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First-Mover Bias in Gradient Boosting Explanations: Mechanism, Detection, and Resolution

Drake Caraker, Bryan Arnold, David Rhoads

Year: 2026Venue: arXiv preprintArea: cs.LGType: PreprintEmbeddings: 79

Intelligence

Status: succeeded | Model: google/gemini-3.1-flash-lite-preview | Prompt: intel-v1 | Confidence: 98%

Last extracted: 3/26/2026, 1:31:27 AM

Summary

The paper identifies 'first-mover bias' as a mechanistic cause of SHAP instability in gradient-boosted trees under multicollinearity, where sequential residual fitting creates path-dependent feature importance. The authors propose DASH (Diversified Aggregation of SHAP), a pipeline that uses model independence and diversity-aware selection to restore attribution stability, alongside diagnostic tools like the Feature Stability Index (FSI) and Importance-Stability (IS) Plot.

Entities (6)

DASH · method · 99%First-mover bias · phenomenon · 99%Gradient Boosting · algorithm · 99%SHAP · algorithm · 99%Feature Stability Index · diagnostic-tool · 98%Importance-Stability Plot · diagnostic-tool · 98%

Relation Signals (3)

DASH → provides → Feature Stability Index

confidence 99% · DASH additionally provides two diagnostic tools -- the Feature Stability Index (FSI) and Importance-Stability (IS) Plot

Gradient Boosting → causes → First-mover bias

confidence 97% · a path-dependent concentration of feature importance caused by sequential residual fitting in gradient boosting

DASH → resolves → First-mover bias

confidence 95% · DASH (Diversified Aggregation of SHAP) and simple seed-averaging (Stochastic Retrain) restore stability by breaking the sequential dependency chain

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Abstract

Abstract:We isolate and empirically characterize first-mover bias -- a path-dependent concentration of feature importance caused by sequential residual fitting in gradient boosting -- as a specific mechanistic cause of the well-known instability of SHAP-based feature rankings under multicollinearity. When correlated features compete for early splits, gradient boosting creates a self-reinforcing advantage for whichever feature is selected first: subsequent trees inherit modified residuals that favor the incumbent, concentrating SHAP importance on an arbitrary feature rather than distributing it across the correlated group. Scaling up a single model amplifies this effect -- a Large Single Model with the same total tree count as our method produces the worst explanations of any approach tested. We demonstrate that model independence is sufficient to resolve first-mover bias in the linear regime, and remains the most effective mitigation under nonlinear data-generating processes. Both our proposed method, DASH (Diversified Aggregation of SHAP), and simple seed-averaging (Stochastic Retrain) restore stability by breaking the sequential dependency chain, confirming that the operative mechanism is independence between explained models. At rho=0.9, both achieve stability=0.977, while the single-best workflow degrades to 0.958 and the Large Single Model to 0.938. On the Breast Cancer dataset, DASH improves stability from 0.32 to 0.93 (+0.61) against a tree-count-matched baseline. DASH additionally provides two diagnostic tools -- the Feature Stability Index (FSI) and Importance-Stability (IS) Plot -- that detect first-mover bias without ground truth, enabling practitioners to audit explanation reliability before acting on feature rankings. Software and reproducible benchmarks are available at this https URL.

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First-Mover Bias in Gradient Boosting Explanations: Mechanism, Detection, and Resolution Drake Caraker Bryan Arnold David Rhoads Independent Researchers puremath86@gmail.com (Arnold) drhoads9@gmail.com (Rhoads) Corresponding author: drakecaraker@gmail.com; ORCID: 0009-0009-5639-7899ORCID: 0009-0007-8589-8989ORCID: 0009-0005-3015-5948 (March 2026) Abstract We investigate a specific form of explanation instability that we term first-mover bias—a path-dependent concentration of feature importance associated with sequential residual fitting in gradient boosting—as a mechanistic contributor to the well-known instability of SHAP-based feature rankings under multicollinearity. When correlated features compete for early splits, gradient boosting creates a self-reinforcing advantage for whichever feature is selected first: subsequent trees inherit modified residuals that favor the incumbent, concentrating SHAP importance on an arbitrary feature rather than distributing it across the correlated group. Scaling up a single model amplifies this effect—a Large Single Model with the same total tree count as our method produces the poorest attribution reproducibility of any approach tested. We provide evidence that model independence is sufficient to largely neutralize first-mover bias in the linear, high-collinearity regime we study, and that it remains the most effective mitigation under nonlinear data-generating processes. Both our proposed method, DASH (Diversified Aggregation of SHAP), and simple seed-averaging (Stochastic Retrain) restore stability by breaking the sequential dependency chain, supporting the view that the operative mechanism is independence between explained models, not any particular aggregation strategy. At ρ=0.9ρ=0.9, both methods achieve stability =0.977=0.977, while the standard single-best workflow degrades to 0.9580.958 and the Large Single Model to 0.9380.938. On the Breast Cancer dataset, DASH improves stability from 0.320.32 to 0.930.93 (+0.61+0.61) over the training-budget-matched Single Best (M=200M=200). DASH additionally provides two novel diagnostic tools—the Feature Stability Index (FSI) and Importance-Stability (IS) Plot—that detect first-mover bias without ground truth and can be applied independently of the full DASH pipeline, enabling practitioners to audit explanation reliability before acting on feature rankings. Software and reproducible benchmarks are available at https://github.com/DrakeCaraker/dash-shap. Keywords: first-mover bias, SHAP, feature importance, multicollinearity, model independence, gradient boosting, explainability, Rashomon effect 1 Introduction The standard workflow for explaining gradient-boosted tree predictions is deceptively simple: train a model, compute SHAP values, report the feature importance ranking. This ranking drives consequential decisions across science, industry, and regulation—it selects features for production pipelines, generates hypotheses in biomedical research, and satisfies regulatory auditors reviewing algorithmic systems. The workflow is ubiquitous, but under correlated predictors its resulting feature rankings may be substantially less reliable than their routine use suggests. When features are correlated, SHAP-based importance rankings can become unstable. At each split, a gradient-boosted tree must choose one feature from a correlated set. Since correlated features carry nearly identical predictive signal, the choice is governed by marginal numerical differences—effectively arbitrary. The model’s predictions are robust to this choice, but the SHAP values are not: changing the random seed, the learning rate, or the tree depth can swap the positions of correlated features in the importance ranking without meaningfully altering predictive accuracy. This is a manifestation of the Rashomon effect (Breiman, 2001) applied to explanations rather than predictions. The problem is pervasive because multicollinearity is pervasive. In clinical datasets, radius, perimeter, and area measure the same underlying tumor geometry. In materials science, atomic-level properties of constituent elements are correlated by construction. In economics and social science, income, education, and occupation form tightly coupled clusters. Any dataset where features were not specifically decorrelated before modeling is susceptible. Why bigger models make it worse. The intuitive response to unstable explanations is to train a more powerful model. Our results suggest that this can be counterproductive. A single large XGBoost model with thousands of trees and the same total tree count as DASH (M×∼75≈15,000M× 75≈ 15,000 trees, where ∼75 75 is the average number of trees per population model after early stopping) produces the poorest attribution reproducibility among all methods tested. We hypothesize, and our experiments support, that the primary mechanism is sequential residual dependency: in gradient boosting, each tree fits the residuals of all previous trees. If tree 1 selects feature A from a correlated pair (A,B)(A,B), it partially removes A’s signal from the residuals. Subsequent trees find both A and B less useful, but A slightly more so because the residual structure favors the feature that was partially captured. Over thousands of iterations, this creates a “first-mover advantage” that concentrates importance on whichever feature happened to be selected first—an artifact of optimization path dependence, not a property of the data. We use the term first-mover bias to denote this specific path-dependent concentration effect in sequential boosting; our claim is not that this is the only source of SHAP instability, but that it is an important and previously under-emphasized contributor in gradient-boosted trees under correlation. We note that with low colsample_bytree (0.1–0.5 in our population), correlated features A and B are not always present in the same column sample, so the first-mover advantage is probabilistic rather than deterministic: over many trees, whichever feature accumulates slightly more early selections gains a cumulative residual advantage that is attenuated—but not eliminated—by column subsampling. Our contribution. We propose DASH (Diversified Aggregation of SHAP), a five-stage pipeline that produces stable and reproducible feature importance explanations. DASH is not intended to outperform tuned single models on prediction; its objective is reproducible attribution under multicollinearity while maintaining competitive predictive performance. A substantial portion of explanation instability appears to arise from individual models’ optimization paths rather than solely from the data distribution itself: training enough diverse models and averaging their SHAP values causes path-dependent arbitrary choices to cancel, producing a more reproducible importance ranking. Specifically, DASH: 1. Trains a population (M=200M=200) of XGBoost models with randomly sampled hyperparameters, including deliberately low colsample_bytree (0.1–0.5) to force feature diversity. 2. Filters for predictive quality, retaining only models within ε of the best validation score. 3. Selects a diverse subset (K≤30K≤ 30) via greedy max-min dissimilarity on feature utilization vectors. 4. Computes interventional TreeSHAP for each selected model and averages the SHAP matrices element-wise. 5. Provides diagnostic tools (Feature Stability Index, IS Plot, local disagreement maps) for auditing explanation reliability. We make four contributions: • Mechanistic framing. Feature selection bias in ensemble methods is well known (Strobl et al., 2007; Hooker and Mentch, 2019); we articulate first-mover bias as a specific path-dependent concentration effect arising from sequential residual dependency in gradient boosting, and provide evidence that it concentrates SHAP-based feature attributions on arbitrary features under collinearity. • Principle. We provide evidence that model independence is sufficient to largely neutralize first-mover bias in the linear, high-collinearity regime we study, and that it remains the most effective mitigation under nonlinear data-generating processes. Both DASH (deliberate diversity) and Stochastic Retrain (seed diversity) restore stability to the same level, consistent with the view that the operative mechanism is independence rather than any particular aggregation strategy. • Diagnostics. The Feature Stability Index (FSI) and Importance-Stability (IS) Plot detect first-mover bias without access to ground truth, enabling practitioners to audit explanation reliability. • Method. DASH (Diversified Aggregation of SHAP) is an engineered pipeline that operationalizes the independence principle with forced feature restriction, diversity-aware model selection, and integrated diagnostics. • Infrastructure. The fit_from_attributions() interface decouples the DASH aggregation stage from XGBoost, making the pipeline applicable to any attribution method (LIME, Integrated Gradients, neural network SHAP) that produces feature-level attribution vectors. This positions DASH as a general-purpose stability layer for model explanation rather than an XGBoost-specific tool. On synthetic data, our “accuracy” metric evaluates agreement with a predefined equitable decomposition within correlated groups; it should be interpreted as agreement with a chosen attribution target rather than as direct recovery of uniquely identifiable ground truth (Section 5). 2 Related Work SHAP and model explanations. SHAP values (Lundberg and Lee, 2017) provide a theoretically grounded decomposition of predictions into feature contributions, drawing on the Shapley value framework from cooperative game theory (Shapley, 1953). TreeSHAP (Lundberg et al., 2020) enables efficient exact computation for tree-based models. While SHAP satisfies desirable axiomatic properties (local accuracy, missingness, consistency), these guarantees are conditioned on a fixed model. When the model changes— even slightly—the SHAP values can change substantially. Instability of feature importance. The instability of SHAP values under model perturbation has been noted by several authors. Fisher et al. (2019) formalize the Rashomon set—the collection of models with near-optimal performance—and show that variable importance can vary widely across this set. Dong and Rudin (2020) visualize the “cloud” of variable importance across Rashomon-set models, demonstrating that importance rankings are inherently ambiguous when many near-optimal models exist. Semenova et al. (2022) further characterize the Rashomon set’s structure and its implications for model selection. Marx et al. (2023) demonstrate that SHAP-based feature attributions are sensitive to reference distribution choices. Covert et al. (2021) provide a unified framework connecting removal-based explanations (including SHAP) and discuss stability considerations across methods. The problem is especially acute for correlated features, where SHAP must distribute credit among features that carry overlapping information (Kumar et al., 2020; Chen et al., 2020). Ensemble explanations. Paillard et al. (2025) address a distinct consistency problem: given a single already-fitted ensemble model, they argue for computing one SHAP attribution over the full ensemble rather than averaging per-tree attributions, for internal consistency within that model. Their setting does not address cross-fit reproducibility—whether retraining the model on the same data yields the same attributions. Our results show that this cross-fit instability (our focus) is not resolved by the single-ensemble approach: the single-ensemble baseline (“Ensemble SHAP”) does not improve stability over Single Best, and the Large Single Model, which maximizes sequential tree dependency, produces the worst stability of any method tested. Stable explanations. Alvarez-Melis and Jaakkola (2018) propose metrics for explanation stability. Krishna et al. (2022) study disagreement among different explanation methods applied to the same model. Our work addresses a different source of disagreement: the same explanation method (SHAP) applied to different-but-equally-valid models. Explanation reliability and aggregation. Molnar et al. (2022) provide a general framework for model-agnostic feature importance that connects permutation-based and SHAP-based approaches, noting that instability under feature dependence is a shared concern across methods. Slack et al. (2020) demonstrate that SHAP explanations can be sensitive to adversarial perturbations of the classifier, raising broader concerns about explanation reliability beyond the multicollinearity setting we address. Feature selection under multicollinearity. Classical approaches to multicollinearity include variance inflation factors (O’Brien, 2007), principal component regression, and elastic net regularization (Zou and Hastie, 2005). Stability selection (Meinshausen and Bühlmann, 2010) addresses a related problem by subsampling data and tracking which features are consistently selected across subsamples. Permutation importance (Altmann et al., 2010) offers an alternative to SHAP with different stability properties. Causal Shapley values (Heskes et al., 2020) provide principled handling of correlated features through causal structure. These methods operate at the model-fitting or feature-selection stage. DASH operates at the explanation stage, preserving the original feature space while stabilizing the attributions. 3 Problem Formulation 3.1 Setup Let ∈ℝN×PX ^N× P be a dataset of N observations and P features, with target ∈ℝNy ^N. Let fθf_θ denote a gradient-boosted tree model trained with hyperparameters θ. Let ϕj(i)(fθ) _j^(i)(f_θ) denote the SHAP value of feature j for observation i under model fθf_θ. The global feature importance vector is I¯j(fθ)=1N′∑i=1N′|ϕj(i)(fθ)|, I_j(f_θ)= 1N _i=1^N | _j^(i)(f_θ)|, (1) where N′N is the number of reference observations. 3.2 The instability problem Consider two models fθ1f_ _1 and fθ2f_ _2, both trained on the same data with different hyperparameters θ1≠θ2 _1≠ _2, such that their predictive performance is comparable: |RMSE(fθ1)−RMSE(fθ2)|<ε|RMSE(f_ _1)-RMSE(f_ _2)|< . Despite this, the importance rankings rank(I¯(fθ1))rank( I(f_ _1)) and rank(I¯(fθ2))rank( I(f_ _2)) can differ substantially when features are correlated. Formally, let =G1,…,GLG=\G_1,…,G_L\ be a partition of 1,…,P\1,…,P\ into groups of correlated features, where features within group GlG_l have pairwise correlation ≥ρ≥ρ. A single model fθf_θ produces importance I¯j I_j that is concentrated on an arbitrary subset of each group—typically the feature(s) selected at early splits. This concentration is unstable: different θ values produce different concentrations within the same group. 3.3 Sequential residual dependency In gradient boosting, model f is constructed as f=∑t=1Thtf= _t=1^Th_t, where tree hth_t is fit to the residuals rt=y−∑s<ths(x)r_t=y- _s<th_s(x). If tree h1h_1 splits on feature j∈Glj∈ G_l, it partially removes j’s signal from r2r_2. Since feature k∈Glk∈ G_l (k≠jk≠ j) carries overlapping signal, k’s marginal gain for r2r_2 is also reduced—but j retains a slight residual advantage from its own partial fit. Over T iterations, this creates a path-dependent concentration of splits on the first-selected feature within each correlated group. We use the term sequential residual dependency to describe this mechanism, which is related to the well-known feature selection bias in boosted ensembles but specifically concerns its effect on post-hoc feature attributions. Empirical hypothesis. We hypothesize that for a gradient-boosted model f=∑t=1Thtf= _t=1^Th_t with T trees, if features j,kj,k belong to a correlated group with pairwise correlation ρ→1ρ→ 1 and tree h1h_1 splits on feature j, then [|ϕj(f)|]>[|ϕk(f)|]E[| _j(f)|]>E[| _k(f)|] under TreeSHAP, with the gap increasing in T. The expectation is over the randomness in data sampling and split selection. We test the T-dependence indirectly in Section 6.1 via the Large Single Model comparison: the LSM uses ∼15,000 15,000 sequential trees and produces the poorest reproducibility of any method, consistent with the prediction that more sequential iterations amplify first-mover concentration. A direct isolation experiment varying T while holding other factors constant is available in the code repository and shows monotonically increasing concentration with tree count. 3.4 Desiderata A good feature importance method under multicollinearity should satisfy: 1. Stability: Repeated runs with different random seeds or hyperparameters should produce consistent rankings. 2. Accuracy: The ranking should correlate with the true data-generating process when ground truth is available. 3. Equity: Correlated features contributing equally to the target should receive similar importance. (We use “equity” throughout to mean balanced credit allocation within correlated feature groups, distinct from its use in algorithmic fairness literature.) 4. Safety: The method should not degrade explanations or predictions when features are uncorrelated. 4 Method: DASH DASH is a five-stage pipeline (Figure 1): PopulationGenerationPerformanceFilteringDiversitySelectionConsensusSHAPStabilityDiagnosticsM=200M=200 modelsε -thresholdMaxMin, K≤30K≤30InterventionalTreeSHAPFSI, IS Plot Figure 1: The DASH five-stage pipeline. Models are trained independently (Stage 1), filtered for quality (Stage 2), selected for diversity (Stage 3), explained via TreeSHAP and averaged (Stage 4), and audited for stability (Stage 5). 4.1 Stage 1: Population Generation We train M XGBoost (Chen and Guestrin, 2016) models with hyperparameters randomly sampled from a search space Θ (Table 1). The critical parameter is colsample_bytree, sampled from 0.1,0.15,0.2,0.25,0.3,0.4,0.5\0.1,0.15,0.2,0.25,0.3,0.4,0.5\, which restricts each tree to a random subset of features. This forces different models to rely on different members of correlated groups. Each model is trained independently with early stopping, using a separate random seed to diversify initialization. Table 1: Hyperparameter search space for population generation. Parameter Values max_depth 3,4,5,6,8,10,12\3,4,5,6,8,10,12\ learning_rate 0.01,0.03,0.05,0.1,0.2,0.3\0.01,0.03,0.05,0.1,0.2,0.3\ colsample_bytree 0.1,0.15,0.2,0.25,0.3,0.4,0.5\0.1,0.15,0.2,0.25,0.3,0.4,0.5\ subsample 0.5,0.6,0.7,0.8,0.9,1.0\0.5,0.6,0.7,0.8,0.9,1.0\ reg_alpha 0,0.01,0.1,1.0,5.0,10.0\0,0.01,0.1,1.0,5.0,10.0\ reg_lambda 0,0.01,0.1,1.0,5.0,10.0\0,0.01,0.1,1.0,5.0,10.0\ min_child_weight 1,3,5,10,20\1,3,5,10,20\ 4.2 Stage 2: Performance Filtering We retain models whose validation score is within ε of the best. Two modes are supported: ℱabs=i:|si−s∗|≤ε,ℱrel=i:|si−s∗|≤ε⋅|s∗|,s∗=maxi⁡si,F_abs=\i:|s_i-s^*|≤ \, _rel=\i:|s_i-s^*|≤ ·|s^*|\, s^*= _is_i, (2) where sis_i is the negative RMSE (for regression) or AUC (for classification) of model i. This ensures that all explanations come from models that have learned meaningful signal. We use ε=0.08 =0.08 (absolute mode, ℱabsF_abs) for synthetic data and ε=0.05 =0.05 (relative mode, ℱrelF_rel, retaining models within 5% of the best score) for real-world datasets. 4.3 Stage 3: Diversity Selection From the filtered set ℱF, we select K≤KmaxK≤ K_ models to maximize feature utilization diversity. We compute a preliminary importance vector iv_i for each model i∈ℱi using XGBoost’s gain-based importance (faster than SHAP, sufficient for measuring feature utilization patterns). MaxMin selection (default). We use greedy max-min dissimilarity selection: 1. Initialize with the highest-performing model. 2. At each step, add the candidate c that maximizes mins∈⁡d(c,s) _s d(c,s), where d(c,s)=1−^c⋅^sd(c,s)=1- v_c· v_s and v denotes L2L_2-normalized importance vectors. 3. Stop when KmaxK_ is reached or the minimum distance falls below threshold δ. This ensures each selected model is maximally different from all previously selected models in its feature utilization pattern, without requiring knowledge of the feature correlation structure. Alternative: Deduplication selection. A simpler variant removes near-duplicate models (pairwise Spearman ρ>0.95ρ>0.95 on importance vectors), retaining the better-performing model from each pair. This provides a minimal-overhead diversity guarantee. We focus on MaxMin selection throughout this paper; deduplication results are available in the code repository. 4.4 Stage 4: Consensus SHAP We compute interventional TreeSHAP (Lundberg et al., 2020) for each selected model i∈i using a randomly sampled background dataset of size B=100B=100. In our experiments, SHAP values are computed on a held-out explain set XexplainX_explain, which is disjoint from the training set, the validation set used for performance filtering (Stage 2), and the test set used for RMSE evaluation. This four-way split (train/val/explain/test) prevents any overlap between the data used for model selection, explanation computation, and predictive evaluation. In particular, computing SHAP values on training data would inflate attributions for features the model has memorized, conflating overfitting with genuine importance. Φ(i)∈ℝN′×P,i∈. ^(i) ^N × P, i . (3) The consensus SHAP matrix is the element-wise average: Φ¯=1||∑i∈Φ(i). = 1|S| _i ^(i). (4) Because each model i was trained independently, its arbitrary feature selections within correlated groups are independent across models. Averaging causes these arbitrary choices to cancel, distributing importance proportionally across the group. 4.5 Stage 5: Stability Diagnostics We introduce two diagnostic tools that quantify explanation reliability without requiring ground-truth importance: Feature Stability Index (FSI). For each feature j: FSIj=σ¯jI¯j+ϵ0,FSI_j= σ_j I_j+ _0, (5) where σ¯j=1N′∑istdk[ϕj(i)(fk)] σ_j= 1N _istd_k[ _j^(i)(f_k)] is the mean (across observations) of the standard deviation (across models) of SHAP values, I¯j I_j is the consensus global importance (Eq. 1), and ϵ0=10−8 _0=10^-8 is a smoothing constant to avoid division by zero. High FSI indicates that a feature’s SHAP values vary substantially across models relative to its importance— a signature of explanation instability, typically caused by collinearity. Importance-Stability (IS) Plot. A scatter plot of (I¯j,FSIj)( I_j,FSI_j) for each feature j, partitioned into four quadrants by median thresholds: • Quadrant I (high importance, low FSI): Robust drivers—features that are genuinely important and whose importance is stable across models. • Quadrant I (high importance, high FSI): Collinear cluster members—features that are important but whose specific attribution is unstable, indicating collinearity. • Quadrant I (low importance, low FSI): Confirmed unimportant—features that all models agree are unimportant. • Quadrant IV (low importance, high FSI): Fragile interactions—features with small but unreliable attributions. The IS Plot functions as an unsupervised collinearity detector: features in Quadrant I are likely members of correlated groups, even without computing the correlation matrix directly. 5 Experimental Design 5.1 Synthetic data We generate data with N=5,000N=5,000 observations and P=50P=50 features arranged in 10 groups of 5, with within-group correlation ρ. Data is split 4-way: 56% train, 16% validation (for performance filtering), 8% explain (SHAP background), 20% test (RMSE evaluation). The target follows a linear data-generating process (DGP): y=∑g=110βg⋅z¯g+ϵ,ϵ∼(0,0.52),y= _g=1^10 _g· z_g+ε, ε (0,0.5^2), (6) where z¯g z_g is the mean of features in group g and βg∈2.0,1.5,1.0,0.8,0.6,0.4,0.3,0.2,0.1,0.0 _g∈\2.0,1.5,1.0,0.8,0.6,0.4,0.3,0.2,0.1,0.0\. By construction, the true importance of each feature within group g is defined as |βg|/5| _g|/5 (uniform within group). Caveat on ground-truth definition. This uniform definition presupposes equitable credit distribution within correlated groups—precisely the property DASH is designed to achieve. Alternative decompositions are valid: a single model that correctly uses feature A (not B) from a correlated pair has a legitimate attribution where A is important and B is not. Our accuracy metric therefore measures agreement with the equitable decomposition, not “correctness” in an absolute sense. The accuracy advantage of DASH should be interpreted as a consequence of its equity properties rather than independent evidence of superiority. Similarly, DASH’s equity advantage is partially a design property: forced colsample_bytree restriction distributes feature usage across correlated groups by construction, so the equity results should be understood as showing that the pipeline achieves its design intent rather than as independent empirical findings. For the nonlinear DGP, the target includes quadratic terms, interactions, and a sinusoidal component: y=β1z12+β2z1z2+β3sin⁡(πz3)+∑g=410βgzg+ϵ.y= _1z_1^2+ _2z_1z_2+ _3 (π z_3)+ _g=4^10 _gz_g+ε. (7) We sweep ρ∈0.0,0.5,0.7,0.9,0.95ρ∈\0.0,0.5,0.7,0.9,0.95\ with Nreps=20N_reps=20 repetitions at each level, regenerating data (same coefficients, new random draws) for each repetition. 5.2 Real-world datasets Breast Cancer Wisconsin. 30 features derived from digitized images of fine-needle aspirates. Heavy natural collinearity: 21 feature pairs have |r|>0.9|r|>0.9 (radius ≈ perimeter ≈ area). Binary classification task. Superconductor. 81 features describing physical and chemical properties of 21,263 superconducting materials. Regression task predicting critical temperature. We use ε=0.05 =0.05 in relative mode (retaining models within 5% of the best validation score). California Housing. 8 features describing housing characteristics of 20,640 California census blocks. Regression task predicting median house value. Moderate collinearity: several feature pairs with |r|>0.7|r|>0.7 (e.g., rooms and bedrooms, latitude and longitude). We use relative ε=0.05 =0.05 for scale-appropriate filtering. Repetition procedure. For synthetic data, each of the 20 repetitions regenerates the dataset (same coefficients, new random draws) and retrains all models, capturing both data-sampling and model-selection variance. For real-world datasets, each repetition retrains all models with different random seeds on the same fixed data split, isolating model-selection variance from data-sampling variance. This distinction means that real-world stability estimates reflect only the instability due to arbitrary model choices, not data variability. 5.3 Methods compared We compare 9 methods (Table 2): Table 2: Methods compared in the benchmark. All use XGBoost as the base learner. Method Description Dependent Single Best Best of 30 hyperparameter-tuned models (standard practice) Single Best (M) Best of M=200M=200 models (training-budget-matched to DASH) Large Single Model One XGBoost with ∼ 15K trees, low colsample_bytree LSM (Tuned) Grid search over max_depth, learning_rate Ensemble SHAP Single 2000-tree ensemble (colsample_bytree=0.8) Independent Stochastic Retrain K models, different seeds, single fixed hyperparameter config (best of 100 random draws from the same grid as DASH) Random Selection DASH population + filtering, random K selection Naive Top-N Top K models by score, no diversity selection DASH (MaxMin) Full pipeline with MaxMin diversity selection 5.4 Evaluation metrics Stability. Mean pairwise Spearman correlation across Nreps=20N_reps=20 repeated runs of each method: Stability=2R(R−1)∑r<r′ρS(I¯(r),I¯(r′)).Stability= 2R(R-1) _r<r _S ( I^(r), I^(r ) ). (8) Accuracy. Spearman correlation between estimated global importance and ground truth (available for synthetic data only): Accuracy=ρS(I¯,Itrue)Accuracy= _S( I,I^true). Within-group equity. Mean coefficient of variation within correlated feature groups: Equity=1L′∑l:|μl|>0SD(I¯Gl)|μl|,Equity= 1L _l:| _l|>0 SD( I_G_l)| _l|, (9) where μl=mean(I¯Gl) _l=mean( I_G_l) and groups with near-zero mean are excluded.111We exclude groups whose mean importance |μl|<10−6| _l|<10^-6, which in practice corresponds to groups with βg=0 _g=0 in the synthetic DGP. The threshold is set conservatively to avoid division-by-zero artifacts without discarding any group that receives non-trivial importance. Predictive performance. Test RMSE, to verify that DASH does not sacrifice prediction quality for explanation quality. 5.5 Statistical tests Pairwise comparisons use Wilcoxon signed-rank tests with Holm–Bonferroni step-down correction. Effect sizes are reported as Cohen’s d. 5.6 Pipeline configuration All experiments use: M=200M=200 population, Kmax=30K_ =30, ε=0.08 =0.08 (synthetic), δ=0.05δ=0.05 (diversity threshold), τ=0.3τ=0.3 (cluster threshold), background size B=100B=100. 6 Results 6.1 The mechanism: evidence for first-mover bias The central question is whether sequential residual dependency causes the instability described in Section 3. We test this with a controlled comparison: DASH and the Large Single Model (LSM) both use the same low colsample_bytree (0.1–0.5) and the same total tree count—though wall-clock time and model architecture differ substantially (Table 9): “tree-count-matched” refers here to the total number of trees (DASH vs. LSM), not wall-clock time or FLOPs. Separately, Single Best (M) is “training-budget-matched” in the sense that it trains the same number of models as DASH. The comparison isolates the sequential vs. independent distinction rather than claiming cost parity. The primary design contrast is that DASH’s models are trained independently, while LSM’s trees are trained sequentially on progressively modified residuals. Table 3 presents results for the four principal methods across ρ∈0.0,0.5,0.7,0.9,0.95ρ∈\0.0,0.5,0.7,0.9,0.95\ with 20 repetitions per level. The remaining five baselines (Ensemble SHAP, Single Best M=200M=200, LSM Tuned, Random Selection, Naive Top-N) are evaluated at ρ=0.9ρ=0.9 only (Table 4), as their primary purpose is to contextualize the mechanism at high correlation. The key finding is that LSM achieves the poorest stability of any method at every correlation level, despite matching DASH’s total tree count and feature restriction. This is consistent with the first-mover bias hypothesis: sequential residual dependency concentrates importance on arbitrary features, and the effect worsens with correlation severity (LSM stability degrades from 0.9530.953 at ρ=0ρ=0 to 0.9250.925 at ρ=0.95ρ=0.95). Meanwhile, DASH’s stability is effectively flat (0.9720.972–0.9770.977), demonstrating immunity to the mechanism it is designed to break. Table 3: The mechanism experiment: DASH vs. Single Best vs. Large Single Model across correlation levels (20 repetitions per ρ). Both DASH and LSM use the same low colsample_bytree; the critical contrast for our hypothesis is that DASH’s models are trained independently while LSM trains trees sequentially. Bold indicates best per metric per ρ level. The four principal methods are shown; all nine are compared at ρ=0.9ρ=0.9 in Table 4. ρ Method Stability (± ) DGP Agreement Equity (CV↓ ) RMSE 0.0 Single Best .973±.001.973±.001 .985 .168 .609 Large Single Model .953±.003.953±.003 .974 .170 .771 Stoch. Retrain .975±.001.975±.001 .987 .175 .581 DASH (MaxMin) .972±.002.972±.002 .985 .164 .596 0.5 Single Best .975±.002.975±.002 .987 .178 .617 Large Single Model .965±.002.965±.002 .981 .194 .767 Stoch. Retrain .980±.001.980±.001 .989 .173 .585 DASH (MaxMin) .977±.001.977±.001 .988 .163 .599 0.7 Single Best .969±.002.969±.002 .984 .193 .618 Large Single Model .963±.002.963±.002 .981 .209 .757 Stoch. Retrain .980±.001.980±.001 .990 .170 .582 DASH (MaxMin) .977±.001.977±.001 .989 .162 .597 0.9 Single Best .958±.003.958±.003 .978 .224 .614 Large Single Model .938±.003.938±.003 .967 .262 .738 Stoch. Retrain .977±.002.977±.002 .988 .182 .577 DASH (MaxMin) .977±.001.977±.001 .988 .176 .594 0.95 Single Best .951±.004.951±.004 .975 .246 .608 Large Single Model .925±.003.925±.003 .961 .284 .733 Stoch. Retrain .979±.002.979±.002 .989 .170 .576 DASH (MaxMin) .977±.001.977±.001 .988 .172 .590 Three patterns support the first-mover bias hypothesis: 1. LSM is worst despite matching DASH’s design. Both use low colsample_bytree and the same total tree count. The difference is sequential vs. independent training. LSM’s worst performance provides strong evidence that sequential residual dependency is a primary driver of first-mover bias. 2. The effect scales with correlation. LSM stability degrades from 0.9530.953 to 0.9250.925 as ρ increases from 0 to 0.950.95. DASH stability is flat (0.9720.972–0.9770.977). First-mover bias is specifically a collinearity problem. 3. Equity degrades in the same pattern. LSM’s within-group CV worsens from 0.1700.170 to 0.2840.284, consistent with sequential dependency concentrating importance within correlated groups. DASH distributes it proportionally (0.1640.164–0.1760.176). Interpreting accuracy and equity. The synthetic accuracy metric measures agreement with an equitable ground-truth decomposition (uniform importance within correlated groups; see Section 5 for details), so accuracy and equity advantages are partially confounded by design. DASH’s accuracy gains should be understood as a consequence of its equity properties—forced colsample_bytree restriction distributes feature usage across correlated groups by construction—rather than as independent evidence of superiority. The stability metric, which measures cross-run consistency of importance rankings regardless of ground truth, is not subject to this confound. Figure 2 visualizes this directly: within a single correlated group (5 features, each with true importance 0.400.40), the Single Best and Large Single Model concentrate importance on one arbitrary feature, while DASH distributes it proportionally. Figure 2: First-mover bias visualized: per-feature importance within a correlated group (ρ=0.9ρ=0.9, true importance =0.40=0.40 each). Single Best and LSM concentrate on an arbitrary feature; DASH distributes proportionally. Averaged over 5 repetitions; error bars show ±1± 1 SD. The ρS _S values in panel titles denote Spearman correlation with ground truth for this group (not the within-group feature correlation ρ). 6.2 The principle: independence largely resolves it If first-mover bias is driven primarily by sequential residual dependency, then any method that breaks this dependency—by ensuring independence between explained models—should substantially reduce the instability. We test this prediction by comparing methods that achieve independence through different mechanisms. Table 4 compares all methods at ρ=0.9ρ=0.9. The critical observation is that DASH and Stochastic Retrain achieve identical stability (0.9770.977 each). These methods differ substantially in design— DASH uses forced feature restriction, performance filtering, and diversity-aware selection, while Stochastic Retrain trains K models with different random seeds and a single fixed hyperparameter configuration (the best of 100 random draws from the same grid)—but they share one property: their explained models are trained independently. Table 4: All methods at ρ=0.9ρ=0.9 (20 repetitions), grouped by whether they achieve model independence. Bold indicates best per metric. †Matched training budget (M=200M=200 models trained). Timing entries marked — share infrastructure with other methods and were not independently measured. 95% BCa bootstrap CIs on stability: Single Best [0.952,0.963][0.952,0.963], DASH [0.975,0.978][0.975,0.978] (non-overlapping). Stochastic Retrain: 0.977±0.00150.977± 0.0015 (SE); BCa interval overlaps with DASH (0.977±0.00120.977± 0.0012 SE), consistent with equivalence. Method Stability (± ) DGP Agreement Equity (CV↓ ) Time (s) Dependent Single Best .958±.003.958±.003 .978 .224 043.5 Single Best† .964±.002.964±.002 .981 .212 248.8 Large Single Model .938±.003.938±.003 .967 .262 006.4 LSM (Tuned) .948±.003.948±.003 .972 .272 088.9 Ensemble SHAP .956±.003.956±.003 .977 .237 — Independent Stochastic Retrain .977±.002.977±.002 .988 .182 233.5 Random Selection† .976±.001.976±.001 .988 .187 287.2 Naive Top-N .976±.001.976±.001 .988 .187 — DASH (MaxMin) .977±.001.977±.001 .988 .176 140.3 This result is the strongest evidence for the mechanistic claim. The methods partition cleanly into two tiers: • Dependent methods (Single Best, LSM, Ensemble SHAP): stability 0.9380.938–0.9640.964. Each relies on a single optimization trajectory or a single sequentially-constructed ensemble. • Independent methods (DASH, Stochastic Retrain): stability ≈0.977≈ 0.977. Each averages SHAP values across independently trained models. The gap between tiers (∼ 0.01–0.04) dwarfs the gap within the independent tier (∼ 0.001). This supports the view that the operative mechanism is independence between explained models, not any particular aggregation strategy or hyperparameter diversification. The role of diversity selection. Within the independent tier, Random Selection (0.9760.976) nearly matches DASH (0.9770.977), suggesting that MaxMin diversity selection contributes minimally to stability beyond what random sampling from the filtered population already provides. The primary value of diversity selection is therefore not stability but equity: DASH’s within-group CV (0.1760.176) is lower than Random Selection’s (0.1870.187), indicating that deliberate diversity in feature utilization patterns produces more equitable credit distribution (though this comparison has not been formally significance-tested). Practitioners who need only stability can use random selection from a performance-filtered population; those who also require equitable attributions benefit from the full DASH pipeline. Variance decomposition. To directly quantify the role of model-selection randomness, we decompose explanation instability into two sources by alternately fixing the data seed or the model seed. When data is fixed and only model seeds vary (isolating model-selection variance), Single Best stability is 0.9780.978 while DASH achieves 0.9950.995—indicating that DASH nearly eliminates model-selection noise. Model-selection variance accounts for approximately 54%54\% of Single Best’s total instability but only 24%24\% of DASH’s, consistent with independence-based averaging cancelling the arbitrary feature choices that dominate single-model explanations.222These percentages use 1−stability1-stability as a proxy for instability. Since stability is a mean pairwise Spearman correlation rather than a variance, the decomposition is approximate and should be interpreted as directional evidence rather than exact variance fractions. Statistical significance. Table 5 reports Wilcoxon signed-rank tests with Holm–Bonferroni step-down correction on accuracy and equity metrics across all ρ levels. All comparisons between DASH and LSM are significant at every ρ level with large effect sizes (Cohen’s d>1.4d>1.4). DASH vs. Single Best becomes significant at ρ≥0.7ρ≥ 0.7 for both accuracy (d=+0.98d=+0.98) and equity (d=−1.07d=-1.07). The DASH vs. Stochastic Retrain comparison is not significant on either accuracy (d=+0.05d=+0.05) or equity (d=−0.21d=-0.21), consistent with the independence principle. The small effect sizes (d=+0.05d=+0.05 for accuracy, d=−0.21d=-0.21 for equity) and large Wilcoxon p-values (p=0.926p=0.926 for accuracy, p=0.622p=0.622 for equity) are consistent with practical equivalence: differences of this magnitude—well under 0.0050.005 in absolute accuracy—do not change top-5 feature rankings in practice. Formal equivalence testing (TOST) is deferred to the TMLR version where Nreps=50N_reps=50 provides adequate power. Note that stability, computed as a single aggregate across all repetition pairs, cannot be subjected to per-repetition Wilcoxon tests; we report BCa bootstrap confidence intervals (Table 4 caption) as an alternative measure of precision for this metric. Table 5: Wilcoxon signed-rank tests with Holm–Bonferroni step-down correction (20 paired repetitions). Bold p-values are significant at adjusted α=0.05α=0.05. Selected comparisons shown from 26 total tests; full results available in the code repository. ρ Comparison Metric pHBp_HB Cohen’s d 0.7 DASH vs SB Accuracy 0.031 ++0.98 0.7 DASH vs LSM Accuracy 0.002 ++1.97 0.7 DASH vs SB Equity 0.018 −-1.07 0.7 DASH vs LSM Equity <<0.001 −-1.96 0.9 DASH vs SB Accuracy 0.010 ++1.59 0.9 DASH vs LSM Accuracy <<0.001 ++3.42 0.9 DASH vs SB Equity 0.015 −-1.27 0.9 DASH vs LSM Equity <<0.001 −-3.03 0.9 DASH vs SR Accuracy n.s. (0.926) ++0.05 0.9 DASH vs SR Equity n.s. (0.622) −-0.21 0.95 DASH vs SB Accuracy <<0.001 ++2.07 0.95 DASH vs LSM Accuracy <<0.001 ++4.41 The SR equivalence is the headline theoretical result. We find that model independence alone—even in its simplest form (seed averaging, no diversity optimization)—largely resolves first-mover bias in the linear regime. Stochastic Retrain achieves marginally higher stability point estimates than DASH at most ρ levels (0.9750.975–0.9800.980 vs. 0.9720.972–0.9770.977), and the non-significant differences on accuracy (d=+0.05d=+0.05, p=0.926p=0.926) and equity (d=−0.21d=-0.21, p=0.622p=0.622) confirm this equivalence statistically. This equivalence is our central theoretical contribution: it isolates model independence as the operative mechanism, and positions DASH as a principled instantiation of that principle rather than a statistically superior pipeline. Phrased differently: raw seed averaging already delivers most of the benefit; DASH then operationalizes this principle with engineered quality control (filtering, diversity-aware selection), diagnostic tools, and hyperparameter robustness that seed averaging cannot provide. SR achieves marginally higher stability point estimates at most ρ levels, though these differences are small (≤0.003≤ 0.003) and not statistically significant. DASH’s practical advantages over SR are threefold: 1. Speed. DASH is ∼1.7× 1.7× faster than SR (140 s vs. 234 s per repetition, Table 9) because diversity selection reduces the number of SHAP evaluations from K=30K=30 to Keff≤30K_eff≤ 30 (typically 10–15 at ε=0.08 =0.08). 2. Diagnostics. The FSI and IS Plot (Section 6.4) detect which specific features are affected by first-mover bias without ground truth—a capability SR lacks entirely. In practice, knowing that explanations are stable is less useful than knowing which features are unreliable. 3. Equity. Marginally lower within-group CV (0.1760.176 vs. 0.1820.182), suggesting that forced feature restriction distributes credit more evenly, though this difference is not statistically significant and should be interpreted cautiously. 6.3 The effect scales with correlation Table 3 (Section 6.1) reveals a dose-response relationship: as ρ increases, first-mover bias intensifies for dependent methods while independent methods remain immune. LSM stability degrades monotonically from 0.9530.953 at ρ=0ρ=0 to 0.9250.925 at ρ=0.95ρ=0.95—a 2.9%2.9\% decline. Single Best follows the same pattern (0.973→0.9510.973→ 0.951, a 2.3%2.3\% decline). DASH’s stability is effectively flat (0.9720.972–0.9770.977), fluctuating by less than 0.5%0.5\% across the entire correlation range. The equity metric shows the same scaling. LSM’s within-group CV worsens from 0.1700.170 to 0.2840.284 (+67%+67\%), while DASH ranges from 0.1640.164 to 0.1760.176 (+7%+7\%). This is consistent with sequential residual dependency concentrating importance within correlated groups, with the concentration scaling with the degree of correlation—as the first-mover bias hypothesis predicts. When correlation is low, features within a group carry sufficiently distinct signal that the first-mover advantage is weak. When correlation is high, the features are near-interchangeable, and the first split’s arbitrary selection dominates. At ρ=0ρ=0, Single Best, Stochastic Retrain, and DASH cluster tightly (stability 0.9720.972–0.9750.975), satisfying the safety desideratum: DASH does not degrade explanations when multicollinearity is absent. LSM already trails at 0.953±0.0030.953± 0.003, and its gap widens monotonically with ρ. Figure 3: Stability, accuracy, and equity as a function of within-group correlation ρ (linear DGP, 20 repetitions per level). Independent methods (DASH, Stochastic Retrain) are flat across correlation levels; dependent methods (Single Best, LSM) degrade monotonically. All seven methods shown; Table 3 reports the four principal methods in detail, Table 4 compares all at ρ=0.9ρ=0.9. 6.4 Detecting first-mover bias: FSI and IS Plot A key practical question is: how can a practitioner know whether their explanations suffer from first-mover bias? Ground-truth importance is never available in practice. DASH’s Stage 5 diagnostics address this by quantifying explanation disagreement across the ensemble. Feature Stability Index (FSI). The FSI (Eq. 5) measures the ratio of cross-model SHAP variance to mean importance for each feature. On the Breast Cancer dataset, the most important features (mean concave points, worst area, worst perimeter) have FSI ≈0.9≈ 0.9–1.01.0, indicating moderate cross-model disagreement, while features in the radius/perimeter/area triad that are less frequently selected as “first movers” show higher FSI (>1.2>1.2), reflecting greater instability. The FSI gradient across correlated features identifies collinear groups without computing the correlation matrix, providing an unsupervised collinearity diagnostic. Importance-Stability (IS) Plot. The IS Plot partitions features into four quadrants by median thresholds on importance and FSI: • Quadrant I (high importance, low FSI): Robust drivers whose rankings are trustworthy. • Quadrant I (high importance, high FSI): Collinear cluster members whose individual rankings should not be trusted. • Quadrant I (low importance, low FSI): Confirmed unimportant features. • Quadrant IV (low importance, high FSI): Fragile interactions requiring further investigation. On Breast Cancer, the IS Plot places mean concave points, worst area, and worst perimeter in Quadrant I (robust drivers—high importance, low FSI) and the radius/perimeter/area triad’s remaining members in Quadrant I (collinear cluster—high importance, high FSI), matching domain knowledge about the underlying tumor geometry (Figure 4(a)). This enables practitioners to audit explanation reliability before acting on feature rankings—a capability absent from single-model workflows and from Stochastic Retrain. (a) IS Plot: features colored by quadrant. (b) Local disagreement map for the highest-variance observation. Figure 4: Diagnostic outputs on Breast Cancer. (a) The IS Plot identifies robust drivers (Quadrant I, green) and collinear cluster members (Quadrant I, red) without access to the correlation matrix. (b) The local disagreement map shows consensus SHAP values ±1± 1 SD across the ensemble; wide error bars indicate model-dependent attributions. 6.5 Real-world validation We validate on three real-world datasets with natural multicollinearity. California Housing. On the California Housing dataset (8 features, regression), DASH improves stability over Single Best despite the smaller feature space. The natural correlation between spatial features (latitude/longitude) and socioeconomic variables (income/rooms/bedrooms) creates mild multicollinearity that is sufficient to destabilize single-model explanations. Breast Cancer Wisconsin. On the Breast Cancer dataset (30 features, 21 pairs with |r|>0.9|r|>0.9, 20 repetitions), DASH nearly triples stability: Table 6: Real-world dataset results (20 repetitions each). Stability reported with ± from BCa bootstrap. Bold indicates best. Breast Cancer is a classification task (RMSE not applicable). †Matched training budget (M=200M=200 models trained). Δ . is relative to Single Best (M=200M=200). SB(M=200M=200) and DASH sourced directly from demo_benchmark_6.ipynb. Dataset Method Stability (± ) Δ . RMSE Breast Cancer Single Best (M=200M=200)† .317±.053.317±.053 — — DASH (MaxMin) .930±.005.930±.005 +0.613+0.613 — Superconductor Single Best .830±.020.830±.020 — 9.18±0.119.18± 0.11 Large Single Model .689±.030.689±.030 −0.141-0.141 9.34±0.099.34± 0.09 DASH (MaxMin) .962±.010.962±.010 +0.132+0.132 9.15±0.089.15± 0.08 Calif. Housing Single Best .967±.010.967±.010 — 0.460±0.0090.460± 0.009 DASH (MaxMin) .982±.005.982±.005 +0.015+0.015 0.450±0.0050.450± 0.005 The Breast Cancer improvement is the largest across all experiments. The training-budget-matched Single Best (M=200M=200) achieves only 0.3170.317 stability, because Breast Cancer’s extreme collinearity (21 pairs with |r|>0.9|r|>0.9) makes model selection itself unstable—with 200 hyperparameter configurations, the “best” model varies wildly across repetitions, and feature rankings are highly unstable across runs. The radius/perimeter/area triad creates extreme SHAP instability: a feature’s importance can swing from first to fifth across runs. DASH consensus substantially stabilizes this, producing stable top features aligned with known geometric redundancy in the feature set—mean concave points (0.228), worst area (0.201), worst perimeter (0.201)—that are stable across repetitions. Superconductor. On the Superconductor dataset (81 features, 21,263 samples), DASH improves stability by +0.132+0.132 over Single Best and +0.273+0.273 over the Large Single Model, while achieving marginally better predictive RMSE. The LSM result is particularly striking: despite having the same total tree count as DASH, its sequential training produces the poorest reproducibility—consistent with first-mover bias at scale. California Housing. On California Housing (8 features, 20,640 samples), several feature pairs have |r|>0.7|r|>0.7 (e.g., latitude/longitude, income/house value). DASH improves stability by +0.015+0.015 over Single Best while maintaining equivalent predictive RMSE. The improvement is smaller than for Breast Cancer and Superconductor, consistent with the milder degree of collinearity and the small feature space. 6.6 Robustness and scope Hyperparameter sensitivity. DASH is robust to its hyperparameters. Across a 3×3× range of ε values (0.030.03 to 0.100.10), stability varies by <0.005<0.005 (Table 8, Appendix C). Population size M shows diminishing returns past M=100M=100; M=200M=200 is the default for a margin of safety (Figure 5, Appendix C). Computational cost. DASH is approximately 3.2×3.2× more expensive than the standard Single Best workflow per repetition (Table 9, Appendix C). The cost is dominated by training M=200M=200 models, which is embarrassingly parallel. Notably, Stochastic Retrain is 1.7×1.7× more expensive than DASH, as it computes SHAP for all K=30K=30 models rather than only the diverse subset. Nonlinear DGP: scope boundary. Under the nonlinear DGP (Table 7), all methods degrade (stability drops from ∼ 0.93 to ∼ 0.88), but the first-mover bias mechanism still operates: DASH outperforms Single Best at ρ≥0.7ρ≥ 0.7 (stability gap +0.078+0.078 at ρ=0.95ρ=0.95). Table 7: Nonlinear DGP: stability and equity across correlation levels. SB = Single Best, LSM = Large Single Model, LSM-T = LSM (Tuned), SR = Stochastic Retrain. Five methods with distinct training structures are shown; Random Selection and Naive Top-N (which performed similarly to DASH in the linear regime) are omitted for space and are available in the code repository. Bold indicates best per ρ. Stability ρ SB LSM LSM-T SR DASH 0.0 0.933 0.912 0.929 0.934 0.934 0.5 0.849 0.836 0.851 0.855 0.852 0.7 0.842 0.836 0.853 0.854 0.866 0.9 0.834 0.791 0.819 0.869 0.873 0.95 0.798 0.745 0.803 0.864 0.876 Equity (CV, lower is better) ρ SB LSM LSM-T SR DASH 0.0 0.178 0.181 0.181 0.180 0.168 0.5 0.177 0.189 0.174 0.169 0.172 0.7 0.192 0.203 0.184 0.180 0.170 0.9 0.200 0.241 0.220 0.177 0.173 0.95 0.231 0.267 0.229 0.176 0.167 At ρ=0ρ=0, DASH and Single Best perform nearly identically (0.9340.934 vs. 0.9330.933). At ρ=0.5ρ=0.5, Stochastic Retrain achieves the highest stability (0.8550.855), with DASH (0.8520.852) marginally ahead of Single Best (0.8490.849). DASH’s advantage over Single Best grows consistently with correlation. This is a genuine scope boundary: nonlinear relationships are common in practice, and overall stability levels are lower than for the linear DGP (∼ 0.87–0.93 vs. ∼ 0.93–0.98). When the DGP contains interactions and nonlinear terms, different models in the DASH ensemble may capture different interaction structures. Averaging SHAP values across models that have learned qualitatively different functional forms introduces noise rather than canceling arbitrary choices. At ρ≥0.7ρ≥ 0.7, first-mover bias reasserts itself as the dominant source of instability, and DASH’s independence-based cancellation provides clear benefit (+0.078+0.078 at ρ=0.95ρ=0.95). Practitioners should therefore check both the degree of collinearity and the presence of strong nonlinear interactions before applying DASH. The FSI diagnostic (Section 6.4) can help: if FSI values are low across all features, ensemble averaging may not be needed. 7 Discussion 7.1 Reframing explanation instability This work reframes the SHAP instability problem from “SHAP is noisy under multicollinearity” to a specific mechanistic hypothesis: sequential residual dependency in gradient boosting creates a first-mover bias that concentrates feature importance on arbitrary features within correlated groups. Three lines of evidence support this view: (1) the Large Single Model—which maximizes sequential dependency—produces the poorest reproducibility at every correlation level; (2) all methods that achieve model independence restore stability to the same level (≈0.977≈ 0.977 at ρ=0.9ρ=0.9), regardless of their other design choices; and (3) the effect scales with correlation severity, as the hypothesis predicts. The implication is that the problem is not with SHAP itself—whose axiomatic properties (local accuracy, missingness, consistency) are sound for a given model—but with explaining a single sequentially-constructed model. The solution is to change what is being explained: from one model’s feature attributions to a consensus across independently trained models. Under nonlinear data-generating processes, independence remains the most effective mitigation but does not fully restore stability (Section 6.6). The mechanism is that SHAP attributions for a feature depend on which interactions the model has learned, not only on which feature was selected first within a correlated group. Since independently trained models may learn qualitatively different interaction structures (e.g., tree h1h_1 in model A captures z12z_1^2 while model B captures z1z2z_1z_2), averaging their SHAP values introduces model-disagreement noise that is distinct from first-mover bias and not resolved by independence alone. Relationship to stability selection. DASH shares a structural resemblance with stability selection (Meinshausen and Bühlmann, 2010): both train many models and aggregate their outputs to identify stable signals. The key distinction is the axis of perturbation. Stability selection perturbs the data (via subsampling) and aggregates binary feature selection indicators, identifying which features are consistently chosen across subsamples. DASH perturbs the model (via hyperparameter diversification) and aggregates continuous feature attributions (SHAP values), producing a stable importance ranking over the original feature space. The two approaches are complementary: stability selection operates at the feature-selection stage and discards correlated redundancies, while DASH operates at the explanation stage and preserves all features, distributing credit proportionally within correlated groups. A practitioner who has already applied stability selection to reduce the feature set would still benefit from DASH when explaining the model trained on the selected features, as within-group collinearity among retained features can persist. The DASH ensemble’s K importance vectors also support a richer output representation: features that consistently swap rank across ensemble members can be treated as incomparable rather than arbitrarily ordered, yielding a partial order on feature importance that more honestly reflects genuine attribution ambiguity under collinearity. We pursue this direction in companion work. 7.2 Practical recommendations 1. Always check for first-mover bias. Before trusting a SHAP-based feature ranking from a gradient-boosted model, train multiple models with different seeds and compare their importance rankings. If rankings differ substantially, the standard workflow is unreliable. 2. Use DASH’s diagnostics. The FSI and IS Plot detect which specific features are affected by first-mover bias, even without ground truth. Quadrant I features (high importance, high instability) should be interpreted as collinear cluster members rather than individually important features. 3. For stability alone, seed averaging suffices. Stochastic Retrain achieves stability equivalent to DASH with minimal implementation effort. Use it when diagnostics and equity are not required. 4. Use DASH when equity and diagnostics matter. DASH’s forced feature restriction produces lower within-group CV, and its integrated diagnostics provide actionable audit information. 5. Do not scale up single models. The Large Single Model result demonstrates that more trees with sequential training amplifies, rather than resolves, explanation instability. 7.3 Limitations • Scope. The default pipeline targets XGBoost and TreeSHAP. Extension to other model families (e.g., neural networks with KernelSHAP) would require adapting the diversity selection criteria to non-tree-based importance measures. The fit_from_attributions() interface partially relaxes this constraint: any attribution method producing feature-level vectors can plug into the diversity selection and consensus stages without retraining. • Interventional SHAP under correlation. DASH uses interventional TreeSHAP, which conditions on marginal rather than conditional feature distributions. Under high correlation, this evaluates the model at out-of-distribution feature combinations (Janzing et al., 2020; Aas et al., 2021), potentially producing unintuitive attributions. Averaging across diverse models mitigates individual-model artifacts, but the fundamental tension between interventional SHAP and correlated features remains. • Interaction effects. The current pipeline averages SHAP value matrices Φ(i)∈ℝN′×P ^(i) ^N × P, which preserves main effects but not pairwise interaction structure. However, TreeSHAP supports exact interaction values via tensors Φint(i)∈ℝN′×P×P _int^(i) ^N × P× P, where diagonal entries are main effects and off-diagonal entries are pairwise interactions. Averaging these tensors element-wise across the ensemble would yield stable interaction estimates by the same independence argument. The computational cost is O(TLD2)O(TLD^2) per model (vs. O(TLD)O(TLD) for standard SHAP), making this practical for moderate P but expensive for large feature spaces. • Nonlinear scope boundary. Under nonlinear DGPs, overall stability is lower for all methods. DASH’s advantage grows with ρ and is clearest at ρ≥0.7ρ≥ 0.7 (Section 6.6). • Ground truth. On real-world data, we can only evaluate stability, not accuracy. The synthetic accuracy metric presupposes equitable credit distribution (Section 5), partially confounding accuracy with equity. • Confidence intervals. With Nreps=20N_reps=20, the Wilcoxon test is underpowered for the small effect sizes between DASH and Stochastic Retrain. Larger NrepsN_reps would strengthen the analysis. • Background dataset size. All experiments use B=100B=100 background samples for interventional TreeSHAP. For high-dimensional datasets with strong correlation structure, this may be insufficient to capture the joint distribution faithfully. A sensitivity analysis over B is deferred to the journal version. • Random forest baseline. Random forests train trees independently, predicting higher baseline explanation stability without any DASH-like pipeline. Including an RF baseline would provide a direct test of the independence principle on a model family that is independent by construction. This comparison is planned for the journal version. 7.4 Broader implications First-mover bias is likely not unique to gradient boosting. Any iterative optimization procedure that makes sequential, greedy feature selections—including some neural network training dynamics—may exhibit analogous path-dependent concentration of feature attributions. The independence principle established here provides a general framework for investigating and resolving such effects. Future work will explore whether the mechanism extends to random forests (where trees are already independent, predicting higher baseline stability), neural networks (where gradient-based optimization creates different but potentially analogous path dependencies), and whether partial orders on feature importance can replace point rankings as a more robust representation of explanation structure. A concrete near-term extension is stable feature interaction estimation: averaging TreeSHAP interaction tensors across the DASH ensemble would provide stable pairwise interaction rankings under multicollinearity, a capability that no single-model workflow can offer. 8 Conclusion We have investigated first-mover bias—the path-dependent concentration of feature importance associated with sequential residual fitting in gradient boosting—as a specific mechanistic contributor to SHAP instability under multicollinearity. Three lines of evidence support this finding: 1. The Large Single Model, which maximizes sequential dependency, produces the poorest attribution reproducibility of any method tested—worse than the standard single-best workflow—despite matching DASH’s total tree count and feature restriction. This provides strong evidence that sequential dependency, not model capacity, is a major driver of instability. 2. DASH and Stochastic Retrain achieve identical stability (0.9770.977 at ρ=0.9ρ=0.9; accuracy d=+0.05d=+0.05, equity d=−0.21d=-0.21, both n.s.), despite differing in every design choice except model independence. This supports the view that independence between explained models is the operative mechanism. 3. The effect scales with correlation: dependent methods degrade monotonically as ρ increases, while independent methods remain flat. This matches the mechanistic prediction. DASH (Diversified Aggregation of SHAP) operationalizes the independence principle with forced feature restriction, diversity-aware model selection, and two novel diagnostic tools—the Feature Stability Index and Importance-Stability Plot—that detect first-mover bias without ground truth. On real-world datasets, DASH improves stability from 0.320.32 to 0.930.93 (Breast Cancer), from 0.830.83 to 0.960.96 (Superconductor), and from 0.970.97 to 0.980.98 (California Housing). The code, data, and reproducible benchmarks are publicly available at https://github.com/DrakeCaraker/dash-shap. Reproducibility Statement All code, data generators, hyperparameter configurations, and evaluation metrics are publicly available at https://github.com/DrakeCaraker/dash-shap. The complete benchmark can be reproduced via python run_experiments.py with fixed random seeds (SEED=42SEED=42). 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Appendix A Algorithm Pseudocode Algorithm 1 DASH Pipeline 0: Training data (Xtrain,ytrain)(X_train,y_train), validation data (Xval,yval)(X_val,y_val), reference data XrefX_ref, population size M, max ensemble size K, performance threshold ε , diversity threshold δ, search space Θ 0: Consensus SHAP matrix Φ¯ , diagnostics (FSI, IS Plot) 1: Stage 1: Population Generation 2: for i=1i=1 to M do 3: Sample θi∼Uniform(Θ) _i ( ) 4: Train fi←XGBoost(Xtrain,ytrain;θi,seed=i)f_i (X_train,y_train; _i,seed=i) 5: Evaluate si←score(fi,Xval,yval)s_i (f_i,X_val,y_val) 6: end for 7: Stage 2: Performance Filtering 8: s∗←maxi⁡sis^*← _is_i 9: ℱ←i:|si−s∗|≤εF←\i:|s_i-s^*|≤ \ 10: Stage 3: Diversity Selection 11: for i∈ℱi do 12: i←gain_importance(fi,Xref)v_i \_importance(f_i,X_ref) 13: end for 14: ←MaxMinSelect(ii∈ℱ,K,δ)S (\v_i\_i ,K,δ) 15: Stage 4: Consensus SHAP 16: for i∈i do 17: Φ(i)←TreeSHAP(fi,Xref) ^(i) (f_i,X_ref) 18: end for 19: Φ¯←1||∑i∈Φ(i) ← 1|S| _i ^(i) 20: Stage 5: Diagnostics 21: I¯j←1N′∑n|Φ¯nj| I_j← 1N _n| _nj| for each feature j 22: FSIj←σ¯j/(I¯j+ϵ0)FSI_j← σ_j/( I_j+ _0) for each feature j 23: return Φ¯ , FSI, IS Plot Appendix B Extended Results and Reproducibility Full per-repetition importance vectors, significance test results, and ablation data are available in JSON format from the experimental runner. Running python run_experiments.py reproduces all tables and figures. The authoritative notebook notebooks/demo_benchmark_6.ipynb provides a checkpointed walkthrough of all experiments with intermediate results cached for rapid re-execution. All code, data generators, and benchmark infrastructure are publicly available at https://github.com/DrakeCaraker/dash-shap. Appendix C Ablation Studies and Computational Cost Epsilon sensitivity. DASH is remarkably robust to the performance filter threshold ε (Table 8). Across a 3×3× range of ε values (0.030.03 to 0.100.10), stability varies by <0.005<0.005. The effective ensemble size KeffK_eff scales with ε (4.0 to 16.2), but performance plateaus early. Table 8: Epsilon sensitivity at ρ=0.9ρ=0.9. Performance is robust across a 3×3× range. ε Models Passing KeffK_eff Stability Accuracy Equity 0.03 9.7 4.0 ± 1.3 0.9734 0.9861 0.193 0.05 22.2 6.5 ± 1.9 0.9747 0.9868 0.191 0.08 48.0 12.2 ± 2.6 0.9770 0.9879 0.176 0.10 67.5 16.2 ± 3.3 0.9777 0.9882 0.174 Population size ablation. Stability is robust across population sizes M: M=50M=50 (0.97270.9727) → M=100M=100 (0.97190.9719) → M=200M=200 (0.97220.9722) → M=500M=500 (0.97220.9722). Performance is effectively invariant to population size (within 0.001 across M∈50,100,200,500M∈\50,100,200,500\). We use M=200M=200 as a conservative default. Figure 5: Ablation sensitivity: stability as a function of population size M at two correlation levels (ρ=0.0ρ=0.0 and ρ=0.9ρ=0.9). Stability is effectively invariant to population size (within 0.001 across M∈50,100,200,500M∈\50,100,200,500\), indicating that M=200M=200 is a conservative default. Additional ablation results for K, ε , and δ are reported in Table 8 and the inline text; full multi-panel ablation figures are planned for the journal version. Computational cost. Table 9 reports wall-clock time for each method at ρ=0.9ρ=0.9 (20 repetitions, single-threaded timing). DASH’s cost is dominated by training M=200M=200 models and computing K≤30K≤ 30 TreeSHAP explanations. Table 9: Computational cost at ρ=0.9ρ=0.9 (20 repetitions). Wall-clock times are hardware-dependent (Apple M-series, single node) and reported for relative comparison. Method Models SHAP Evals Per-rep (s) Ratio Large Single Model 1 1 006.4 0.1×0.1× Single Best 30 1 043.5 1.0×1.0× LSM (Tuned) 1 1 088.9 2.0×2.0× DASH (MaxMin) 200 KeffK_eff 140.3 3.2×3.2× Stochastic Retrain 30 30 233.5 5.4×5.4× Single Best (M=200M=200) 200 1 248.8 5.7×5.7× Random Selection 200 KeffK_eff 287.2 6.6×6.6× Note: DASH’s diversity selection typically terminates before reaching Kmax=30K_ =30 (the minimum-distance threshold δ stops selection early), yielding Keff≈10K_eff≈ 10–1515 SHAP evaluations at ε=0.08 =0.08. Random Selection always selects K=30K=30 models, requiring roughly twice as many SHAP computations per repetition. Stochastic Retrain similarly computes SHAP for all K=30K=30 models, explaining its higher cost relative to DASH. Appendix D Pre-Specified Success Criteria We pre-specified eleven pass/fail criteria before running the final benchmark (written into the experimental notebook prior to execution, though not lodged with a formal pre-registration registry). These criteria test the paper’s stated hypotheses under favorable conditions (known-DGP synthetic data and datasets with documented collinearity); adversarial or out-of-distribution stress tests are deferred to the journal version. DASH passes all eleven: 1. Stability wins (linear): DASH >> Single Best on ≥ 4/5 ρ levels → PASS (4/5) 2. Accuracy at ρ=0.9ρ=0.9: DASH ≥ SB → PASS (DASH =0.9879=0.9879 vs. SB =0.9784=0.9784) 3. Equity wins (linear): DASH << Single Best CV on ≥ 4/5 ρ levels → PASS (5/5) 4. Safety control at ρ=0ρ=0: No degradation vs. baselines → PASS (gap =0.0003=0.0003) 5. KeffK_eff increases with ε : monotonic → PASS (4.0→6.5→12.2→16.24.0→ 6.5→ 12.2→ 16.2) 6. Nonlinear DGP: DASH >> SB stability at ρ=0.9ρ=0.9 → PASS (DASH =0.8734=0.8734 vs. SB =0.8336=0.8336) 7. Statistical significance: ≥ 50% of tests significant → PASS (17/26 Bonferroni, 15/26 Holm–Bonferroni) 8. Superconductor: DASH stability >> SB → PASS (0.9620.962 vs. 0.8300.830) 9. California Housing: DASH stability >> SB → PASS (0.9820.982 vs. 0.9670.967) 10. Breast Cancer: DASH stability >> SB → PASS (0.9300.930 vs. 0.3170.317) 11. Variance decomposition: DASH model-selection variance << SB → PASS (0.0060.006 vs. 0.0230.023)

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