Parallel worlds account

As explained in Causal AI

The parallel worlds account is an approach to counterfactuals that represents an alternative outcome in a world differing from the observed world in a causal event.

A parallel worlds account answers a counterfactual by holding the observed world as evidence and modeling an alternative world where a causal event changed. It addresses questions such as whether a different decision would have produced a better outcome, rather than merely predicting what usually happens. section 1.2.3 section 8.0

The account separates the worlds and their roles:

• An actual world contains observed event outcomes; a hypothetical world contains no observed outcomes. section 8.4.1
• Potential outcomes are outcomes of the same variable across differing possible worlds. section 8.4.1
• Parallel worlds share common attributes while differing in the causal event under consideration. section 8.4.1
• A parallel world graph represents these worlds and supports counterfactual identification and inference. section 8.4.1

Operationally, construct or derive a generative causal model, condition on evidence from the actual world, apply the alternative action in a hypothetical world, and infer its outcome. Conditioning preserves information about the particular observed case, distinguishing counterfactual distributions from broader interventional distributions. section 9.2 section 9.3.4

Monty Hall: switching after a loss

A player who stayed with the first door and lost can ask whether switching would have won. Build a parallel-world model, condition on the observed outcome in one world, and infer the outcome under switching in the other. The model represents the familiar result that switching wins two times out of three, while also answering the case-specific counterfactual question. section 9.2

Intervention versus counterfactual prediction

For a model that sets femur length to 46 cm, sampling from the intervention model estimates the hypothetical population distribution. Reusing the posterior distribution of exogenous variables from the actual case produces counterfactual samples, which can be narrower because they retain observed-world constraints. section 9.3.4

Figure 9.7 The Monty Hall problem. Assuming the player initially chooses the first door, two out of three times the switching strategy will lead to a win. This illustration assumes the first door is chosen, but the results are the same regardless of the initial choice of door.

Use the Monty Hall outcome diagram to compare possible switching outcomes and see why switching wins two times out of three. section 9.2

How Causal AI covers it

How deep it goes

Builds possible-world terminology, graphical models, interventions, evidence conditioning, and counterfactual sampling workflows.

Examples

Uses relationship decisions, aspirin outcomes, Monty Hall switching, femur-length interventions, and generative image models.

What it assumes

Assumes a causal model and observed-world evidence while defining possible-world terminology explicitly.

What you can do after

Evaluate alternative actions by conditioning on observed evidence and simulating outcomes in a causal model.

How it connects

Connects counterfactuals with causal inference, potential outcomes, interventions, causal models, and generative graphical models.

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Related concepts

• pyro.doproduced by · pyro.do is a Pyro function that transforms a probabilistic model to represent an intervention fixing a named variable to a specified value.
• counterfactual outcomeuses · A counterfactual outcome is a hypothetical result that would have occurred under a condition, action, or intervention different from the one observed.
• counterfactual reasoningused by · Counterfactual reasoning examines hypothetical outcomes under conditions, actions, or policies different from those that actually occurred.
• parallel world graphimplemented by · A parallel world graph is a graph representation that places variables from multiple counterfactual worlds together without necessarily permitting the same separation relations as a counterfactual graph.

This explainer was generated by Manning's knowledge graph from the text of Causal AI. The section links point to the parts of the book it draws on.