# P2C: Path to Counterfactuals

arXiv: https://arxiv.org/abs/2508.20371 · HTML: https://mlsanity.com/paper/2508.20371/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 28 Aug 2025.

## Builds on (most cited first, 10 of 10)

- [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)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Efficient Search for Diverse Coherent Explanations](https://mlsanity.com/paper/1901.04909/) (2019)
- [Interpretable Predictions of Tree-based Ensembles via Actionable Feature Tweaking](https://mlsanity.com/paper/1706.06691/) (2017)
- [Constraint Answer Set Programming without Grounding](https://mlsanity.com/paper/1804.11162/) (2018)
- [FOLD-SE: An Efficient Rule-based Machine Learning Algorithm with Scalable Explainability](https://mlsanity.com/paper/2208.07912/) (2022)
- [Answer-Set Programs for Reasoning about Counterfactual Interventions and Responsibility Scores for Classification](https://mlsanity.com/paper/2107.10159/) (2021)

## Abstract (arXiv)

Machine-learning models are increasingly driving decisions in high-stakes settings, such as finance, law, and hiring, thus, highlighting the need for transparency. However, the key challenge is to balance transparency -- clarifying `why' a decision was made -- with recourse: providing actionable steps on `how' to achieve a favourable outcome from an unfavourable outcome. Counterfactual explanations reveal `why' an undesired outcome occurred and `how' to reverse it through targeted feature changes (interventions). Current counterfactual approaches have limitations: 1) they often ignore causal dependencies between features, and 2) they typically assume all interventions can happen simultaneously, an unrealistic assumption in practical scenarios where actions are typically taken in a sequence. As a result, these counterfactuals are often not achievable in the real world. We present P2C (Path-to-Counterfactuals), a model-agnostic framework that produces a plan (ordered sequence of actions) converting an unfavourable outcome to a causally consistent favourable outcome. P2C addresses both limitations by 1) Explicitly modelling causal relationships between features and 2) Ensuring that each intermediate state in the plan is feasible and causally valid. P2C uses the goal-directed Answer Set Programming system s(CASP) to generate the plan accounting for feature changes that happen automatically due to causal dependencies. Furthermore, P2C refines cost (effort) computation by only counting changes actively made by the user, resulting in realistic cost estimates. Finally, P2C highlights how its causal planner outperforms standard planners, which lack causal knowledge and thus can generate illegal actions.