Note on an Axiomatization of the Baldwin Rule

Goto and Nakada (2026) showed that the Baldwin rule can be characterized using Neutrality, Bottom Consistency, Faithfulness, Cancellation and Bottom Independence. While their proof relies on the technique of linear algebra and graph theory, in this note, we provide a simpler proof using purely combinatorial arguments based on permutations and amplified preference profiles, thereby providing a more transparent proof of the characterization.