Entertaining maths

There’s loads of talk about corporations and how they’re stupid and/or incompetent. There’s then wonderment expressed at how this can come to pass in a competitive environment that should filter out incompetence quite viciously. This amuses me to no end because I know that pretty much by definition any large, hierarchical entity—corporate, governmental or otherwise—must be incompetent. Any claim that this isn’t true is risible on the face of it.

The model

We will model here a fairly typical mid-sized corporation on its way to growing into a large-sized one. In such a corporation it’s not uncommon to have about 13 layers from the lowest worker to the CEO and/or board.

Flowing uphill

Information typically flows from observations of the workers to their supervisors. Supervisors collate that information and pass it up to foremen. Foremen summarize that information up for their lower managers. The lower managers compile it into reports for their middle managers. This process of communication goes up and up through twelve transitions before it reaches the CEO in some summarized form.

Flowing downhill

Now based upon this summary of observations communicated through the chain of the company’s hierarchy the CEO makes an executive decision. This decision is sent down to the vice presidents as policy. The vice presidents translate the corporate policy for their departments and ship it down ot the directors as, say, a road map. The directors take the road map and build an action plan from this. The action plan is further subdivided and elaborated upon with greater detail all the way down the chain until such a time as it turns into specific tasks for the workers at the bottom.

Stimulus/response

This whole system, in the end, is a stimulus/response chain passed through a hierarchical control system where each person is a node in said system that acts as both a sensor (uphill) and as an actuator (downhill). When a stimulus is sensed, the signal is transmitted up, a decision is reached and the actuators are activated on the way down to respond to it.

Only…

Signal loss rears its ugly head

Let us make a flattering caricature of corporate communication. This is the kind of caricature where the flabby jowls of a chubby guy are turned into the chiseled jawline of a romance novel cover model or where the frumpy and slightly plump middle-aged woman is drawn as a Hollywood hottie.

Let’s assume, in short, that the accuracy of communication through each layer is 95%. I think anybody who’s ever spoken with another human being one-to-one knows that this is a ludicrously high percentage of signal fidelity, but I’m going to pretend that I believe that corporate communications is just that efficient. This means that each transition layer that information flows up the hierarchy has a 95% chance of being transmitted correctly. Now with a 13-layer entity, that’s 12 transitions up the chain. 1 layer has a 0.95×100=95% chance of getting the information right. 2 layers has a 0.95×0.95×100≅90% chance of getting it right. (To keep things easier this is will be written like 0.95↑2×100 from now on.) 3 layers is 0.95↑3×100≅86% and so on until we go 12 layers at which point the odds are 0.96↑12×100≅54% chance of the information being transmitted correctly to the CEO.

Read that again. The odds of the CEO getting the wrong information from the hierarchy below him are nearly half. Almost half the time the CEO is getting bad information from his employees, and this is with the Hollywood hottie/romance novel cover model version of communication! (Remember, 95% accuracy is ludicrously high for human communication!)

But it gets worse. The CEO, based on this information (which, recall, is wrong almost half the time!), makes his decision and communicates it downward. This downward communication works at that same 95% accuracy. That means the round-trip stimulus/response has a 0.95↑24×100≅29% chance of providing the right response to a given stimulus.

The scary implications.

Again, look at those numbers. Almost three quarters of the time the company will do the wrong thing. And this is with the pert-breasted/chiseled-jaw version of corporate communication!

Now let’s have the breasts sag just a bit and the jowls get just a bit flabby. Let’s assume that corporate communication is 75% accurate (which is still ridiculously optimistic, note!). The odds of the CEO getting the right information from the hierarchy under him are now 0.75↑12×100≅3% and the odds of a proper response to a given stimulus now drop to 0.75↑24×100≅0.1%.

That, my dear friends, is why large companies always come across as clowns who do the dumbest thing possible whenever they’re given a chance to. They simply cannot be any other way.

“Solutions”

Now I can already hear some of the objections. “But Michael,” some are saying, “no company forces all information to flow from the bottom to the top and back down again. Managers are given leeway and discretionary power. This offsets the problem.”

While it is true that some managers in some companies are given some measure of independent authority (it’s a lot less common than you think, however!), this doesn’t solve the problem. It just means that the incompetence is focused on precisely the most important problems. Such a corporation will, on minor issues, make what looks like smart decisions frequently. This will lull them into a false sense of security while important decisions that do travel the whole stack fall through undetected. This could be even more devastating than having all decisions done stupidly because nobody would expect that degree of stupidity. (I personally suspect that a lot of sudden corporate deaths stem from this kind of false security.)

Other objections include the objection that not all miscommunication causes things to be diametrically wrong. It could be a small mistake. While this is true, the larger the drop in signal (70% is a pretty huge one, not to mention 99.9%!) the lower the chances are that the response to a given stimulus will be even close to what’s required.

“But Michael,” others will now comment, “any mistakes can be corrected as the corporation assesses and reacts.” Well, any such assessments and reactions also travel the communication stack. They’ll be just as incompetently executed. The company is just going to lurch from crisis to crisis and getting farther and farther away from anythign resembling balance.

Also, another factor enters here that I haven’t yet addressed: communication lag. There’s not only signal loss to contend with, there’s retransmission delay. Even if by some fluke the CEO gets the right information, by the time it reaches him it’s days to weeks to even months too late.

There’s one final objection that has a patina of truth to it: CEOs don’t rely just on their hierarchy to get information. They have consultants, the press, etc. as well. That sounds good in theory, but think about it for a minute: that’s more layers and more signal loss. This is going to exacerbate the problem (especially when the CEO starts to get conflicting information!), not mitigate it.

Nope, I’m sorry, but if you’re a large, hierarchical organization you’re just doomed to be stupid.

And evil. But that’s a rant for a different time.