When a decision-tree attribute is categorical rather than continuous, the tree may split it into one branch per value — a multiway split — which removes the need to search for an optimal split point but produces sprawling trees that lose interpretability, raise variance, and exhaust the data along each branch. Multiway splitting also introduces a systematic bias toward attributes with many values, because finer partitions are more likely to yield pure leaves regardless of true predictive relevance; the gain ratio corrects this by normalizing information gain against the gain achievable from an arbitrary partition of the same arity, so an attribute is preferred only when it beats a random split of equal width. Because any multiway split is reproducible by recursive binary splits, multiway splitting adds no expressive power to the hypothesis class, which is why binary splits remain the default in supervised decision-tree learning.
When a decision-tree attribute is categorical rather than continuous, the tree may split it into one branch per value — a multiway split — which removes the need to search for an optimal split point …