Split Decisions, One Node at a Time

CART-style decision trees are grown greedily, and at each node they typically choose the split that maximizes Gini impurity or entropy reduction rather than the split that most directly reduces misclassification error. Why?

Misclassification error can only be used with continuous features, while Gini and entropy require categorical features

Gini and entropy are more sensitive to shifts in class probabilities, so they can distinguish between splits that raw misclassification error would rate as equally good, even though the search is still greedy and only optimizes one node at a time

Misclassification error cannot be defined once there are more than two classes

Gini and entropy always produce a globally optimal tree, unlike greedy misclassification-based splitting