This is a common misconception. Ships never sail with empty cabins. Every ship from every major cruise line sails at over 95% occupancy. And most often, they are at absolute 100% occupancy.
http://www.f-cca.com/downloads/2013-cruise-industry-overview.pdf (See Page 6, bullet point #10). Now, they may have to "flash sale" some cabins, or dole them out to the highest producing agents to re-sell to their best customers for a song. Or blast email their most loyal guests within driving distance of the departure port. But they do not leave port with empty beds. Given
DCL's pricing structure, they have a lot of leeway (pardon the nautical pun) to play around with pricing to make sure that every cabin is full. If they can't fill the cabin at $1,600 per person, they will lower the price until they do. You may never see these lower prices as they may not be offered to the general public. But no cruise line is going to turn down the on board expenditures generated by a cabin, even if they have to get people on the ship for $1 per person.