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.