Crimes against humanity have existed in customary international law for over half a century and are also evidenced in prosecutions before some national courts. The most notable of these trials include those of Paul Touvier, Klaus Barbie, and Maurice Papon in France, and Imre Finta in Canada. But crimes against humanity are also deemed to be part of jus cogens—the highest standing in international legal norms. Thus, they constitute a non-derogable rule of international law. The implication of this standing is that they are subject to universal jurisdiction, meaning that all States can exercise their jurisdiction in prosecuting a perpetrator irrespective of where the crime was committed. It also means that all States have the duty to prosecute or extradite, that no person charged with that crime can claim the “political offense exception” to extradition, and that States have the duty to assist each other in securing evidence needed to prosecute. But of greater importance is the fact that no perpetrator can claim the “defense of obedience to superior orders” and that no statute of limitation contained in the laws of any State can apply. Lastly, no one is immune from prosecution for such crimes, even a head of State.It would thus seem that prosecution of "crimes against humanity" requires a view of international law that, to say the least, places sovereignty concerns beneath those of human rights. In other words, it is essentially cosmopolitan, valuing humans as humans rather than as citizens.
As Adrian L. Jones writes in "Continental Divide and the Politics of Complex Sovereignty: Canada, The United States and the International Criminal Court," found in the Canadian Journal of Political Science, June 2006,
Though without territorial jurisdiction as such, its legal jurisdiction is potentially universal, and without regard to state borders (Rome Statute, 1998: art. 4(2)). In this crucial respect, the Rome Statute establishes a direct nexus between the ICC and individual persons. Individuals are both its primary subjects, pursuant to the principle of individual criminal responsibility (art. 25), and its ultimate objects, given the transnational values of human security that it embodies (Preamble, paras. 1-2). Though the ICC is in practical terms mediated by states under the complementary jurisdictional framework of the Rome Statute (arts. 1 and 17), the legal and normative significance of this relationship is fundamentally supranational in nature.However, there is one critical point that both sides must recognize: the ICC allows for States to prosecute their own criminals; it is only when they fail to do so that the ICC takes over jurisdiction. In other words, the cosmopolitan aim of the Court operates within certain sovereigntist constraints. Jones, again:
[A] case is inadmissible where it is being investigated or prosecuted by a State that has jurisdiction over it, unless the State is unwilling or unable genuinely to carry out the investigation or prosecution (art. 17(1)(a)).Now, all this is to say that the LD resolution does not literally prescribe defending or attacking the ICC; however, you can make a strong case that the perfect "test case" for the resolution, since it already exists, and since the U.S. has (quite famously) refused to join, is the ICC.
Regardless, nothing in the resolution requires that sovereignty be eliminated and violated willy-nilly in the service of prosecuting "crimes against humanity" in an international court, real or imagined. Then again, nothing requires that it can't. It's something the Affirmative and Negative may have to settle in the debate.