Keep a couple of ducks to keep them happy
You can keep just one duck, obviously, but you shouldn't and here's why. One black hen, a couple or ducks, 3 brown bears, 4 running hares… Remember this verbal game? If you do, you probably drank too much in your early 20's ha-ha… However, my loose point is – it mentions a couple of ducks.
Ducks are very sociable birds and they really love being around each other, in particular, if they are the same breed. On the water, they may venture off a small distance away from each other but more often than not ducks stick close together (almost obsessively).
It's for this reason that I recommend keeping ducks in pairs at least and preferably a male and a female. I once had an inseparable pair of Khaki Campbell ducks and unfortunately one evening a fox got the female. For the next several weeks, my drake was one sad, depressed duck and it took time plus several new additional ducks for him to come good but I reckon if I had left him on his own he would have slowly died of loneliness – true story!
Anyway, no you shouldn't keep just one duck because he or she will be a whole lot happier with a mate or some friends to gaggle around with and quack to.