First, it would never been cheaper to book a double for a single passenger. It could be the same price, but not cheaper.
The total price for a cruise is broken down into three parts; the cruise fare, the port fees (also called non-commissionables or NCF's), and the tax.
Normally, when a single is cruising, the cruise line will charge double the cruise fare, charge single the NCF's, and charge single for the tax. This is referred to as a 200% single supplement. Sometimes, a cruise line will offer a special whereby they only charge a single price for a cabin; this is referred to as a 100% single supplement. Or they may be offering a special where they charge a 125% or 150% single supplements. We use to see these alot more in the past than we do now.
Now, while some cruise lines will charge once for the NCF's, which is the way it's suppose to be done, other cruise lines will charge double the NCF's for a single, which is just another way to make more profit on a single.
And yet NCL does it differently than everyone else. If you book one of their special single cabins, you'll only pay a 100% single supplement and once for the NCF's. However, if you book any other cabin, then they'll charge you a 200% single supplement and double the NCF's.
Hope all that makes sense.
But let's get back to the original statement I made that booking a double when only a single is traveling will never result in a cheaper price. Here's why;
Let's say you book a cabin and the cruise fare is $500, the NCF's are $150, and the taxes are $50. If you book this as a double, the total price for two people would be $1400. Of course, when you show up at the terminal and announce the other person is not coming (or don't tell them - they'll obviously find out when the ship sails), they will refund the taxes to the credit card used for the purchase. So the total amount charged will be $1350.
Now, if you booked this as a single, the price would be $1200 (double the cruise fare, single the NCF's, single the taxes). However, if you're dealing with a cruise line that double sthe NCF's (which some will and some won't), then the price will increase to $1350.
So, as you can see, there is no benefit whatsoever to book two people in a cabin knowing that only one person will be sailing. And, if anything, this could actually hurt someone else since cruise lines passenger loads are based on how many people are booked in each type of cabins. I won't go into a long explanation about how all that works, but understand that on a cruise that's full, it could mean the difference between a family of four being able to get a quad cabin or having to buy two double cabins.
Bottom line is for singles to look at the total amount for the cabin when comparing cruises. Sometimes what appears to be a more expensive price on one cruise could actually end up costing less than another cruise that's advertised for less money.
Now, with all that said, I'll add a postscript; it is possible a cruise line would advertise a special that is based on double occupancy only and not allow the special for singles, triples or quads. However, I've not seen a situation like this in a very very long time. So the chances of that being the case is extremely slim and none.