The renvoi paradox in choice of law arises when two states’ laws each purport to select the other’s law. The barber paradox in the foundations of mathematics arises when a set is defined to contain all sets that do not contain themselves, or, more famously, when a barber shaves all men who do not shave themselves. Which state’s law applies? Does the set contain itself? Does the barber shave himself? Each answer implies its opposite.
Conflict of laws is not mathematics, but it could learn from how mathematicians escape the barber paradox: by modifying their theories to to exclude the kind of self-reference that can go so badly wrong. Renvoi too is a paradox of self-reference. Ordinary choice of law blows up into paradox not when one state’s laws refer to another’s, but when a single state’s laws refer back to themselves. The purpose of renvoi rules is to prevent this paradoxical self-reference from occurring; they work by ignoring some aspect of a state’s laws. When a choice-of-law rule selects a state’s law, it always necessarily selects something less than whole law.
The essay also features a dozen diagrams, extensive Sweeney Todd references, some subtle shade on your favorite choice-of-law methodology, and discussion of restricted and unrestricted versions of the Axiom of Comprehension.2 It may be the nerdiest thing I have ever written, and I do not say that lightly.