In this paper we look for a solution to a land division problem that could be applied to different types of disputes when the arbitrator has a very limited information about the agents’ preferences. The solution must be fair and efficient under the constraint of the limited information available to the arbitrator. To this scope, we propose to use the concept of equal-opportunity equivalence defined by Thomson (Soc Choice Welfare 11:137–156 1994). We prove the existence of an efficient and equal opportunity equivalent allocation for a land division problem and we present a simple procedure to implement a rule that selects such allocation at each preference profile.