What Carneades did was basically public forum debate like that practiced by the scholastic National Speech and Debate Association. There is a different question about public policy established every month. For example in April of this year the question was "Resolved: On balance, the benefits of creating the United States Space Force outweigh the harms." Teams of two debaters engage in a timed, judged debate, switching back and forth with 8 speeches and 3 cross examinations. The judge picks the winning team based on how persuasive their arguments and final summation were, just like a court case.
In a single tournament, students will debate the con side twice and the pro side once, or vice versa based on a random drawing. How the young debaters actually feel about the question, or what they think the truth is doesn't matter. The whole point is to win the debate, the truth be damned. This has been going on since 1925 by the way, and it has been a major training ground for lawyers and politicians in our country. I did it for four years in high school and it was one of the best things that has ever happened to me intellectually. I met a lot of smart, pretty girls at the tournaments too.