My take is that separating the two is basically intractable and I wouldn't even try to quantify it.

One person doesn't have to work very hard to communicate all his/her ideas and priorities to him/her self so there's zero communication overhead there. A few executives are going to have to communicate a lot in order to all stay on the "same page" regarding the multitude of issues that a company might face trying to execute the overarching vision irrespective of it that's from one or a couple of people.

The more time these people spend communicating with one another to ensure that they all understand one another, the less time they have to spend with their group managers, thus lowing the number of groups they can oversee. As the number of groups an exec can oversee drops, you need more execs.

But as you get more execs, now you have a coordination problem at the executive level. The problem is recursive. The CEO can only oversee so many executives, so you get a CEO/COO/CFO triple team. But those people have to spend time ensuring that they all understand one another. Rinse and repeat.

Obviously there's a "management ratio" that a person could glean out of all of this and just employ that to structure an organization indefinitely, at least in theory. The problem is that all communication is lossy. If you can communicate with 85% effectiveness (which is PHENOMENAL!) then that kind of limits how many layers you can use.

0.85 ^ 2 = 72%

0.85 ^ 3 = 64%

0.85 ^ 4 = 52%

0.85 ^ 5 = 44%

0.85 ^ 6 = 37%

This sort-of tracks with real world businesses too, it's not often that you see an org chart which has 10 layers on it because the company would be totally dysfunctional and go bust very rapidly.

The "Peter Principle" applies to businesses too, the continue to grow and gobble up more market share until eventually they stop being as effective and growth slows or stops.

It applies to society as well as Joseph Tainter points out in "The Collapse of Complex Societies" each additional unit of complexity has a fixed cost and diminishing returns for the society (or the company, or whatever) until eventually you're adding complexity which is a net negative. Things then start to go downhill.

Obviously there are exceptions to this (think "natural monopolies" and the like) and there may be years or decades of lag between the start of net negative complexity growth and collapse. Unless there's "refactoring" of the system where complexity is removed somehow, everything will eventually trend towards collapse. And achieving refactoring in real life is generally impossible since there tend to be entrenched interests in favor of some complexity since it directly benefits them.

A great example of this is the healthcare debate. Doesn't matter which side you're on. Complexity nearly always wins.

I think communication structures should inherently be clear enough to pass all critical information over, and if there become communication issues or misunderstandings then you have to eliminate that communication break - whatever that means.

I feel some of these issues can be managed by having specialized teams - but those teams would have to managing a context, not merely certain functions or tasks of a business, otherwise they won't have their hands and attention on everything that will matter.

85% communication effectiveness seems very possible - at least with enough time and enough opportunities.