"I suppose that if you have a very light food bag, then one bag and one rope is all you need. Back when I led group trips, we were dealing with a lot of food, so splitting it up into two bags always made sense, so doing the double rope counterbalance method always seemed to work best.
"I can't attest to this, but it was once claimed that a bear can get to the (PCT method single rope), bite it, and pull it until the stick breaks, thereby releasing the food bag to drop."
I'll remain dubious of this kind of anecdote, repeated second hand, in the absence of documented reports. The UL ropes generally used for the PCT method are very slippery and thin, which basically turns said rope into very expensive bear floss in the event one should try to clamp down and pull on it. One thing for sure; he'd have the cleanest teeth in the 'hood. That said, in real bear country it would be prudent to use a spare tent stake instead of a stick, and a heavier biner.
"I think that with any method, as long as the rope is not tied off to a tree, and if the food bag or bags are high enough that a person can't reach them or any dangling ropes, then it ought to work. It certainly demands that the rope be over the tree branch way out from the trunk so that the little cubbies can't get to it, and the tree branch has to be tapering out from the trunk, yet strong enough to support the food weight plus the weight of anybody hauling the ropes."
Mostly agree, although I have long been dubious of the counterbalance method. It is hard to get both bags to weigh the same and, therefore, a bear can start pulling the branch up/down/sideways and cause one bag to slowly slide down into reach from the ground.
"In summary, the PCT method might be best for a small amount of food, and for a single rope, assuming that you have a carabiner and a stick."
A carabiner and a stick/stake are the essence of the PCT method. The method has worked for me quite nicely up to ~10# of food. Above that, it gets to be uncomfortable to haul the bag up. Your point about wrapping the rope around a stick is well taken, and will be incorporated into my technique.
"The two-rope method might be best for a larger amount of food and for two ropes."
Or just divide the food and do 2 PCT hangs. ;0)
"The big fly in the ointment for beginners was that they would always select a tree branch that was too low. Then, by the time you split that height and add some rope dangles, you ended up with food hanging that was just barely out of reach. An enterprising black bear might get lucky with that."
Nothing can be made foolproof in the hands of fools. ;0))