The Causal Uncertainty Principle

TL;DR

This paper introduces the concept of evidential states to explain the inherent trade-off between internal and external validity in causal inference, showing that the order of study operations affects causal conclusions.

Contribution

It presents a novel structural framework using evidential states to elucidate why causal study operations are non-commutative and how this impacts validity and generalisability.

Findings

Operations on evidential states do not commute, affecting causal claims.

Order of study steps influences the validity and transportability of findings.

Trade-off between causal precision and applicability is structurally explained.

Abstract

This paper explains why internal and external validity cannot be simultaneously maximised. It introduces "evidential states" to represent the information available for causal inference and shows that routine study operations (restriction, conditioning, and intervention) transform these states in ways that do not commute. Because each operation removes or reorganises information differently, changing their order yields evidential states that support different causal claims. This non-commutativity creates a structural trade-off: the steps that secure precise causal identification also eliminate the heterogeneity required for generalisation. Small model, observational and experimental examples illustrate how familiar failures of transportability arise from this order dependence. The result is a concise structural account of why increasing causal precision necessarily narrows the world to which findings apply.