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L4-09 · Counterfactual reasoning

Use abduction, action, and prediction to answer a counterfactual in an explicit structural model.

Level 4 icon Level 4 · Undergraduate
Objective. Use abduction, action, and prediction to answer a counterfactual in an explicit structural model.
Before this lesson. L4-01, L4-06, L4-07
Hands-on lab. Confounding and intervention

Learn

A counterfactual asks what would have happened to the same unit under a different action. It links an observed situation to an alternative situation through shared background factors. An interventional population average alone does not usually specify this cross-situation link for one observed individual.

Structural models answer counterfactual questions in three steps. Abduction updates beliefs about background variables using the observed evidence. Action replaces the mechanism specified by the alternative intervention. Prediction computes the outcome under the modified model using the updated background beliefs from the original situation.

The answer can depend on untestable details of the structural functions. Two models can agree on observed data and even on some intervention distributions, yet disagree on individual counterfactuals. Report the model and evidence explicitly. A fitted predictor with one input edited is not automatically a counterfactual model.

Practice

Solution

Abduction gives U=10-3(2)=4. The alternative action sets X to zero. Prediction with the same U gives Y=3(0)+4=4 for this modeled unit.

Check your understanding

Which step uses the factual evidence to update background variables?

Show the answer

B. Abduction

Abduction infers background information from factual evidence. Action changes the mechanism, and prediction evaluates the changed model with that information.

Sources

This lesson draws on Pearl, 2009Peters et al., 2017.

Next: L4-10 · Causal machine learning, transport, and fairness

References
  1. Pearl, J. (2009). Causal inference in statistics: An overview. Statistics Surveys, 3(none), 96–146. 10.1214/09-ss057
  2. Peters, J., Janzing, D., & Scholkopf, B. (2017). Elements of Causal Inference. https://mitpress.mit.edu/9780262037310/elements-of-causal-inference/
  3. Bareinboim, E. (2025). Causal Artificial Intelligence: A Roadmap for Building Causally Intelligent Systems. https://causalai-book.net/