We consider a natural analogue of the graph linear arrangement problem for posets. Let be a poset that is not an antichain, and let be an order-preserving bijection, that is, a linear extension of . For any relation of , the distance between and in is . The average relational distance of , denoted , is the average of these distances over all relations in . We show that we can find a linear extension of that maximises in polynomial time. Furthermore, we show that this maximum is at least , and this bound is extremal.