A counterfactual outcome is what would happen under a hypothetical condition, considered alongside facts about what did happen. The question is not simply “What happens if engagement is high?” It is “For a player whose engagement was low and whose purchases were at most $50, what would their purchases have been if engagement had been high?” The observed low engagement conflicts with the hypothetical high engagement; the answer concerns that player under the alternative condition. section 8.2.4
Observed facts narrow the hypothetical
Let E be side-quest engagement and I be in-game purchases. The query P(I_{E=high} | E=low, I≤50) asks for possible purchases under high engagement, conditional on the player’s observed low engagement and purchases of at most $50. By contrast, P(H_{F=46}) asks about height under a hypothetical femur length of 46 cm without specifying an observed person; P(H_{F=46} | F=44, H=165) adds observed femur length and height to make it a counterfactual question. section 8.2.4 section 9.3
To reason about the alternative, a parallel-world model uses observations from the factual world as evidence and changes the condition in a hypothetical world. Inference then produces a distribution over outcomes in that world. This differs from predicting an outcome using the observed conditions alone: the question asks what could have happened after a different action. section 1.2.3 section 9.2
A practical workflow is:
- State the observed facts, the condition to change, and the outcome of interest. section 8.1.6
- Write a conditional query that separates the hypothetical intervention from the factual evidence. section 8.2.4
- Run inference with an appropriate causal model, and check what assumptions support the answer. section 8.1.6 section 10.6.2
Counterfactual outcomes can inform future decisions even when the original choice cannot be changed. A streaming service might ask whether subscribers who left would have stayed had a content deal succeeded; a promotion team might ask whether a customer who churned without an offer would have remained if offered one. Such answers are not automatically recoverable from ordinary records. Most records contain only one realized outcome per unit, and identifying a counterfactual from observational or experimental data can require additional assumptions. Deterministic allocation policies and simulations are special cases where an alternative outcome can sometimes be generated for the same initial case. section 8.1.2 section 10.1.3 section 10.6.2
