Post 2 of Towards Causal Foundations of Safe AGI, see also Post 1 Introduction.

By Lewis Hammond, Tom Everitt, Jon Richens, Francis Rhys Ward, Ryan Carey, Sebastian Benthall, and James Fox, representing the Causal Incentives Working Group. Thanks also to Alexis Bellot, Toby Shevlane, and Aliya Ahmad.

Causal models are the foundations of our work. In this post, we provide a succinct but accessible explanation of causal models that can handle interventions, counterfactuals, and agents, which will be the building blocks of future posts in the sequence. Basic familiarity with (conditional) probabilities will be assumed.

What is causality?

What does it mean for the rain to cause the grass to become green? Causality is a philosophically intriguing topic that underlies many other concepts of human importance. In particular, many concepts relevant to safe AGI, like influence, response, agency, intent, fairness, harm, and manipulation, cannot be grasped without a causal model of the world, as we mentioned in the intro post and will discuss further in subsequent posts.

We follow Pearl and adopt an interventionist definition of causality: the sprinkler today causally influences the greenness of the grass tomorrow, because if someone intervened and turned on the sprinkler, then the greenness of the grass would be different. In contrast, making the grass green tomorrow has no effect on the sprinkler today (assuming no one predicts the intervention). So the sprinkler today causally influences the grass tomorrow, but not vice versa, as we would intuitively expect.

Interventions

Causal Bayesian Networks (CBNs) represent causal dependencies between aspects of reality using a directed acyclic graph. An arrow from a variable A to a variable B means that A influences B under some fixed setting of the other variables. For example, we draw an arrow from sprinkler (S) to grass greenness (G):

*A causal graph representing our running example. The sprinkler (S) influences the greenness of the grass (G).*

For each node in the graph, a causal mechanism of how the node is influenced by its parents is specified with a conditional probability distribution. For the sprinkler, a distribution $p (S)$ specifies how commonly it is turned on, e.g. $P (S = on) = 30 %$ . For the grass, a conditional distribution $p (G ∣ S)$ specifies how likely ...