# Recourse under Model Multiplicity via Argumentative Ensembling (Technical Report)

arXiv: https://arxiv.org/abs/2312.15097 · HTML: https://mlsanity.com/paper/2312.15097/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 65 references that are in the map.
- First posted on arXiv 22 Dec 2023.

## Builds on (most cited first, 30 of 35)

- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Predictive Multiplicity in Classification](https://mlsanity.com/paper/1909.06677/) (2019)
- [Towards Robust and Reliable Algorithmic Recourse](https://mlsanity.com/paper/2102.13620/) (2021)
- [On the Existence of Simpler Machine Learning Models](https://mlsanity.com/paper/1908.01755/) (2019)
- [Exploring the Whole Rashomon Set of Sparse Decision Trees](https://mlsanity.com/paper/2209.08040/) (2022)
- [Interpretable Predictions of Tree-based Ensembles via Actionable Feature Tweaking](https://mlsanity.com/paper/1706.06691/) (2017)
- [On Counterfactual Explanations under Predictive Multiplicity](https://mlsanity.com/paper/2006.13132/) (2020)
- [Argumentative XAI: A Survey](https://mlsanity.com/paper/2105.11266/) (2021)
- [Characterizing Fairness Over the Set of Good Models Under Selective Labels](https://mlsanity.com/paper/2101.00352/) (2021)
- [NICE: An Algorithm for Nearest Instance Counterfactual Explanations](https://mlsanity.com/paper/2104.07411/) (2021)
- [Robust Counterfactual Explanations for Tree-Based Ensembles](https://mlsanity.com/paper/2207.02739/) (2022)
- [Rashomon Capacity: A Metric for Predictive Multiplicity in Classification](https://mlsanity.com/paper/2206.01295/) (2022)
- [Robust Counterfactual Explanations for Neural Networks With Probabilistic Guarantees](https://mlsanity.com/paper/2305.11997/) (2023)
- [Empirical observation of negligible fairness-accuracy trade-offs in machine learning for public policy](https://mlsanity.com/paper/2012.02972/) (2020)
- [Predictive Multiplicity in Probabilistic Classification](https://mlsanity.com/paper/2206.01131/) (2022)
- [Interpreting Neural Networks as Gradual Argumentation Frameworks (Including Proof Appendix)](https://mlsanity.com/paper/2012.05738/) (2020)
- [A Survey on the Robustness of Feature Importance and Counterfactual Explanations](https://mlsanity.com/paper/2111.00358/) (2021)
- [Consistent Counterfactuals for Deep Models](https://mlsanity.com/paper/2110.03109/) (2021)
- [An Interpretable Model with Globally Consistent Explanations for Credit Risk](https://mlsanity.com/paper/1811.12615/) (2018)
- [Formalising the Robustness of Counterfactual Explanations for Neural Networks](https://mlsanity.com/paper/2208.14878/) (2022)
- [Selective Ensembles for Consistent Predictions](https://mlsanity.com/paper/2111.08230/) (2021)
- [Provably Robust and Plausible Counterfactual Explanations for Neural Networks via Robust Optimisation](https://mlsanity.com/paper/2309.12545/) (2023)
- [Variable Importance Clouds: A Way to Explore Variable Importance for the Set of Good Models](https://mlsanity.com/paper/1901.03209/) (2019)
- [Counterfactual Plans under Distributional Ambiguity](https://mlsanity.com/paper/2201.12487/) (2022)
- [Robust Bayesian Recourse](https://mlsanity.com/paper/2206.10833/) (2022)

## Built on by (most cited first, 15 of 15)

- [Robust Counterfactual Explanations in Machine Learning: A Survey](https://mlsanity.com/paper/2402.01928/) (2024)
- [Predictive Multiplicity of Knowledge Graph Embeddings in Link Prediction](https://mlsanity.com/paper/2408.08226/) (2024)
- [Interval Abstractions for Robust Counterfactual Explanations](https://mlsanity.com/paper/2404.13736/) (2024)
- [Rigorous Probabilistic Guarantees for Robust Counterfactual Explanations](https://mlsanity.com/paper/2407.07482/) (2024)
- [RobustX: Robust Counterfactual Explanations Made Easy](https://mlsanity.com/paper/2502.13751/) (2025)
- [Counterfactual Explanations for Model Ensembles Using Entropic Risk Measures](https://mlsanity.com/paper/2503.07934/) (2025)
- [Representation Consistency for Accurate and Coherent LLM Answer Aggregation](https://mlsanity.com/paper/2506.21590/) (2025)
- [Learning-Augmented Robust Algorithmic Recourse](https://mlsanity.com/paper/2410.01580/) (2024)
- [Robust Counterfactual Explanations under Model Multiplicity Using Multi-Objective Optimization](https://mlsanity.com/paper/2501.05795/) (2025)
- [Optimal Robust Recourse with Lp-Bounded Model Change](https://mlsanity.com/paper/2509.21293/) (2025)
- [ElliCE: Efficient and Provably Robust Algorithmic Recourse via the Rashomon Sets](https://mlsanity.com/paper/2602.07674/) (2026)
- [Argumentative Ensembling for Robust Recourse under Model Multiplicity](https://mlsanity.com/paper/2506.20260/) (2025)
- [Synthesising Counterfactual Explanations via Label-Conditional Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/2510.04855/) (2025)
- [Density-Guided Robust Counterfactual Explanations on Tabular Data under Model Multiplicity](https://mlsanity.com/paper/2605.30901/) (2026)
- [Target-confidence Recourse Using tSeTlin machines: TRUST](https://mlsanity.com/paper/2606.18832/) (2026)

## Abstract (arXiv)

Model Multiplicity (MM) arises when multiple, equally performing machine learning models can be trained to solve the same prediction task. Recent studies show that models obtained under MM may produce inconsistent predictions for the same input. When this occurs, it becomes challenging to provide counterfactual explanations (CEs), a common means for offering recourse recommendations to individuals negatively affected by models' predictions. In this paper, we formalise this problem, which we name recourse-aware ensembling, and identify several desirable properties which methods for solving it should satisfy. We show that existing ensembling methods, naturally extended in different ways to provide CEs, fail to satisfy these properties. We then introduce argumentative ensembling, deploying computational argumentation to guarantee robustness of CEs to MM, while also accommodating customisable user preferences. We show theoretically and experimentally that argumentative ensembling satisfies properties which the existing methods lack, and that the trade-offs are minimal wrt accuracy.