From Apenwarr’s “What do executives do, anyway?”:

To paraphrase the book [High Output Management, by Andy Grove], the job of an executive is: to define and enforce culture and values for their whole organization, and to ratify good decisions.

That’s all.

Not to decide. Not to break ties. Not to set strategy. Not to be the expert on every, or any topic. Just to sit in the room while the right people make good decisions in alignment with their values. And if they do, to endorse it. And if they don’t, to send them back to try again.

There’s even an algorithm for this.

It seems too easy to be real. For any disagreement, identify the lead person on each side. Then, identify the lowest executive in the corporate hierarchy that both leads report into (in the extreme case, this is the CEO). Set up a meeting between the three of them. At the meeting, the two leads will present the one, correct decision that they have agreed upon. The executive will sit there, listen, and ratify it.

But… wait. If the decision is already made before the meeting, why do we need the meeting? Because the right decision might not happen without the existence of that meeting. The executive gives formal weight to a major decision. The executive holds the two disagreeing leads responsible: they must figure out not what’s best for them, but what’s best for the company. They can’t pull rank. They can’t cheat. They have to present their answer to a person who cares about both of their groups equally. And they want to look good, because that person is their boss! This puts a lot of pressure on people to do the right thing.

From HBR’s “Problems of Matrix Organizations”:

Another possible source of decision strangulation in matrix organizations occurs when managers frequently or constantly refer decisions up the dual chain of command. Seeing that one advantage of the conventional single chain of command is that two disagreeing peers can go to their shared boss for a resolution, managers unfamiliar with the matrix worry about this problem almost more than any other. They look at a matrix and realize that the nearest shared boss might be the CEO, who could be five or six echelons up. They realize that not too many problems can be pushed up to the CEO for resolution without creating the ultimate in information overload. So, they think, will not the inevitable disagreement lead to a tremendous pileup of unresolved conflict?

Certainly, this can happen in a malfunctioning matrix. Whether it does happen depends primarily on the depth of understanding that exists about required matrix behavior on the part of managers in the dual structure. Let us envision the following scene: a manager with two bosses gets sharply conflicting instructions from his product and his functional bosses. When he tries to reconcile his instructions without success, he quite properly asks for a session with his two bosses to resolve the matter. The three people meet, but the discussion bogs down, no resolution is reached, and neither boss gives way.

The two bosses then appeal the problem up a level to their respective superiors in each of the two chains of command. This is the critical step. If the two superiors properly understand matrix behavior, they will first ascertain whether the dispute reflects an unresolved broader policy issue. If it does not, they know their proper step is to teach their subordinates to resolve the problem themselves—not to solve it for them. In short, they would not let the unresolved problem escalate, but would force it back to the proper level for solution, and insist that the solution be found promptly.

Often, conflict cannot be resolved; it can, however, be managed, which it must be if the matrix is to work. Any other course of action would represent management’s failure to comprehend the essential nature of the design.