The Ladder Without a Ruler

When a client asks why the branch is a recursion level and the team within it is not, we answer with an argument about identity. The argument is usually a good one. It is still an argument rather than a reading.

Beer offers a good criterion for recursion: the candidate system must be viable in its own right and one of the units that do what the containing system does; Chapter 10 states it in full, with Beer’s own fences.^[1] Around the criterion he supplied more than nothing and less than a ruler. There is a heuristic: the operational units are the ones that between them produce the enterprise, and if you count more than seven or eight of them, “you may be missing a whole level of recursion.” There is a workbook step, “Choose and clearly define the System-in-focus,” and there is, in principle, a test of predictive usefulness.^[2] None of it tells two competent analysts how to settle a tie between two drawings that both pass. Beer granted as much: two observers “will not necessarily agree on … the boundaries of any system.”^[3] He also chose the mathematical term recursion, he wrote, because it reminds us “we are not talking loosely about any kind of system contained inside another — but about an absolutely precise definition of viability,” and he held that the levels answer “to mathematical criteria.”^[4] The precision is asserted and never supplied.

The gap is not small, and we cannot blame it on anyone else’s neglect. We draw levels and call the drawing a diagnosis. Nothing in our practice tells us in advance what result a second analyst would get, and, as Chapter 9 sets out, nothing in our commercial arrangements has ever made it costly for us to find out. We have a ladder and no ruler.

Four neighboring literatures each supply something the VSM↗ lacks at this point, and each lacks something the VSM has. Set beside Beer’s criterion, they show what an instrument would have to do. A fifth body of work, Ostrom’s, says something less comfortable: in the one large evidence base we have habitually cited in support of recursion, recursion is the weakest thing in it.

Koestler supplied the noun

The Ghost in the Machine appeared in 1967. Koestler named the thing: a holon, the unit that is a whole to what it contains and a part to what contains it. “Parts and wholes in an absolute sense do not exist in the domains of life.”^[5] Beer’s nouns are relative. He says “System-in-focus,” or calls the contained systems “recursions of the viable system,” always measured from a focus someone has chosen.^[6] Koestler gave one term for the unit’s double role, which in our experience is one reason VSM diagrams are harder to read than holonic ones. Naming was Koestler’s contribution, and it was not a small one.

Naming has its limits, and they need stating as plainly as the achievement. A noun makes a structure discussable; it does not make it detectable. Koestler gave us a way to talk about the recursing unit without circumlocution, and Chapter 11 traces how that vocabulary reached us alongside Simon’s and Jaques’s. He did not give us a way to walk into an organization and find out how many holons are in it. What we can say with confidence is narrower: the relative nouns in Beer’s presentation impose a cost on readers, and the holonic literature does not pay it.

PROSA turned the word into engineering

The word also acquired an engineering literature, and that literature is the most useful thing in this chapter. Holonic manufacturing systems took Koestler’s word into factory automation in the nineteen-nineties. In 1998 Van Brussel and colleagues published PROSA, a reference architecture with a fixed small vocabulary of holon types: product, resource, order, and an advisory staff holon whose failure degrades the holarchy to a heterarchy rather than killing it. That last is a design idea Beer does not have; the VSM’s metasystem↗ is not optional in the same way.^[7] PROSA has been cited some fourteen hundred times.^[8]

Two separate features of that architecture concern us. The first is the fixed small vocabulary. PROSA does not invite each practitioner to decide what the holon types are. The types are given, and a design either uses them or is not a PROSA design. That constraint makes independent implementations comparable, and comparability is the precondition for accumulating evidence at all. Our own practice runs the other way: the five systems are fixed, but what counts as an instance of System One↗ at a given level is settled case by case.

The second is graceful degradation. A staff holon that is by construction only an advisor can be removed, and the execution system continues in a heterarchical mode: less predictable, less well optimized, still running. We make no equivalent claim. Our metasystem is constitutive rather than advisory, so in our account a metasystem failure is a loss of viability, not a degradation. Whether this is a real difference between the two architectures or a difference in how each states its commitments is worth settling, and a comparison of documented implementations could settle it. Chapter 15 takes the thirty-year manufacturing record at length. Here it is enough that a neighboring literature made a design commitment about partial failure that we have not made.

Jaques supplied a ruler

Jaques claims that the level of work in a role is measurable by a single quantity, the time-span of discretion: the longest period a subordinate exercises discretion before the results become reviewable. He also claims that organizational strata are discrete, with boundaries at roughly three months, one year, two years, five, ten and twenty.^[9] Beer’s criterion for a recursion level produces a judgment about a system’s identity. Jaques’s produces a number attached to a role. That is the whole of the difference, and it is enormous. Two analysts who disagree about whether a unit is viable in its own right and one of the units that do what the containing system does have no procedure for settling it, and Beer’s rules of thumb do not provide one.

The limit deserves the same volume as the contrast. The validity of Jaques’s ruler is contested, and we do not endorse it here. Whether time-span measures level of work or something correlated with it, whether the strata are genuinely discrete or an artifact of the measuring convention, and whether the upper boundaries have any support at all are open questions in the literature that grew around requisite organization. From Jaques we take the form of the answer, and leave the answer itself open: a single quantity, defined operationally, that two analysts can independently obtain from the same role and then compare. A contested measurement is a different kind of object from an uncontested judgment call, because a contested measurement can be tested and a judgment call cannot.

Panarchy shows what the diagram cannot hold

The contrast with Beer is the sharpest in this chapter. His recursion is structurally invariant: the same five systems at every level, always. Beer does describe modes of behavior, among them growth, retrenchment and crisis, and a cohesion that varies with the system’s purpose.^[10] He does not describe phases coupled across levels, and the diagram has no notation for either. Panarchy’s nesting is temporal. Each level is somewhere in a cycle, different levels are in different phases at once, and the coupling between them changes with phase.^[11] A System One in release does not need the System Three↗ that a System One in conservation needs. A VSM diagram cannot represent that, and every restructuring produces exactly that situation.

The limit reaches past the diagram to our ability to use the alternative. Holling’s phases are considerably easier to identify after the fact than in the present tense, and coupling that varies with phase is actionable only if the phase of each level can be read while the work is going on. We are not aware of a procedure that does this reliably for organizations. The finding is therefore asymmetric. Panarchy identifies a real representational limit in our diagrams without yet supplying the instrument that would remove it. What it does establish is that the invariance we treat as a strength (five systems, every level, always) is at least in part a modeling choice. Beer himself called the choice of five “somewhat arbitrary,” later declared the five-fold system closed “in logic,” and announced a topological proof of the invariance that we have not found stated as such.^[12] Choice or discovery, the invariance costs us the ability to say that two levels of the same organization are in different regimes at the same moment. Chapter 4 makes the neighboring point about channels: what the notation cannot express tends to drop out of the diagnosis.

The evidence base we counted on says otherwise

Ostrom’s evidence base yields one finding that bears directly on recursion, and it is uncomfortable. The least supported of the principles is the nested one, the principle closest to recursion. Nested enterprises came out at the bottom of the eleven in the 2010 review: alone at the bottom, still within the range the reviewers call moderately supportive, but the only one of the eleven whose association with success failed to reach significance at the five per cent level. Proportionality between what a member puts into a commons and what they take out came out near the top, and it is also one of the two conditions the 2016 configural analysis found holding across all three sectors. Nesting held nowhere in particular.^[13]

We had counted this literature as support, and at this point it counts against us. Ostrom’s multi-level organization is an independent arrival at something like recursion. It is also the principle her own literature supports least: support ratio 2.0, Fisher’s exact P = 0.065 and phi = 0.262.^[13:1]

Reading the result fairly takes care in both directions. It does not refute recursion. Nesting remains inside the band the reviewers themselves call moderately supportive. The review is a synthesis of case studies, with all the selection and coding problems that implies, and a principle can be real and still fail to show a strong association with success in a body of cases where it is unevenly present and inconsistently coded. Nor does the result transfer cleanly: common-pool resource institutions are not firms, and the nesting Ostrom’s coders looked for is not identical to the nesting we draw. But we cannot have it both ways. We have cited this literature as independent corroboration when the direction of the result suited us, and the same citation obliges us to report that the corroboration is thinnest precisely where we most wanted it. More citation will not settle the matter. A coding scheme for organizational recursion would, if another team could apply it to the same cases and reach the same levels. Chapter 14 sets out what such an evidence base would have to contain, and Chapter 9 takes up the second finding Ostrom’s data forces on us, about viability confirmed only in retrospect.

The one attempt to measure it used the organization chart

Somebody has now had to put recursion into an instrument, and what he did with it is the clearest evidence we have.

Michael Pfiffner’s 2017 Utrecht dissertation operationalizes the Viable System Model into a questionnaire and applies it to 135 organizations. It is the most serious quantitative work this tradition has produced, and Chapter 18 examines it at length.^[14] The recursion principle is one of the properties he has to measure, and two items cover it. The first asks whether the system in focus’s “overarching units (e.g. company, division, holding company) are themselves able to act as independent organizations at their level with all necessary functions which can fulfil their remit independently.” The second asks the same of its “subordinate units (e.g. department, area, group).”

Beer’s criterion survives in the item: the contained system must be viable in its own right. The discovery step does not survive. The organization chart supplies the levels to the respondent, in its own vocabulary: company, division, holding, department, area, group. The instrument does not ask where the levels are. It tells the respondent where to look, using the formal hierarchy as the answer, and then asks whether what is found there is viable.

We do not fault the design for this; nothing else was available. A questionnaire cannot ask an informant to derive a recursion level from first principles, because the model supplies no procedure for doing so, which is the charge of this chapter. Faced with the need to measure, the most careful attempt in the literature substituted the thing the model was supposed to improve on.

Beer had done the same thing first, and corrected it after the fact. His 1971 model for the Chilean state sector drew the recursions along lines of ownership. Events, he wrote later, “powerfully suggested that two levels of recursion were mixed together in that preliminary model,” and a new level had to be inserted.^[15] The first drawing followed the formal structure; the second followed what happened. Neither was produced by a ruler. Beer had warned against the first move in his own terms: if recursion becomes “a meaningless appendage to the term organizational level, then we do not have a valid model.”^[16] A recursion is not an organizational level, and the managerial systems at a level are not viable systems: “Systems Two, Three, Four, and Five are not in themselves viable systems at any level of recursion.”^[17] The neighbors in this chapter, Jaques’s strata and Ostrom’s nested enterprises among them, describe a related object, not the same one. Chapter 10 states his criterion once and compares each neighbor to it.

One number completes the point. Of thirty-five independent variables in that study, exactly one exceeded the threshold for missing data: the upward recursion item, at 5.9 per cent. Every other variable came in below five per cent, most far below. Informed professionals with close knowledge of the organization, among them bankers, recovery officers and consultants, were asked whether the units above this one could stand as viable systems in their own right, and they left that question blank more often than any other in the instrument. The number is small and should not be made to carry more than it can. It suggests that the ladder is hardest to see in exactly the direction where the model requires it to be visible.

What this chapter hands forward

Koestler supplied the missing noun; Jaques, a ruler whose validity remains contested; Holling, phases that are difficult to identify in the present tense; PROSA, a graceful-degradation contrast. Beer supplied a criterion he called precise and rules of thumb that resolve to a judgment call. None of them supplied an instrument for discovering levels rather than drawing them. Chapter 11 draws the joint result: five traditions saw the structure, and none could measure it.

That absence is why the criterion, good as it is, cannot do the work we ask of it. A test tells us whether a proposed level survives scrutiny. It does not generate the proposal, and it does not adjudicate between two proposals that both survive. Chapter 3 finds the same pattern in our handling of requisite variety: an idea we treat as a law works in practice as a vocabulary for describing what we have already decided. In both cases the remedy is a cheaper experiment, not a better argument.

Receipt — blind comparison of a diagnosis and an interaction matrix. Take one organization with an existing VSM diagnosis and usable message, transaction or incident data. Register the block-detection rule before either analyst sees the other’s result: a nested degree-corrected stochastic block model, with the number of levels chosen by minimum description length, which leaves no free threshold to tune after the fact.^[18] One analyst receives the interaction matrix; the other receives the diagnostic material. Compare the detected blocks, the diagnosed recursion levels and, where records permit, Jaques’s time-spans of discretion. Price: two analyst-weeks plus data preparation. If the blocks do not coincide, the negative result is that the diagnosed levels have no proxy in observed interaction structure. The full multi-organization design returns in Part Five, and Chapter 29 places this among the two cheapest experiments available to us.