coherence in LLMs may break down under prompt variations or differing anchor regimes, cautioning against simplistic model-to-human analogies (Valencia-Clavijo, 7 Nov 2025).
• Current ABSS methodologies are limited to tasks with well-defined anchors and quantifiable outputs; generalizing to free-form domains remains challenging.
• No direct neuron-level mechanistic analysis accompanies most reported LLM ABSS; all conclusions are at the distributional or attribution level.
• Despite partial mitigation via "reasoning" prompts or model architecture, anchoring bias is never completely eliminated in either humans or LLMs (Huang et al., 21 May 2025, Takenami et al., 28 Aug 2025).

Future research targets include applying ABSS to other cognitive biases (framing, availability), integrating log-prob attributions with circuit-level interpretability, and building comprehensive cognitive-bias atlases for both human and machine reasoning (Valencia-Clavijo, 7 Nov 2025, Huang et al., 21 May 2025).