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Hierarchical structures are not more efficient; they are less efficient. In these structures, the people making the decisions are fundamentally less connected with the facts on the ground and must rely upon report, which inherently compresses context.
The mythology of efficient authoritarian structures roots from the misunderstanding that time minimization is "efficient." A dictator could order everyone in a group to throw the products of their labor off a cliff, burn down their factory, and commit suicide. Is that efficient?
Efficiency, in regards to decision-making structures, is the attempt to minimize error in the decision being made and maximize progress toward the inherent end-goal of the group. The people most oriented to know what that min-max'ing looks like, are therefore the group themselves
If a hierarchical structure is the mechanism by which decisions about minimizing error and maximizing progress are filtered, by its very nature it will make decisions that fit within the managers' own internal mental framework and the framework of their bureaucratic environment.
Thus, upon each degree that decision-making is separated from the population of the group, the decision-makers will tend to make less and less efficient decisions in the interests of the group and more and more efficient decisions in the interests of their office of authority.
Unfortunately, history and reflection will provide ample evidence that what benefits the manager is not what benefits the managed population. The more degrees of bureaucracy, the more that this tendency will be exaggerated. Thus, efficiency will drop by degree of stratification.
And we must not only point to dictatorships in order to demonstrate this fact. Just take a look at America's Republic. cambridge.org/core/journals/…
The previously linked study demonstrates that, even though America is a "Democratic Republic," the government is effectively an oligarchy.

Why has this happened? Stated simply: elected officials are shielded from all accountability and therefore affect their own interests.
We don't need to be constrained by public governance examples either. When comparing co-ops to corporations, we see that they perform more efficiently by our measures as well. democracyatwork.info/the_performanc…
The only reason corporations have been considered "efficient" is because an erroneous understanding of group efficiency has been used. Co-ops, which are much less hierarchical, preserve jobs better, have higher wages and benefits, and experience bankruptcy less often.
And this does not even begin to detail the incredibly inefficient boom-bust cycle of the capitalist economy, a system in which millionaires and billionaires play games with the lives of the global populace with no legal repercussion and zero democratic recourse.
I will neglect the obvious citation of the thousands of incompetent monarchies and collapsed dictatorships throughout history. The examples are so replete as to be well-known.

Hierarchies are both empirically and logically, not efficient.
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