Kenneth G. Wilson (1923). The Columbia Guide to Standard American English. 1993.
debate (v.)
All Standard users approve the use of debate plus direct object: you may debate an issue or an opponent. Some Standard users also assert that you may debate about or on a subject as well and that you may debate in or within your own mind on, about, over, or concerning a question. Certain conservatives object to this use, however, so assess your audience carefully.