A New Debate on AI and Management
Everywhere we look, articles promise that AI will radically transform management. The integration of AI and span of control is essential in these discussions. Some claim that “the bottom of the pyramid will disappear” or that “the pyramid will become a diamond.” Others argue that AI agents will take on routine tasks, freeing managers to lead larger and more autonomous teams.
The idea is fascinating: fewer managers, flatter hierarchies, and more agility. But there is one problem: human relationships are not linear. And this is something we have known since the work of V.A. Graicunas in the 1930s.
The Graicunas Insight
Graicunas showed that the complexity of a manager’s role grows exponentially, not linearly, with the number of people reporting to them. Why? Because managers don’t just manage individual relationships. They must also deal with:
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Direct relationships with each subordinate
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Cross-relationships among subordinates (that still require oversight)
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Group relationships when decisions involve the whole team
His formula is striking:
N+N(N−1)2+N(2N−1−1)N + \frac{N(N-1)}{2} + N(2^{N-1} – 1)
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With 4 subordinates, a manager faces 44 potential relationships
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With 8 subordinates, the number jumps to 1,080
Even modest increases in team size create huge leaps in complexity. AI may help managers, but it does not erase this fundamental law of organizational design.
HOW4: From Theory to Practice
Graicunas gave us the theory. HOW4 brings it to life with data.
By analyzing both hierarchical links and work links, HOW4 reveals the real span of control:
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How many subordinates a manager actually coordinates (beyond what the org chart says)
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Whether reporting lines are recognized and mutual, or only formal
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How dispersed subordinates are across teams, functions, or geographies
The result is a weighted span of control that shows not just “how many people” report to a manager, but “how complex it really is to manage them.”
This is a crucial step forward. While many discussions about AI and management remain abstract, HOW4 grounds the debate in real relational data.
What AI Really Changes
AI agents can certainly help managers by:
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Automating administrative tasks
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Providing real-time insights
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Reducing some coordination costs
This means managers can spend less time firefighting and more time coaching, mentoring, and guiding their teams.
But AI does not make Graicunas irrelevant. If anything, as AI agents themselves become part of workflows, the number and speed of interactions increase. Organizations become more dynamic, not simpler.
So the true role of AI is not to make spans of control infinite. It is to improve the quality of management within the natural limits of human relationships.
Conclusion: Optimize, Don’t Maximize
The future of management will not be about maximizing how many people a manager oversees. It will be about optimizing spans of control for effectiveness.
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Too wide → leaders lose contact with people, engagement drops
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Too narrow → organizations become bureaucratic and rigid
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Well-calibrated → teams thrive, performance improves
Graicunas’ insight remains valid. What has changed is our ability to measure it. With HOW4, companies can finally understand their real spans of control, integrate them with relational data, and design structures that are scalable, adaptive, and human-centered.
👉 AI will not abolish complexity. But combined with HOW4, it can help managers focus on what matters most: leading people well.