they face a “seeing like a state” problem

It is natural to assume that management is management, whether you are running a small business or a big corporation. But that is not the case. They are qualitatively different.
With a small enterprise, the business is visible to the owner/manager. In contrast, much of a large corporation is invisible to the CEO, who must try instead to make the business legible.
Think of a simple restaurant, with about a dozen employees. The owner-manager knows every employee and how they are doing. The owner-manager can observe how customers are experiencing the food. The owner-manager can be on top of every aspect of the restaurant, from caring for the facility to setting the menu to managing relationships with suppliers to food preparation and serving. In short, the owner-manager can make decisions based on what is directly visible.
In a large corporation, the CEO has never met most of the employees. The CEO observes very few customer transactions. The CEO is ignorant of many of the functions that support the business. Compared with the restaurant owner/manager, the CEO has a tiny fraction of the information pertinent to running the business. What information the CEO does obtain comes mostly indirectly via memoranda, briefings, and management reports.
Memos, briefings, and management reports are tools for making the business legible to the CEO. I am borrowing the term legible from James C. Scott’s book, Seeing Like a State. Scott’s insight is that many social conventions, including a census, standard weights and measures, and property records, were developed to enable rulers to tax and control populations that were too large to be directly observed.
Rulers of large states are trying to cope with a lack of knowledge about their subjects. Standardization helps to fill some of this knowledge gap.
Similarly, corporate CEOs are handicapped by a lack of knowledge about their organizations. They try to address this gap by implementing systems that facilitate feedback and control. Organization charts and other bureaucratic phenomena are part of this feedback and control mechanism.
Concrete vs. Abstract Thinking
Some psychologists draw a distinction between concrete and abstract thinking. Concrete thinking means that your mind works only with the objects that you see and feel around you. Abstract thinking means incorporating imagination and theorizing into your thought process.
Because the owner-manager of the restaurant can see everything that is relevant to business decisions, the owner-manager can operate mostly on the basis of concrete thinking. The owner-manager does not have to constantly update and revise a “theory” of the restaurant.
But the corporate CEO, operating with a limited information set that arrives indirectly, must use more abstract thinking. We may think of the CEO as trying to navigate in a confusing forest using only little scraps of a map. The CEO operates with a theory of the business and fits those little map scraps into the theory.
Expect Bad Management
So far, I have suggested that corporate CEOs know less about their organizations than small business owner/managers do. Does this mean that corporations should always lose out to small businesses?
In fact, of course, large corporations have major offsetting advantages. An important advantage is that there is a lot of cultural capital embedded in a corporation. As a corporation evolves, its employees and managers acquire habits, customs, procedures, relationships, and techniques that are valuable assets.
When the business environment rewards accumulated cultural capital, expect large corporations to do relatively well. But when the situation makes it paramount that leaders make well-informed decisions, expect a lot of bad management and failure, because good information is scarce within a large organization. It is really difficult for corporate CEOs to avoid messing up.
An explanation for the glass ceiling?
The “glass ceiling” describes the phenomenon that relatively few women reach the top position in large corporations. Most people assume that this is due to discrimination.
As a possible alternative explanation, suppose that the very high level of abstract theorizing that is required of CEOs, while found rarely at all, is relatively more prevalent among males than among females. This is related to the controversial theories of male-female average brain differences suggested by Simon Baron-Cohen. As explained in Wikipedia,
In 1997 Baron-Cohen developed the empathising–systemising theory. His theory is that a cognitive profile with a systemising drive that is stronger than empathising is associated with maths, science and technology skills, and exists in families with autism spectrum disorders. . .
Baron-Cohen’s work in systemising-empathising led him to investigate whether higher levels of fetal testosterone explain the increased prevalence of autism spectrum disorders among males;[18] his theory is known as the “extreme male brain” theory of autism.[12] A review of his book The Essential Difference published in Nature in 2003 summarises his proposal as: “the male brain is programmed to systemize and the female brain to empathize … Asperger’s syndrome represents the extreme male brain”.[19] Critics say that because his work has focused on higher-functioning individuals with autism spectrum disorders, it requires independent replication with broader samples.[20] His prediction that prenatal testosterone would be elevated in autism has been confirmed.[21]
What Baron-Cohen calls systemising may correspond to a propensity for abstract thinking in business. In that case, that could explain the predominance of males as CEOs.
Think of it this way. There are many good women chess players, and certainly many women who could trounce me at chess. But most of the top 100 chess players are male. The same may be true to some extent in the corporate world. It could be that of all of the people who have the background to become CEOs, the majority of those who are really outstanding systemisers, who are gifted at thinking abstractly about their firms, are male.
Conclusion
I am very confident that it is important to understand that corporate CEOs lack the sort of concrete information available to people running much smaller businesses. I am also confident that as a result, large corporations are run differently. Organizational charts, training manuals, and management reporting systems are nearly always required in large corporations, and yet in small organizations such devices can be irrelevant or even counterproductive.
I am mostly confident that the difference in availability of information tends to reward a different style of thinking. In particular, I believe that corporate CEOs have to use relatively more abstract thinking.
I am not at all confident that this difference in thinking styles truly explains the “glass ceiling.” I only offer it as an intriguing possibility, not at all proven.