# Causal Counterfactuals Reconsidered

arXiv: https://arxiv.org/abs/2512.12804 · HTML: https://mlsanity.com/paper/2512.12804/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 14 Dec 2025.

## Builds on (most cited first, 12 of 12)

- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [Personalized Decision Making -- A Conceptual Introduction](https://mlsanity.com/paper/2208.09558/) (2022)
- [Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributions](https://mlsanity.com/paper/2301.05893/) (2023)
- [The Counterfactual NESS Definition of Causation](https://mlsanity.com/paper/2012.05123/) (2020)
- [Personalised Decision-Making without Counterfactuals](https://mlsanity.com/paper/2301.11976/) (2023)
- [Intervention and Conditioning in Causal Bayesian Networks](https://mlsanity.com/paper/2405.14728/) (2024)
- [Modeling Discrimination with Causal Abstraction](https://mlsanity.com/paper/2501.08429/) (2025)
- [Large Language Models as Nondeterministic Causal Models](https://mlsanity.com/paper/2509.22297/) (2025)

## Built on by (most cited first, 1 of 1)

- [Robust Counterfactual Policy Optimisation via Nondeterministic Causal Models](https://mlsanity.com/paper/2608.02893/) (2026)

## Abstract (arXiv)

I develop a novel semantics for probabilities of counterfactuals that generalizes the standard Pearlian semantics: it applies to probabilistic causal models that cannot be extended into realistic structural causal models and are therefore beyond the scope of Pearl's semantics. This generalization is needed because, as I show, such probabilistic causal models arise even in simple settings. My semantics offer a natural compromize in the long-standing debate between Pearl and Dawid over counterfactuals: I agree with Dawid that universal causal determinism and unrealistic variables should be rejected, but I agree with Pearl that a general semantics of counterfactuals is nonetheless possible. I restrict attention to causal models that satisfy the Markov condition, only contain realistic variables, and are causally complete. Although I formulate my proposal using structural causal models, as does Pearl, I refrain from using so-called response variables. Moreover, I prove that my semantics is equivalent to two other recent proposals that do not involve structural causal models, and that it is in line with various comments on stochastic counterfactuals that have appeared in the literature more broadly. Throughout I also reflect on the universality of the Markov condition and explore a novel generalization of causal abstractions