This case of dependency with a relation X − Y may arise for example if the two variables are linked by a logical or mathematical formula, and not related by a causal relation.

As an example, if we write that the productivity P in a firm is equal to the total added value VA of the firm divided by the total number of employees N , the two variables P and VA are linked by a mathematical expression: $P=\frac{VA}{N}$. By observing VA and knowing N we can immediately deduce P , but the opposite is also true as knowing P and N gives VA , with equivalent mathematical relation, without any notion of an underlying system that could have generated one of the variable from the other.

We do not consider this case in the problem setting.