Tuesday, August 21, 2012

Systems Part 3: Condensations And Fluxions

We begin with a paradox of sorts.

Imagine a committee of nine, whose decisions are made by majority vote. It would seem that a cabal of five "insiders" that resolve to act in concert could have its way with such a committee. After all, the four "outsiders" are effectively neutered by the existence of a coherent majority bloc.

But wait: That cabal of five could be dominated by a sub-group of three members who resolve to steer the group's decisions according to their preferences. The two "outside insiders" would not possess the means to override their "inside insider" brethren's collective will. So those three "inside insiders" could rule the bloc of five, and therefore the entire committee.

Wait, we're not done yet! That "inside inside" group of three could be dominated by an alliance of two of its members who always act in concert, effectively disenfranchising the third member. And so two members who stand together would dominate the group of three which dominates the group of five which dominates the committee!

What's wrong with this picture?


The above ridiculousness is what arises from a static, depersonalized picture of collective behavior. We have nine "votes" rather than persons capable of sensing their environment and reacting according to their interests in subsequent interactions. More, the sub-groups above are postulated without process: there is no hint of the negotiations and jockeying for position that always precede the formation of an effective bloc.

Among the most interesting studies in finite mathematics are those that analyze effective decision-making power in committee-like settings. Game theory dedicates enormous effort to the analysis of such things...and mostly fails to reach any firm conclusions. As with so many other aspects of life in society, the observable behavior cannot be shown to conform to a law with predictive power. Nevertheless, plausible explanations are available -- and critically important to the understanding of human-based systems.

Cabals of the sort described above do come into existence within bodies that decide and act collectively. However, their scope is never universal. Such a group of "insiders" will usually unite around a particular topic or range of topics; on matters outside that demesne, cabal members will "vote their consciences." Political scientist Jerome Huyler, in his little book Everything You Have, mentions a particularly interesting case: the "urban-rural coalition" that formed in Congress during the Sixties and early Seventies to countervail the growing political clout of America's suburbs. That coalition functioned mainly to promote the commercial interests of the cities and farm districts against suburban opposition; outside that sphere, it showed no influence.

More, such coalitions are not immortal. Bargaining never ends; neither do appeals to the narrow personal interests of individuals. Atop that, individuals' personal interests and larger commitments of allegiance are dynamic as well; if one cannot freeze Smith's priorities and values into an enduring stasis, neither can he guarantee Smith's loyalty to a larger group over an indefinite period.

These influences, and the dynamics they propel and condition, are important even within the most rigidly hierarchical systems.


In viewing an abstract hierarchical organization such as a corporation, we imagine decision-making as an orderly process. Policies flow downward from the chief executive officer, to be decomposed by subordinates into ever-smaller and more definite units, until front-line supervisors finally reduce them to implementable tasks for their subordinates. Inversely, information gathered during policy decomposition and implementation flows upward from lower to higher levels, effectuating modifications to existing policies and their implementation, and stimulating the development of new ones.

Both views are fatally naive. Consider the following Table of Organization:

A policy promulgated by Acme's CEO Smith to Vice-Presidents Jones and Davis will always be sufficiently general that the VPs can add their own glosses to it. Those accretions will always express the provincial priorities of the VPs to some degree. More, inasmuch as Jones and Davis are rivals -- persons at the same level on the Table of Organization always are -- their addenda will likely address some aspect of the competition between them.

Jones and Davis will further decompose Smith's policy for dispatch to Directors Blake, Swift, Allen, and Frank, who will infect their marching orders with their own personal and organization-provincial desiderata before passing bits of it on to Group Leaders white, Green, Sepia, Black, Scott, Whitt, Flynn, and Kurtz. In similar fashion those worthies will add a dash of personal and provincial seasoning to the bits they pass down to the unnamed grunts they supervise.

The grunts, however, are not without power of their own. Indeed, their degree of control over Acme's behavior might exceed that of the layers above them, for they determine how the implementation of the fully decomposed policy prescription will proceed, and what information about it will be reported upward. Subordinates have always "managed their managers" in this fashion; decision-making depends on information, and control of the most important information resides with the grunts themselves. The process recurs as information passes upward from group leaders to directors to vice-presidents to the Big Kahuna. If each level reports to its supervising level with 90% fidelity to the relevant facts, the reports that reach Smith will be:

(0.90)4 == 0.656 == 65.6% reliable

Thus, Smith will have been deprived of over a third of the information available about "what's really happening." In this organization of four supervisory levels -- a remarkably shallow one for American enterprises of any sort -- where 90% of the relevant facts are faithfully relayed upward by each level -- a highly optimistic estimate, empirically speaking -- the CEO's deductions, inferences, and subsequent decisions will be no better than 65.6% on-target.

This isn't a perfect guarantee that Acme will be in failure mode most of the time...but it comes damned close.


Add to the above simple depiction of the SNAFU Principle the competitive aspects of life in a hierarchy and the personal priorities of individuals at every level, and you have a formula for systems failure.

This is not to suggest that systems never accomplish any of their overt objectives. Rather, it predicts that:

  • Over time, a system will expend its resources, including the time and energies of its members, on priorities other than the overt objectives of the system;
  • To a degree that varies combinatorially with the number of individuals involved;
  • And faster than linearly with the complexity of the command-and-control pathways specified for the system.

This can be good or bad, depending on the nature of the system, the quality of its overt objectives, and the degree of divergence between those objectives and the priorities of its component individuals and sub-groups.

More anon.

1 comment:

Mark Butterworth said...

If you want to see an example of this essay brilliantly executed in a novel, read James Gould Cozzens', Guard of Honor.

It details an Air Force base in Florida, 1942, and its people from top to bottom over the course of three days where almost all the energy of the organization is misdirected by each member's agenda, competence, distractedness and so on.

The best book about men at work and how they work with and against each or simply as screw-ups.