Rashomon Ensemble in Predictive Multiplicity

• Rashomon Ensemble is a collection of near-optimal models differing in structure, predictions, or attributions, enabling diverse insights in prediction and explanation.
• They are constructed using methods like majority voting, Gibbs weighting, and clustering, tailored for tasks including prediction, active learning, and forecasting.
• Rashomon Ensembles enhance trustworthiness by exposing explanation uncertainty and balancing robustness with privacy in complex decision-making applications.

A Rashomon Ensemble is an ensemble constructed from a Rashomon set: a collection of models, trees, rules, forecasters, or policies that are all near-optimal under a specified objective but differ in structure, predictions, feature attributions, or induced decisions. In the recent literature, the term is used both generically and as a named design pattern for replacing a single empirical minimizer with a controlled family of plausible alternatives. The resulting ensemble is not defined by a single aggregation rule. Rather, published formulations include majority voting, weighted voting, Gibbs posteriors, explanation envelopes, utility-based selection, and permissive policies, depending on whether the goal is prediction, explanation, active learning, chaotic forecasting, or formal verification (Cavus et al., 19 Jul 2025, Nguyen et al., 24 Mar 2026, Gross et al., 19 Dec 2025).

1. Formal definitions and the scope of the Rashomon set

The common substrate is the Rashomon set itself. In additive form, many papers define it as the set of hypotheses whose empirical or population risk lies within a tolerance $\epsilon$ of the optimum: $$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$ Equivalent formulations appear for empirical risk,

$$\hat R_\epsilon(\mathcal F)=\{\,f\in\mathcal F:\;L(f)\le L(\hat f)+\epsilon\}\,,$$

for rule sets,

$$RS_\epsilon=\{\,h\in H : f(h)\le f(h^*)+\epsilon\}\,,$$

and for allocation models,

$$\mathcal{R}_\epsilon(\hat p_0)=\Bigl\{\hat p\in \mathcal{H}\;\big|\;\mathbb{L}(\hat p;\mathcal{D}_{\mathrm{train}})\le \mathbb{L}(\hat p_0;\mathcal{D}_{\mathrm{train}})+\epsilon\Bigr\}\,.$$

Other formulations use a multiplicative tolerance. In AutoML, if $\phi$ is a performance metric such as RMSE and $M^*=\arg\min_{M_k\in M}\phi(M_k)$, then

$$R_\epsilon=\{\,M_k\in M \mid \phi(M_k)\le \phi(M^*)\cdot(1+\epsilon)\,\}.$$

Sparse-tree work uses the same relative threshold, writing $$R(T^*,D,\epsilon)=\{\,T\in\mathcal T(d)\mid C(T,D)\le (1+\epsilon)C(T^*,D)\,\}$$ (Cavus et al., 19 Jul 2025, Nguyen et al., 24 Mar 2026, Ciaperoni et al., 2024, Arslan et al., 5 Nov 2025).

Two summary quantities recur. The first is Rashomon set size, such as $|R_\epsilon|$ or $$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$0. The second is a normalized notion of multiplicity, including the Rashomon ratio $$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$1 in AutoML and $$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$2 in sampled hypothesis spaces. In chaotic forecasting, the set becomes horizon-specific,

$$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$3

so multiplicity varies with lead time rather than being fixed over the task (Cavus et al., 19 Jul 2025, Zuin et al., 11 Sep 2025, Kale et al., 17 Apr 2026).

Sequential decision-making introduces a stricter variant. There, a Rashomon set is not merely a near-optimal collection; it is a maximal subset of trained policies such that every distinct pair is behaviourally equivalent—inducing identical DTMCs up to relabeling, or equivalently identical reachability behavior—while differing in internal structure as summarized by a user-specified metric $$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$4. This shifts the notion of multiplicity from prediction-space disagreement to internal-policy diversity under identical external behavior (Gross et al., 19 Dec 2025).

2. Ensemble construction and aggregation patterns

Published Rashomon Ensembles follow a common pipeline: construct or approximate a near-optimal set, remove redundancy or organize diversity, and then aggregate or select members according to the downstream objective. What differs across papers is the object being aggregated—predictions, explanations, uncertainty scores, or policies—and the criterion used to preserve useful diversity.

Setting	Near-optimal set construction	Aggregation or selection
AutoML explanations	Models within $$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$5 of best $$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$6	Pointwise PDP envelopes
Active learning	Exact sparse-tree Rashomon set	Gibbs-weighted vote entropy or unique-pattern committee
Rule sets and sparse trees	Exact or approximate Rashomon-set exploration	Majority vote, weighted vote, or diverse subset
Sequential decision-making	Largest behavioural equivalence class with distinct $$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$7	Majority vote, averaging, or permissive policy
Chaotic forecasting	Horizon-constrained $$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$8	Decision-aligned utility ranking

In the AutoML explanation framework, all models in $$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$9 are evaluated on a common feature grid, and the ensemble output is not a point prediction but a pointwise lower and upper envelope,

$$\hat R_\epsilon(\mathcal F)=\{\,f\in\mathcal F:\;L(f)\le L(\hat f)+\epsilon\}\,,$$0

producing an interval-valued explanation rather than a single PDP curve. In REALITrees, the committee is the exact $$\hat R_\epsilon(\mathcal F)=\{\,f\in\mathcal F:\;L(f)\le L(\hat f)+\epsilon\}\,,$$1-Rashomon set of sparse decision trees, weighted by a PAC-Bayesian Gibbs posterior

$$\hat R_\epsilon(\mathcal F)=\{\,f\in\mathcal F:\;L(f)\le L(\hat f)+\epsilon\}\,,$$2

with disagreement measured through weighted vote entropy. In UNREAL, the committee is pruned further: trees that induce exactly the same classification pattern on the candidate pool are grouped together, and one representative per group is retained. In the explanation-aware ensemble method of "A 6 or a 9?", models that satisfy the performance constraint are clustered in explanation space using $$\hat R_\epsilon(\mathcal F)=\{\,f\in\mathcal F:\;L(f)\le L(\hat f)+\epsilon\}\,,$$3-means on explanation vectors $$\hat R_\epsilon(\mathcal F)=\{\,f\in\mathcal F:\;L(f)\le L(\hat f)+\epsilon\}\,,$$4, and one representative is constructed from each cluster so that diversity is enforced simultaneously in performance space and explanation space (Cavus et al., 19 Jul 2025, Nguyen et al., 24 Mar 2026, Nguyen et al., 9 Mar 2025, Zuin et al., 11 Sep 2025).

Sparse-tree and rule-set papers also describe more conventional prediction ensembles built from enumerated or sampled Rashomon members. These include majority voting, weighted voting by inverse objective or empirical risk, farthest-first selection in prediction-pattern space, Hamming-distance-based diversity selection, and greedy accuracy-diversity trade-offs. The sequential decision-making paper adds a permissive-policy construction,

$$\hat R_\epsilon(\mathcal F)=\{\,f\in\mathcal F:\;L(f)\le L(\hat f)+\epsilon\}\,,$$5

which preserves the action support of all Rashomon members at a state and can then be model-checked directly. In chaotic forecasting, the final selection may be a single model or a small ensemble, but membership is conditioned on surviving horizon-wise near-optimality and then ranked by decision-aligned utility rather than RMSE alone (Xin et al., 2022, Ciaperoni et al., 2024, Arslan et al., 5 Nov 2025, Gross et al., 19 Dec 2025, Kale et al., 17 Apr 2026).

3. Explanatory multiplicity and uncertainty-aware interpretation

One of the clearest uses of a Rashomon Ensemble is to expose explanation uncertainty that is invisible when only the single best model is inspected. For a feature $$\hat R_\epsilon(\mathcal F)=\{\,f\in\mathcal F:\;L(f)\le L(\hat f)+\epsilon\}\,,$$6, the single-model partial dependence profile is

$$\hat R_\epsilon(\mathcal F)=\{\,f\in\mathcal F:\;L(f)\le L(\hat f)+\epsilon\}\,,$$7

Evaluating this quantity for every $$\hat R_\epsilon(\mathcal F)=\{\,f\in\mathcal F:\;L(f)\le L(\hat f)+\epsilon\}\,,$$8 on a common grid yields a family of curves. The Rashomon PDP is then the interval between the pointwise minimum and maximum over the Rashomon set. Two metrics are proposed to quantify explanation uncertainty. The coverage rate is

$$\hat R_\epsilon(\mathcal F)=\{\,f\in\mathcal F:\;L(f)\le L(\hat f)+\epsilon\}\,,$$9

and the mean width of the confidence intervals is

$$RS_\epsilon=\{\,h\in H : f(h)\le f(h^*)+\epsilon\}\,,$$0

Here $$RS_\epsilon=\{\,h\in H : f(h)\le f(h^*)+\epsilon\}\,,$$1 measures how much of the best-model PDP lies inside the Rashomon interval, while $$RS_\epsilon=\{\,h\in H : f(h)\le f(h^*)+\epsilon\}\,,$$2 measures the amplitude of explanation dispersion (Cavus et al., 19 Jul 2025).

On 35 real-world tabular regression tasks from the OpenML CTR23 benchmark suite using H2O AutoML with max_models=20 and $$RS_\epsilon=\{\,h\in H : f(h)\le f(h^*)+\epsilon\}\,,$$3, the reported pattern is that explanation multiplicity is substantial. In a majority of datasets, the coverage rate across features falls below $$RS_\epsilon=\{\,h\in H : f(h)\le f(h^*)+\epsilon\}\,,$$4; over $$RS_\epsilon=\{\,h\in H : f(h)\le f(h^*)+\epsilon\}\,,$$5 of the evaluated features across tasks show $$RS_\epsilon=\{\,h\in H : f(h)\le f(h^*)+\epsilon\}\,,$$6; the average coverage is approximately $$RS_\epsilon=\{\,h\in H : f(h)\le f(h^*)+\epsilon\}\,,$$7; and interval widths vary widely, with narrow intervals in "energy_efficiency" and very wide ones in "forest_fires". A Spearman correlation of $$RS_\epsilon=\{\,h\in H : f(h)\le f(h^*)+\epsilon\}\,,$$8 with $$RS_\epsilon=\{\,h\in H : f(h)\le f(h^*)+\epsilon\}\,,$$9 links higher Rashomon ratios to lower coverage rates, indicating that greater model multiplicity is associated with greater explanation uncertainty. The interpretive implication is direct: the best model’s PDP can fall outside the envelope traced by other near-optimal models over substantial parts of the feature domain, so a single-model PDP is not a stable object of interpretation in many cases (Cavus et al., 19 Jul 2025).

Explanation diversity is also used as a selection signal rather than only as an uncertainty diagnostic. "A 6 or a 9?" computes an explanation vector $$\mathcal{R}_\epsilon(\hat p_0)=\Bigl\{\hat p\in \mathcal{H}\;\big|\;\mathbb{L}(\hat p;\mathcal{D}_{\mathrm{train}})\le \mathbb{L}(\hat p_0;\mathcal{D}_{\mathrm{train}})+\epsilon\Bigr\}\,.$$0 for each near-optimal model, clusters these vectors by minimizing within-cluster Euclidean dispersion, and chooses $$\mathcal{R}_\epsilon(\hat p_0)=\Bigl\{\hat p\in \mathcal{H}\;\big|\;\mathbb{L}(\hat p;\mathcal{D}_{\mathrm{train}})\le \mathbb{L}(\hat p_0;\mathcal{D}_{\mathrm{train}})+\epsilon\Bigr\}\,.$$1 by maximizing average silhouette score. This yields clusters that are homogeneous internally in explanation space but differ across clusters. The same paper uses Jensen–Shannon distance between predictive distributions as a deployment-time agreement signal: low JSD is treated as likely in-distribution agreement, while high JSD is treated as a sign of an unknown regime (Zuin et al., 11 Sep 2025).

Sparse-tree Rashomon-set exploration supports a related interpretability objective through Model Class Reliance. Instead of reporting feature importance for a single tree, it computes an interval over the full Rashomon set,

$$\mathcal{R}_\epsilon(\hat p_0)=\Bigl\{\hat p\in \mathcal{H}\;\big|\;\mathbb{L}(\hat p;\mathcal{D}_{\mathrm{train}})\le \mathbb{L}(\hat p_0;\mathcal{D}_{\mathrm{train}})+\epsilon\Bigr\}\,.$$2

where $$\mathcal{R}_\epsilon(\hat p_0)=\Bigl\{\hat p\in \mathcal{H}\;\big|\;\mathbb{L}(\hat p;\mathcal{D}_{\mathrm{train}})\le \mathbb{L}(\hat p_0;\mathcal{D}_{\mathrm{train}})+\epsilon\Bigr\}\,.$$3 is defined by permuting feature $$\mathcal{R}_\epsilon(\hat p_0)=\Bigl\{\hat p\in \mathcal{H}\;\big|\;\mathbb{L}(\hat p;\mathcal{D}_{\mathrm{train}})\le \mathbb{L}(\hat p_0;\mathcal{D}_{\mathrm{train}})+\epsilon\Bigr\}\,.$$4 and comparing the resulting loss-plus-penalty to the original loss-plus-penalty. This reframes variable importance as a set-valued property of near-optimal models rather than a property of one selected tree (Xin et al., 2022).

4. Enumeration, sampling, and scalability

The practical viability of a Rashomon Ensemble depends on how the Rashomon set is explored. Three broad strategies appear in the literature: exact enumeration, approximate counting and sampling, and local stochastic perturbation around an empirical minimizer.

Exact enumeration is most developed for discrete interpretable model classes. "Exploring the Whole Rashomon Set of Sparse Decision Trees" builds a compressed representation called the Model Set, composed of Model Set Instances indexed by subproblem and objective value. Dynamic programming with branch-and-bound is used to prune any partial tree whose lower bound exceeds the threshold $$\mathcal{R}_\epsilon(\hat p_0)=\Bigl\{\hat p\in \mathcal{H}\;\big|\;\mathbb{L}(\hat p;\mathcal{D}_{\mathrm{train}})\le \mathbb{L}(\hat p_0;\mathcal{D}_{\mathrm{train}})+\epsilon\Bigr\}\,.$$5. The resulting representation supports exact enumeration, efficient querying, and uniform sampling by unranking. "SORTeD Rashomon Sets of Sparse Decision Trees" refines this idea into SORTD, an anytime framework that enumerates trees in nondecreasing order of the objective value. It combines cached optimal subproblem values, helper nodes for leaves and branches, sorted Cartesian sums for combining left and right subtree solutions, upper-bound propagation to children, and a depth-two specialization with an $$\mathcal{R}_\epsilon(\hat p_0)=\Bigl\{\hat p\in \mathcal{H}\;\big|\;\mathbb{L}(\hat p;\mathcal{D}_{\mathrm{train}})\le \mathbb{L}(\hat p_0;\mathcal{D}_{\mathrm{train}})+\epsilon\Bigr\}\,.$$6 subroutine. Across 30 real-world binary-classification benchmarks with $$\mathcal{R}_\epsilon(\hat p_0)=\Bigl\{\hat p\in \mathcal{H}\;\big|\;\mathbb{L}(\hat p;\mathcal{D}_{\mathrm{train}})\le \mathbb{L}(\hat p_0;\mathcal{D}_{\mathrm{train}})+\epsilon\Bigr\}\,.$$7, $$\mathcal{R}_\epsilon(\hat p_0)=\Bigl\{\hat p\in \mathcal{H}\;\big|\;\mathbb{L}(\hat p;\mathcal{D}_{\mathrm{train}})\le \mathbb{L}(\hat p_0;\mathcal{D}_{\mathrm{train}})+\epsilon\Bigr\}\,.$$8, and target Rashomon-set sizes up to $$\mathcal{R}_\epsilon(\hat p_0)=\Bigl\{\hat p\in \mathcal{H}\;\big|\;\mathbb{L}(\hat p;\mathcal{D}_{\mathrm{train}})\le \mathbb{L}(\hat p_0;\mathcal{D}_{\mathrm{train}})+\epsilon\Bigr\}\,.$$9 trees, SORTD is reported to reduce runtime by up to two orders of magnitude relative to TreeFARMS and to use an order of magnitude less memory; even at depth $\phi$0, most sets of $\phi$1 trees are produced under $\phi$2, whereas TreeFARMS often times out at $\phi$3 (Xin et al., 2022, Arslan et al., 5 Nov 2025).

For rule sets, exact exploration is complemented by approximate counting and sampling. The branch-and-bound method incrementally expands partial rule sets while using hierarchical, look-ahead, and rule-set-size bounds to prune supersets that cannot satisfy $\phi$4. When exact enumeration is unnecessary, approximate counting uses random parity constraints in the style of ApproxMC, and nearly uniform sampling uses a UNIGEN-style procedure that searches for XOR-constrained cells of acceptable size. The reported effect is that exact enumeration can fully explore $\phi$5 when $\phi$6 in seconds to minutes, approximate counting returns $\phi$7-$\phi$8 guarantees in a few seconds even when $\phi$9, and 400 near-uniform samples suffice to recover the same feature-importance profiles and fairness-accuracy trade-offs as the full set (Ciaperoni et al., 2024).

A different approximation strategy is dropout-based exploration. Starting from a minimizer $M^*=\arg\min_{M_k\in M}\phi(M_k)$0, dropout masks $M^*=\arg\min_{M_k\in M}\phi(M_k)$1 are applied to obtain $M^*=\arg\min_{M_k\in M}\phi(M_k)$2, and only those perturbed weights satisfying $M^*=\arg\min_{M_k\in M}\phi(M_k)$3 are retained. The paper provides bounds linking dropout parameters to Rashomon-set membership for linear ridge regression, linear classification with Brier loss, and deep networks with Gaussian dropout. This approach is designed for predictive multiplicity estimation rather than exact enumeration. Empirically, on six UCI datasets and two image-classification benchmarks, dropout sampling with $M^*=\arg\min_{M_k\in M}\phi(M_k)$4 improves multiplicity-metric estimation relative to retraining and achieves speedups of $M^*=\arg\min_{M_k\in M}\phi(M_k)$5–$M^*=\arg\min_{M_k\in M}\phi(M_k)$6 versus retraining on UCI, up to approximately $M^*=\arg\min_{M_k\in M}\phi(M_k)$7 on CIFAR, and $M^*=\arg\min_{M_k\in M}\phi(M_k)$8–$M^*=\arg\min_{M_k\in M}\phi(M_k)$9 versus adversarial weight perturbation on UCI (Hsu et al., 2024).

These exploration methods imply different ensemble regimes. Exact enumeration supports exhaustive post hoc filtering by fairness, balanced accuracy, F1-score, or user preferences. Approximate counting and uniform sampling support representative committees when the full set is too large. Local perturbation methods support rapid estimation of multiplicity and efficient ensemble formation in continuous hypothesis spaces. A plausible implication is that the meaning of “Rashomon Ensemble” depends partly on the exploration regime: exhaustive methods emphasize coverage of the hypothesis space, whereas stochastic methods emphasize tractable approximation.

5. Active learning, forecasting, and sequential decision-making

Rashomon Ensembles have been used not only for static prediction but also as a committee mechanism in active learning. REALITrees defines the committee as the exact $$R_\epsilon=\{\,M_k\in M \mid \phi(M_k)\le \phi(M^*)\cdot(1+\epsilon)\,\}.$$0-Rashomon set of sparse decision trees under the regularized empirical objective

$$R_\epsilon=\{\,M_k\in M \mid \phi(M_k)\le \phi(M^*)\cdot(1+\epsilon)\,\}.$$1

After exact enumeration via SORTD_Enumerate, committee members are weighted by a Gibbs posterior, an Effective Committee Size is computed as

$$R_\epsilon=\{\,M_k\in M \mid \phi(M_k)\le \phi(M^*)\cdot(1+\epsilon)\,\}.$$2

and each unlabeled point is scored by weighted vote entropy

$$R_\epsilon=\{\,M_k\in M \mid \phi(M_k)\le \phi(M^*)\cdot(1+\epsilon)\,\}.$$3

The point with maximal entropy is queried. The reported behavior is strongest in moderately noisy environments, where expanded model multiplicity yields faster convergence: BREAL reaches its accuracy plateau up to 100 iterations earlier than QBC-RF in moderate-noise settings, truncated-AUC efficiency ratios $$R_\epsilon=\{\,M_k\in M \mid \phi(M_k)\le \phi(M^*)\cdot(1+\epsilon)\,\}.$$4 indicate that it spends fewer than half the labels of passive sampling to reach $$R_\epsilon=\{\,M_k\in M \mid \phi(M_k)\le \phi(M^*)\cdot(1+\epsilon)\,\}.$$5 of its accuracy ceiling, and it outperforms random-forest QBC in over $$R_\epsilon=\{\,M_k\in M \mid \phi(M_k)\le \phi(M^*)\cdot(1+\epsilon)\,\}.$$6 of 20 real-world benchmarks (Nguyen et al., 24 Mar 2026).

UNREAL adopts a stricter distinctness criterion. After enumerating all near-optimal trees with TreeFARMS, it groups trees by identical classification patterns on the current unlabeled pool and keeps one representative per group. Query selection again uses vote entropy,

$$R_\epsilon=\{\,M_k\in M \mid \phi(M_k)\le \phi(M^*)\cdot(1+\epsilon)\,\}.$$7

Across Iris, MONK-1, MONK-3, Bar7, and COMPAS, UNREAL is reported to demonstrate empirical improvements of up to $$R_\epsilon=\{\,M_k\in M \mid \phi(M_k)\le \phi(M^*)\cdot(1+\epsilon)\,\}.$$8 in predictive accuracy and to outperform Passive and RF with Wilcoxon $$R_\epsilon=\{\,M_k\in M \mid \phi(M_k)\le \phi(M^*)\cdot(1+\epsilon)\,\}.$$9, while also producing a parsimonious, directly inspectable committee (Nguyen et al., 9 Mar 2025).

In chaotic forecasting, multiplicity becomes horizon-dependent. The horizon-constrained Rashomon set is

$$R(T^*,D,\epsilon)=\{\,T\in\mathcal T(d)\mid C(T,D)\le (1+\epsilon)C(T^*,D)\,\}$$0

The paper proves an exponential contraction result,

$$R(T^*,D,\epsilon)=\{\,T\in\mathcal T(d)\mid C(T,D)\le (1+\epsilon)C(T^*,D)\,\}$$1

introduces a Lyapunov-weighted Rashomon ratio, and then selects models by downstream utility rather than forecast error alone. Experiments on Lorenz-96, Kuramoto-Sivashinsky, wind power, traffic, and weather report decision quality improvements of $$R(T^*,D,\epsilon)=\{\,T\in\mathcal T(d)\mid C(T,D)\le (1+\epsilon)C(T^*,D)\,\}$$2–$$R(T^*,D,\epsilon)=\{\,T\in\mathcal T(d)\mid C(T,D)\le (1+\epsilon)C(T^*,D)\,\}$$3 over Single Best while maintaining competitive predictive performance. The recommended practical regime is to choose $$R(T^*,D,\epsilon)=\{\,T\in\mathcal T(d)\mid C(T,D)\le (1+\epsilon)C(T^*,D)\,\}$$4 so that $$R(T^*,D,\epsilon)=\{\,T\in\mathcal T(d)\mid C(T,D)\le (1+\epsilon)C(T^*,D)\,\}$$5 has 10–100 members (Kale et al., 17 Apr 2026).

Sequential decision-making further broadens the notion of a Rashomon Ensemble. Policies are trained by behavioral cloning, grouped by identical induced DTMCs verified through probabilistic model checking, and then filtered so that internal summaries $$R(T^*,D,\epsilon)=\{\,T\in\mathcal T(d)\mid C(T,D)\le (1+\epsilon)C(T^*,D)\,\}$$6 differ pairwise. The ensemble policy may be defined by majority vote,

$$R(T^*,D,\epsilon)=\{\,T\in\mathcal T(d)\mid C(T,D)\le (1+\epsilon)C(T^*,D)\,\}$$7

or, for stochastic policies, by averaging action distributions. The permissive policy

$$R(T^*,D,\epsilon)=\{\,T\in\mathcal T(d)\mid C(T,D)\le (1+\epsilon)C(T^*,D)\,\}$$8

is then model-checked directly. In the taxi environment, all Rashomon policies are identical on the training objective of completing 5 jobs, but under the shifted requirement of completing more jobs they diverge; the majority-vote ensemble outperforms any single policy on 6 and 7 jobs, and the permissive ensemble maintains $$R(T^*,D,\epsilon)=\{\,T\in\mathcal T(d)\mid C(T,D)\le (1+\epsilon)C(T^*,D)\,\}$$9 success up to 10 jobs while reducing the induced state space from $|R_\epsilon|$0 to $|R_\epsilon|$1 states (Gross et al., 19 Dec 2025).

6. Trustworthiness, robustness, privacy, and limits

The trustworthiness claims around Rashomon Ensembles are substantial but explicitly qualified in the literature. On the positive side, uncertainty-aware explanations can expose epistemic uncertainty that single-model explanations conceal; wide intervals or low coverage flag features whose interpretation is unreliable, while narrow intervals with high coverage indicate stable feature–outcome relationships across plausible models. This is the central trustworthiness claim of the Rashomon PDP framework, especially for high-stakes domains such as healthcare, finance, or legal settings (Cavus et al., 19 Jul 2025).

A second positive theme is reactive robustness. "The Double-Edged Nature of the Rashomon Set for Trustworthy Machine Learning" analyzes a majority-vote ensemble of $|R_\epsilon|$2 near-optimal models under an adversarial perturbation model. If $|R_\epsilon|$3 with $|R_\epsilon|$4 and the $|R_\epsilon|$5 are independent, then

$|R_\epsilon|$6

so ensemble failure decays exponentially in $|R_\epsilon|$7. In the weaker “at least one model correct” sense,

$|R_\epsilon|$8

Empirical studies on sparse decision trees and linear models show that greater pattern diversity is associated with better adversarial resilience, while a practical compromise often occurs for ensemble sizes of approximately 10–50 models (Hsu et al., 26 Nov 2025).

The same paper emphasizes that this benefit is double-edged because privacy leakage grows with ensemble size. If

$|R_\epsilon|$9

then the expected pointwise KL divergence to the true conditional is bounded by

$$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$00

As $$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$01 increases, the variance term shrinks, so the ensemble more closely approximates the training distribution and leaks more information. The resulting robustness–privacy frontier is therefore intrinsic, not incidental (Hsu et al., 26 Nov 2025).

A different limitation arises in allocation settings. "Allocation Multiplicity: Evaluating the Promises of the Rashomon Set" argues that the set of equally good predictive models need not faithfully represent the space of equal-utility allocations when decisions are made by deterministic top-$$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$02 selection. In a healthcare case study, approximately 1,000 sampled models per method map to far fewer unique allocations; the full equal-utility allocation space can be on the order of $$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$03–$$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$04; less-discriminatory allocations that exist in the full space are not recovered by sampled Rashomon models; pairwise consistency of individual fate remains around $$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$05 for recovered allocations versus around $$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$06 over the full space; and 15–30% of qualified individuals receive zero chance of selection under sampled Rashomon models. The paper attributes these failures to incomplete samplers, deterministic cutoff rules, and structural bias that causes all near-optimal models to view some qualified individuals as risky. This suggests that predictive multiplicity does not automatically translate into allocation diversity or fairness (Jain et al., 20 Mar 2025).

There is also work aimed at reducing multiplicity rather than exploiting it. "Resolving Predictive Multiplicity for the Rashomon Set" proposes outlier correction, local patching, and pairwise reconciliation for a collection of good models approximating a Rashomon set sample. Pairwise reconciliation iteratively identifies the most disagreeing model pairs on a validation set, determines which model is falsified on the disagreement region, and shifts that model’s predictions by a closed-form correction

$$R(\epsilon)=\{\,f\in F : L(f)\le L(f^*)+\epsilon\}\,.$$07

Across Adult, COMPAS, Folktables Mobility, and Folktables Travel, these procedures reduce variance, ambiguity, discrepancy, and disagreement rate by roughly 90%–99% while maintaining competitive accuracy, and the reconciled ensemble can then be distilled into a single interpretable model (Haghighat et al., 14 Jan 2026).

Taken together, these results delimit the concept precisely. A Rashomon Ensemble is not a guarantee of fairness, stability, privacy, or robustness by itself. It is a mechanism for exposing and operationalizing predictive multiplicity. Depending on how the underlying set is explored, filtered, weighted, and mapped to decisions, that multiplicity can support trustworthy explanations, sample-efficient active learning, robust forecasting, and verification-efficient policy design—or can reveal that single-model explanations are unstable, that allocation diversity remains unrealized, or that robustness gains come with increased information leakage.