Oh! So the subgroups are being considered as elements rather than as systems, and condition 3 is actually saying that every set of elements (other than the whole system, I assume) is affected by something outside itself? (Equivalently, however you partition the elements into two partitions there are influences flowing both ways across the boundary.)

You're right: that's a much more sensible definition, and I retract my claim that Ackoff's definition shows bad thinking. I maintain, however, that it shows bad writing -- though perhaps in context it's less ambiguous.

That last quotation, though. At first glance it nicely demonstrates that he has "your" reading in mind rather than "mine"; good for him. But look more closely at the last sentence. "No subset of elements is unrelated to any other subset". In particular, take two singleton subsets; his condition implies once again that every element is "related to" every other. So maybe I have to accuse him of fuzzy thinking again after all :-).