It starts here (and with the Bloggingheads above), then here and here, then here, here, here, and ending (for now) here. The debate is centered on Posner's new book, The Perils of Global Legalism, which I have not yet read but which seems to argue that international law is generally not effective.
One interesting aspect of the debate is the players: Farrell is an international relations scholar, Posner is a lawyer. Posner is advocating more rigorous methodological inquiry by lawyers (e.g. applications of rational choice theory) while Farrell is warning of their limitations. Farrell cited Daniel Davies on the topic:
The Folk Theorem in game theory states that any outcome of a repeated game can be sustained as an equilibrium if the minimax condition for both players is satisfied. In plain language, it can be summarised as stating that “if we take strategic considerations into account, there is a game-theoretic rationale for practically anything”.
To which Posner responded:
I agree with Henry’s discussion of the limits of rational choice theory and so don’t understand why he thinks I commit the fallacies that he describes. It would be one thing if I said that states’ compliance with treaty X is consistent with rational choice because the folk theorem allows for cooperation, while states’ noncompliance with treaty Y is consistent with rational choice because the folk theorem allows for noncooperation. Or if I said that states comply with treaty W because they care about their reputations for complying with W but that states fail to comply with treaty Z because they don’t care about their reputations for complying with Z. But I never make such arguments, instead ruling out the first type of argument as uninformative and the second as circular. My account of international law is parsimonious, and the usual criticism directed at it is not that it can be manipulated so as to explain anything, but that in fact it fails to explain why certain legal regimes have been successful. So, for example, if in fact states do overcome a collective action problem and collectively sanction states that violate human rights, that is a problem for my theory, not something that I try to explain away by asserting that states have an interest in (say) having a good reputation for enforcing human rights treaties.
I'm not going to discuss this exchange more broadly because I don't have the time to do it justice, but this is the blogosphere at its best: two brilliant scholars, from different disciplines, arguing intelligently about real problems and real research. This is the "invisible college" that DeLong refers to. If you are at all interested in international law, human rights, state sovereignty, or high-minded debate, please read these posts.