When scaling leaves a decision unchanged

THE IDEA

Read the example.

A positive affine change of one feature preserves its order. An exact threshold split can move its threshold by the same transformation and keep the same partition. This explains why ordinary decision-tree splits are often insensitive to feature units.

x ≤ t ⇔ ax + b ≤ at + b, for a > 0

Use it well

This is not a universal exemption from preprocessing. Approximate binning, numerical precision, regularisation and other parts of a pipeline may behave differently.