We consider the classical problem of allocating m objects to n agents where \(m \ge n.\) In the \(m=n\) case, we analyze preference domains (called UPN-priority domains) where every strategy-proof, non-bossy and unanimous profile neutral (UPN) allocation rule is a priority rule. We show that a simple condition called the closure property characterizes priority domains. The only domain satisfying the closure property and a mild richness condition is the universal domain. We extend this result to the \(m >n\) case. We also consider the case where allocation rules satisfy a stronger neutrality property.
