We consider a finite number of particles characterised by their positions
and velocities. At random times a randomly chosen particle, the follower,
adopts the velocity of another particle, the leader. The follower chooses
its leader according to the proximity rank of the latter with respect to the
former. We study the limit of a system size going to infinity and, under the
assumption of propagation of chaos, show that the limit equation is akin
to the Boltzmann equation. However, it exhibits a spatial non-locality
instead of the classical non-locality in velocity space. This result relies on
the approximation properties of Bernstein polynomials. We illustrate the
dynamics with numerical simulations.