Background

When and why use this package?

People make intuitive judgments about the relative causal responsibility of events that contributed to an outcome. Recently, cognitive scientists have developed computational models of these causal judgments. This package allows one to compute the predictions of two of these models. It is designed for scientists who want to test these models’ predictions, or for anyone curious about them.

These models have a particular scope: they are focused on causal selection. Causal selection is the process by which people judge the relative contribution of different causes of an outcome. Causal selection occurs for example when you think that a lightning bolt is the main cause of the forest fire, and regard the presence of oxygen in the air as a `background factor’, even though both were necessary for the fire to occur. Or it occurs when you think that the presidential candidate won the election because he won in the swing state rather than because he won in his party’s stronghold (even if winning both states were necessary for the victory).

In contrast, these models are not trying to give an account of causal learning (how people infer what happened in a particular case, or how they learn that some things cause other things in general), or an account of how people decide whether something is a cause or not a cause of an outcome. For more on these important distinctions see p.2 in this paper.

Technical description of the model implementations

The models supported by the package are the Necessity-Sufficiency (NS) model (Icard et al., 2017) and the Counterfactual Effect Size (CES) model (Quillien, 2020; Quillien & Lucas, 2023). See the linked papers for a formal description of these models. Here I discuss particular implementation details.

Both models first generate a probability distribution over counterfactual worlds. The way this distribution is generated is described here. Below I discuss the computations that are then applied on the basis of this distribution.

Necessity-Sufficiency model

Icard et al. (2017) posit that causal judgments are a weighted sum of two measures called Necessity and Sufficiency:

$\kappa_{C\rightarrow E} = P(C)\text{Sufficiency}(C\rightarrow E) + (1-P(C))\text{Necessity}(C\rightarrow E)$,

where $P(\cdot)$ is the probability distribution over possible counterfactual worlds. The authors do not commit to a particular way of operationalizing Sufficiency and Necessity, but we picked operationalizations that i) were based on suggestions in the original paper ii) have done a good job of accounting for causal judgments relative to alternative possible operationalizations.

We compute Sufficiency as:

$\text{Sufficiency}(C=c\rightarrow E=e) = P(E_{C=c}|C=\neg c, E=\neg e)$.

In words, we condition on the counterfactual worlds where $C$ and $E$ do not take their actual-world values, and compute the proportion of these counterfactual worlds where a counterfactual intervention setting $C$ to its actual-world value ends up setting $E$ to its actual-world value.

We define $\text{Necessity}(C=c\rightarrow E=e)$ as 1 if, in the actual world, an intervention setting $C$ to $\neg c$ would prevent $E=e$ from happening. Necessity is 0 otherwise.

Counterfactual Effect Size model

The CES model computes the Pearson correlation between $C=c$ and $E=e$ in the distribution over counterfactual worlds.

Our implementation of the CES model is identical to the version described in Quillien & Lucas (2023), in settings where there is no confounding between $C$ and $E$—that is, settings where $P(E|C)=P(E|\text{Do}(C))$. Those settings constitute the vast majority of published experiments on causal judgment.

In settings where there is confounding, the current implementation differs slightly from the model defined in Quillien & Lucas (2023, supplementary information). In the current implementation, the probability distribution over counterfactual possible worlds is generated in a way that guarantees $C$ is independent from its non-descendants in the causal model (see Step 4 in the description here). This ensures that the correlation between $C$ and $E$ across counterfactual worlds is not confounded.

This procedure differs from the procedure proposed in the CES papers, which requires performing counterfactual interventions in worlds that are already counterfactual (I thank Shubhamkar Ayare for pointing this out to me). Because the new procedure is simpler (and arguably truer to the original spirit of the CES model), and because there are almost no data on people’s causal judgments in confounded cases that would help arbitrate between the old and the new procedure, I choose to implement the new procedure here.