The way I understand master keys work is that the lock has two "breaks" in each pin, instead of just one. So each pin has two positions that allow the lock to open, and you don't know which one belongs to the master key.
I think at least two locks would be required, and depending on how many pins and possible positions there are, more might be needed in case of a collision.
How about looking at the number of people who must be removed in order to bring the bus factor down to 1? We can call it the "bus co-factor" :). With the bus factor we're picking the most critical people first, and removing the least number of them; with the bus co-factor we're picking the least critical people first, and removing the greatest number of them.
There's probably already some name and many theorems in graph theory for both of these ideas.
Text messages are only the relatively boring first step in this kind of project. If these guys go on to implement IP/Vodka they can proudly follow in the footsteps of such
hacks as RFC 1149 :-) "The network smells a little slow today"
I presume that the way the lucid dream induction works is by blinking an LED when the onset of REM sleep is detected. There are other products out there already that do this; the idea is that you'll train yourself to notice any blinking red lights or objects in your dreams and associate that with realizing that you're dreaming.
When the collar closes, its spoke will have pulled apart a little bit under the tension and widened the gap. You'd need some kind of motorized grabber-puller collars to make this work.