Causal Reasoning with Continuous Outcomes

We describe an attempt to understand causal reasoning in situations where a binary cause produces a change on a continuous magnitude dimension. We consider established theories of binary probabilistic causal inference – ΔP and Power PC – and adapt them to continuous non-probabilistic outcomes. While ΔP describes causal strength as the difference of effect occurrence between the presence and absence of the cause, Power PC normalizes this difference with the effect base-rate to obtain a proportional measure of causal power, relative to the maximum possible strength. Two experiments compared the applicability of each approach by creating scenarios where binary probabilistic scenarios were directly mapped onto inference problems involving continuous magnitude dimensions. Results from counterfactual judgments tentatively indicate that people reason about causal relations with continuous outcomes by adopting a proportional approach when evaluation preventive causal powers, and a difference approach in generative scenarios.