An example of a constraint relation, rather than a causal relation, is the mathematical link between a firm's productivity and added value. If the productivity $$P$$ in a firm equals the total added value $$VA$$ divided by the total number of employees $$N$$, the variables are linked by the expression: $$P=\frac{VA}{N}$$. Observing $$VA$$ and knowing $$N$$ allows one to immediately deduce $$P$$, and conversely, knowing $$P$$ and $$N$$ gives $$VA$$. This equivalence exists without an underlying causal system generating one variable from the other, making it a deterministic constraint.

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In generative cause-effect models, the constraint relation assumption excludes cases where a dependency with an undirected relation $$X - Y$$ arises because two variables are linked by a logical or mathematical formula, rather than a causal relation. When variables are linked by an equivalent mathematical relation, one can be deduced from the other without any notion of an underlying causal system generating one variable from the other. Such deterministic, non-causal dependencies are not considered in the standard generative cause-effect problem setting.

Constraint Relation Assumption in Generative Cause-Effect Models

 Isabelle Guyon, Alexander Statnikov, Berna Bakir Batu (2019)
Cause Effect Pairs in Machine Learning (The Springer Series on Challenges in Machine Learning)
https://www.amazon.com/Effect-Machine-Learning-Springer-Challenges/dp/3030218090

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