# Causal Reasoning with Continuous Outcomes

- Ahmad Azad Ab Rashid,
*Cardiff University*
- Marc Buehner,
*Cardiff University*

## Abstract

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.

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