When confronted with cloning which leaves the original alive, there is the known issue that the clone could want to replace the original (e.g. as seen in The 6th day). A shared consciousness is very strange to people as they experience at least twice as much information in a moment and have to deal with it, it's not popular. So if you are a "I wish it were me" person and don't like being at two different places/conversations/etc at once, what can you do?
A proposed solution is the rotating system: Original and clone change their duties daily. One day the original is at home, house-keeping and enjoying the otherwise free time while the clone is working, the next day it is the other way around. At midnight their brains will be synchronized with the Brain Override Security System™ (it is a lot like Version Control, really), so they share the memories of the day and keep the same personality. This way the consciousness is not shared per se, but there is little room for the "I wish it were me" problem. Waking up in the morning can be irritating, though. But usually the pairs can keep track of who is the original and who is the clone, although it's more like a self 1, self 2 mentality.
What could be the psychological consequences of such a rotating system? My guess is that it works for the normal human but there are always the exceptions. What are your thoughts?