Lotteries are a common way to resolve ties in assignment mechanisms that ration resources. We consider a model with a continuum of agents and a finite set of re- sources with heterogeneous qualities, where the agents’ preferences are generated from a multinomial-logit (MNL) model based on the...

We prove that in a market where agents rank objects independently and uniformly at random, there exists an assignment of objects to agents with a constant average rank (i.e., an average rank independent of the market size). The proof builds on techniques from random graph theory and the FKG...