Possible world

As explained in Causal AI

A possible world is a hypothetical state of affairs representing how a causal system might have unfolded under different conditions.

A possible world is a way the world is or could be. In causal reasoning, the actual world contains observed outcomes, while hypothetical worlds represent alternative ways a data-generating process could have unfolded. section 8.4.1

Counterfactual analysis distinguishes related kinds of worlds and outcomes:

• Actual world: the possible world produced by the observed unfolding of the data-generating process. section 8.4.1
• Hypothetical world: a possible world with unobserved event outcomes, often created by changing a condition through intervention. section 8.4.1 section 8.4.3
• Potential outcomes: outcomes of the same variable across different possible worlds. section 8.4.1
• Parallel worlds: a set of possible worlds sharing common and differing attributes, represented for counterfactual queries by a parallel world graph. section 8.4.1

A hypothetical condition is modeled with an ideal intervention. Graph surgery removes incoming edges to the intervened variable, allowing downstream outcomes to differ from those in the actual world. In structural causal models, exogenous variables determine hypothetical-world values; observed actual-world information is propagated into the intervention-defined world. section 8.4.3 section 9.1.3

Changing engagement in an online game

Suppose engagement was low and in-game purchases equaled 50. A counterfactual question asks what purchases might have been if engagement had been high. Intervening on engagement creates a hypothetical world where its incoming causes are removed, so the purchase outcome can differ from the observed outcome. section 8.4.3

Figure 8.16 The graph representing the possible world with the hypothetical conditional is simpler than the graph representing the actual world.

Use the graph comparison to see why an intervention-defined hypothetical world can be simpler than the actual world: its edges may form a subset of the actual world's edges. This descending complexity is an algorithmic rule of thumb for reducing instability. section 8.4.5

How Causal AI covers it

How deep it goes

Defines world types, potential outcomes, graph surgery, and inference, while deferring general counterfactual algorithms.

Examples

Uses an aspirin outcome, an online-gaming intervention, Netflix world graphs, and machine-learning feature changes.

What it assumes

Assumes causal variables and interventions, while defining possible-world terminology and potential outcomes explicitly.

What you can do after

Evaluate counterfactual queries and identify feature changes that could alter predictions or provide algorithmic recourse.

How it connects

Connects counterfactuals, potential outcomes, structural causal models, causal graphs, interventions, and explainable AI.

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Related concepts

• actual worldincludes · An actual world is the causal-model representation corresponding to the observed condition and its realized evidence.
• counterfactual reasoningused by · Counterfactual reasoning examines hypothetical outcomes under conditions, actions, or policies different from those that actually occurred.
• parallel world graphused 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.
• interventionconfigured by · An intervention is a deliberate, externally imposed change or control applied to a variable or system to alter or assess its behavior or outcomes.
• stochastic interventionuses · A stochastic intervention is an intervention that assigns or changes variables according to a probability distribution rather than fixing them to a single value.

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.