I have two very large colonies sitting next to the divisions (splits) from another colony which are much smaller in size. These were cut down splits (and the re-splits from one of those when I was trying to fix my initial splitting mistakes). As such I had four small colonies next to my two big girls (four deeps in one colony and a single deep and six mediums in the other). I put TWO robbing devices on each of the smaller hives after a few hours when it was clear I was going to have a problem.
The inner one is essentially an entrance reducer/mouse guard made of perforated metal. I had it closed down to about a one and half bee width. The outer anti-robbing screen is a more traditional wooden frame with bee-proof screen front and closed down to within a one-bee width. Even after several weeks there were times when there were lots of bees inside the outer layer, but close watching showed that they were just trying to get out, not in to steal some honey, Probably orienting young bees, not robbers. Occasionally when it got too crazy I would take off the outer device briefly and release the bees and let them find their way back in after their flights, which they always did by nightfall.
Of the four smaller colonies one was always queen-right (the original queen), and the other three attempted to make their own. Two of the those three didn't have young-enough eggs/larva for successful conversion to queens (totally operator error) and were eventually recombined with their queen. The fourth made emergency cells (how many I do not know since I was so gun-shy from fouling up the original split that I stayed completely out of the hive the whole time) and a queen was hatched, got herself out and mated and is now laying up a storm, even though the anti-robbing devices were always on her hive through out this process. In fact one is still on and will remain so until her first round of brood hatches and it is large enough to defend it itself once again. The original queen who was just newspaper combined with the last of her failed splits a week ago today should be big enough to be on her own again some time this week.
The experience has made me a believer in a preventive anti-robbing strategy when you have unequal-sized hives in close proximity. It's amazing to me that robber bees are deterred by the screens/frames so well, but they are. Even when their own hives have identical devices. (Though to be one the safe side with my homemade robbing screens, I locate the reduced entrance point in different parts of the framework, so they aren't exactly the same.)
You may think that having a small entrance would result in massive traffic jambs, but the bees seem to cope quite well. My largest hive (1 deep + 6 mediums) is a resolutely top-entrance colony. And that enormous quantitity of bees comes and goes out of a single 1" diameter hole. They do have a conventional lower entrance but it is rarely used, perhaps one or two mortuary and hive-cleaning bees an hour use it. My point is that the bees will get used to quite small entrances, and perhaps may do quite well with robbing screens in place for most of the time. That assumes, of course, that there is other, screened, ventilation capacity beyond the clamped down entrances.
I have toyed with the idea of leaving the outer anti-robbing devices on all the hives most of the time to allow the bees to become accustomed to them. That way in a dearth, or for some other reason, you'd only have the transition to a much-reduced hole, not the sudden imposition of the full screen itself. Seems as if it might make for less panicky confusion.
The reason I use two devices is that it increases the control points for the guard bees. They usually have some stationed outside on the face of the hive near the entrance point. Then there are guards patrolling the space underneath the anti-robbing screen and near the entrance reducer. And I assume there are addtional guard bees just inside there waiting to dispatch any (un?)lucky bee that has managed to get that far. Also if I have two devices on, the outer one can be removed briefly without exposing the entire entrance.
We had a brief mini-dearth a few weeks ago, which was a practice run for late summer when robbing season gets underway in earnest. I was caught out by it last summer (my first year - who'd have thought my sweet girls would morph overnight into hardened honey-felons?) but this year I will have the screens on every entrance and be ready for the inevitable attacks.
Edited to add: I run screened bottom boards over solid bottom boards to allow for sticky boarding all the time. I make sure that the sticky board slot is carefully bee-screened because I found the hives stayed calmer when robbers were kept away from under the screen floor of the hive. I also have ventilation shims with a wide-variety of ventilation holes in them. These are generally screened on the inside to keep bees from using them as alternate entrances. I have taken to double screening them from the outside as well, just to keep robbers farther away from the hive interior. I want my bees to feel secure within the hive and to focused their watchfulnees on the actual entrance points. A side benefit is that I am seeing wax moths caught on the outside of the double screening which makes them easy to find and dispatch.
Enj.