  We study fair allocation of indivisible goods when agents have matroid rank
valuations. Our main contribution is a simple algorithm based on the colloquial
Yankee Swap procedure that computes provably fair and efficient Lorenz
dominating allocations. While there exist polynomial time algorithms to compute
such allocations, our proposed method improves on them in two ways. (a) Our
approach is easy to understand and does not use complex matroid optimization
algorithms as subroutines. (b) Our approach is scalable; it is provably faster
than all known algorithms to compute Lorenz dominating allocations. These two
properties are key to the adoption of algorithms in any real fair allocation
setting; our contribution brings us one step closer to this goal.
