думаю, фразеологизмы следует переводить не в буквальном значении, лучше перевести то, что он означает

Почему бы тогда по-русски просто не сказать "обсуждать"?

Анастасия,
Discussion - это обсуждение в самом общем значении, а дебаты - это официальное публичное мереприятие: a formal discussion on a particular matter in a public meeting or legislative assembly, in which opposing arguments are put forward and which usually ends with a vote.
Вести дебаты:
https://books.google.com/ngrams/graph?content=conduct+debates%2C+run+debates&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cconduct%20debates%3B%2Cc0%3B.t1%3B%2Crun%20debates%3B%2Cc0

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