The United States ought to submit to the jurisdiction of an international court designed to prosecute crimes against humanity.Debaters might wish to use the International Criminal Court in their rhetoric and argumentation, both for the affirmative and the negative.
Since the resolution doesn't specify the ICC, though, if you take your case in this direction, you'd better offer several reasons for the step. Here are several. Note that they might overlap; use the ones you think are best. (Have better ideas or counterarguments? Throw 'em in the comments.)
1. Although some LDers like to say that the word "ought" places the debate in the ethereal realm of ideals, the resolution is already contextualized in the "real world," by referring to the United States rather than to "nations" or "all nations."
2. The U.S. is already (in)famous for refusing to sign on to the ICC, making this topic particularly relevant, timely, and educational, provided that the ICC is the focus of the debate.
3. The phrase "crimes against humanity" is well established in international law; the ICC is expressly designed to prosecute such crimes, and thus offers clear definitions for the key terms in the debate.
4. The ICC is bound to enter the debate anyhow. Anytime an affirmative gushes about universally protecting human rights, or a negative hypothesizes ridiculous risks inherent to an international judicial system, opponents are going to say, "Well, that's an interesting possibility, but not exactly how it's playing out in the real world." Again, if the resolution presumes the existence of the United States, doesn't it also presume an extant global political and legal framework?
Some might cry "Policy!" and complain that this somehow dilutes the purity of Lincoln-Douglas debate. Maybe so. But it's the resolution we have, and we should make the best of it.