Physical interference limits the utility of large-scale multi-robot systems. We present an empirical study of the effects of such interference in systems with hundreds of minimalist robots. We consider the canonical multi-robot foraging task, and define a new parametrized controller. This controller allows for evaluation of spatial arbitration strategies along a continuum with the traditional homogeneous and bucket-brigading algorithms at each end. We present data from thousands of simulations which suggests that methods surprisingly close to homogeneous foraging, but augmented with limited arbitration, can improve both performance and reliability