Research suggests that organizations consciously balance span of control(the resources over which an individual has direct control) and span of accountability(the results and performance outcomes for which they are held responsible) to achieve different outcomes.

If we think about the balance between span of accountability and span of control, there are only three options, and each of them drives a very different set of behaviors.

💡Accountabilities are smaller than the resources you control

In this case it is probable that you are underperforming or perhaps hoarding resources that could be used more effectively elsewhere.
This is not a desirable situation.

💡Accountabilities equal your level of control

This situation can lead to efficiency: we are able simply to get on and do the work without relying on others. However, in a matrix work often crosses traditional vertical silos of function and geography and if each of us is only looking at our narrow area, then we may miss critical issues that fall between the gaps.

Where span of accountability and span of control are equal, jobs can be performed by an individual focusing only on the resources they control. They do not need to take a broader perspective and will tend to concentrate on improving the efficiency of their own area of operation.

💡Accountabilities are broader than the resources you control

At first glance this may seem difficult to handle, but think about the behaviors that it requires. If people need to access resources that are outside their control, they need to think more broadly, seek out other resources, and work with others in order to be successful.

“Accountability and control as catalysts for strategic exploration and exploitation“ Harvard Business School working paper by Robert Simons

Where accountabilities are wider than the resources an individual controls, they have to reach out and explore opportunities to engage with others who control complementary resources to get things done.
These are precisely the behaviors that we want to encourage for breaking across the traditional silos in a matrix. It is therefore preferable in a matrix to design jobs where accountabilities routinely exceed control over resources.

Accountability > Control	Focus on exploring and collaboration
Accountability = Control	Focus on efficiency
Accountability < Control	Over-resourced or poor performance

In his TEDx talk at the University of Nevada, former Navy SEAL, Jocko Willink, spoke about taking responsibility in the most extreme circumstances. A great source of inspiration.