A balloon debate is a debate in which a number of speakers attempt to win the approval of an audience. The audience is invited to imagine that the speakers are flying in a hot-air balloon which is sinking and that someone must be thrown out if everyone is not to die.
Each speaker has to make the case why they should not be thrown out of the balloon to save the remainder. Typically each participant speaks on behalf of a famous person, profession, fictional character, etc.
Modern television has adopted the style, with individuals making their own cases. The first of this genre is probably the Big Brother format of reality television series. It is also used in English GCSE courses.