Stiglitz and Sah on Fallibility, Hierarchies & Organization

Fallibility and Organization — J. Stiglitz and R. Sah on Hierarchies and Polyarchies

Bureaucratic conniptions

Few people have worked for a large enterprise or bureaucracy without experiencing a brain hemorrhage or two. Those endless meetings, board discussions, steering groups, review panels, and task forces are enough to drive anyone crazy. Indeed, the bureaucracy is exactly where busywork and nothingness meet.

I exaggerate, of course. But as the economists Joseph Stiglitz and Raaj Kumar Sah point out in Human Fallibility and Economic Organization, the manner in which we organize ourselves as quorums and societies is important to our success or failure. Yet beyond the high walls of ideological war, few of us pay attention to the details in which we self-organize.

Similarly, conventional economics typically assumes that people are rational, all-calculating beings—that they gather, transmit, and incorporate information without any error or cost. Stiglitz and Kumar remind us, however, that “to err is human”, and that different systems aggregate information and errors in different ways. It goes without saying then that this has consequences for organizational performance.

Hierarchy, polyarchy, and committee

Stiglitz and Kumar, in particular, model three types of organizational architectures: the hierarchy, polyarchy, and committee. The hierarchy, as you know, consists of a bureau that reports to a higher bureau, which also reports to a higher bureau, and so it goes. Decisions are made when approval is given along the chain of command. Put another way, decision-making in a simple hierarchy depends on centralized unanimity.

Polyarchies, by contrast, are decentralized organizations—a panoply of branches. Here, consensus is not needed. In a polyarchy, a decision is made, or a project is accepted, when at least one of the branches approves it.

Finally, we have a committee. This architecture will take on a decision or project if the number of committee members in favor of the initiative reaches or surpasses a pre-agreed level of consensus. In this way, a committee is similar to a hierarchy if it demands complete unanimity; while it is similar to a polyarchy if only one approval is needed to proceed.

So this is where things get interesting. Organizations, after all, must make decisions under uncertainty. Of the portfolio of choices available to them, some projects or decisions will be good, while others will be bad. At the same time, individual decision-makers are fallible. From time to time, they will decide, select, and act incorrectly.

Type I and II errors

Fallibility and uncertainty together implies that Type I and Type II errors are possible. That is, decision-makers may mistakenly see a good project and reject it (Type I error), or a bad project and approve it (Type II error).

There is an analog here to law and order, in which the jury convicts the innocent, or fails to convict the guilty. The same arises in statistics when researchers incorrectly reject a true null hypothesis (Type I error); or when they fail to reject a false null hypothesis (Type II error).

In an organization, we can see that the higher the consensus needed, the less likely a committee is to accept a project or decision. Intuitively, if more people are needed for approval, then it is also more likely that somebody will disapprove. This result tells us that a hierarchy will reject more projects than a polyarchy. This happens because the hierarchy demands unanimity while the polyarchy is decentralized.

We cannot conclude from this, however, that any one system is better. There is a trade-off between Type I and Type II errors. As Stiglitz and Sah note, the polyarchy by design accepts more bad projects than the hierarchy, while the hierarchy rejects more good projects than the polyarchy. (The committee, meanwhile, falls somewhere in between depending on its consensus rule.)

So the preferred system depends then on the distribution and expected returns of good and bad projects, which is hard to know before the fact. That being said, we’d expect the polyarchy to fare better when the relative abundance of good projects is high, and to fare less well when bad projects dominate.

Complex organizations

Organizational architectures also rarely conform to a simple hierarchy, polyarchy, or committee. The market economy, for example, as Stiglitz and Sah observe, appears to “loosely” resemble a polyarchy of hierarchies.

In particular, Stiglitz and Sah show that under the right parameters, a polyarchy of hierarchies actually “rejects more bad projects than the simple polyarchy… and accepts more good projects than a simple hierarchy.” And with enough “levels [in the] complex organization, we [can] obtain perfect screening.”

But why is that? While we will not get into the math here, the economists explain intuitively that “hierarchies improve the ratio of good to bad projects while the polyarchic structure allows a better preservation of the portfolio.” (One assumption being that while people are fallible, they still possess “some discriminating ability” between the good and bad.)

Of course, it is rarely that simple. There is, for one, a trade-off between the gains and costs of scrutiny. In the real world, ‘perfect screening’ would be expensive and impractical. Most of us, I’m sure, are familiar with the enterprise that takes forever to reach a decision, ceding good projects to time and competitors. Similarly, it is not always true that more levels of approval implies more disagreement or filtering. Social herding and other structures may bias our evaluation.

Moreover, I am reminded of executives and politicians who get so overwhelmed by work that they lose all ability to discern. To get by, they default instead to heuristics, gut-feelings, consultants, and the fads of their times. These hierarchies in turn grow brainless at the top—infecting the entire chain below. We must not forget that even human attention is a scarce resource. Stiglitz and Sah agree, writing that “perfection is economically infeasible.” Models that fail to capture such frictions are equally dead.

Successors and subordinates

Related to decision-making and project selection is the problem of succession planning. Indeed, boards, faculties, departments, and legions of headhunters will spend much of their time recruiting, debating, and agonizing over future candidates. Clearly, this is important, for the quality of succession will shape the future course of the organization. But here, uncertainty and fallibility gives rise once again to Type I and Type II errors. As we have all seen or experienced at some point, corporations and voting societies will sometimes confuse incompetence for competence. They select bad candidates and overlook good candidates.

Again, such dynamics can vary with the choice of organizational architecture. Stiglitz and Sah find in particular that “the variance in the number of good managers is lower in a more decentralized system.” By contrast, they find that centralized systems are more likely to tip into extremes—consisting either of only-good managers, or only-bad managers. Decentralized systems are more likely to produce a mixture of good and bad.

While the math is involved, the intuition is straightforward. As Stiglitz and Sah explain, “a good (or bad) manager in a polyarchy improves (or worsens) the choice of his successor, but he [or she] has no impact on the choices being made by other independent decision-making units. In contrast, whether the current hierarchy (the leader of a hierarchy) is good or bad affects not only the choice of his own successor but also that of the future subordinates. This difference between the two systems generates a dynamic process which results in a hierarchy exhibiting a greater tendency towards the extremes of managerial abilities.”

Delays and natural selection

We should emphasize again, however, that Stiglitz and Sah’s findings are based on a simplified model of reality. Decision-making in a hierarchy, for instance, is not always a complete and unanimous chain. Likewise, the dynamics of decision-making, project selection, and succession planning is complicated when you incorporate delays, externalities, and human relationships. Immense hierarchies, for instance, are especially famous for their lack of speed.

People also do not exist independently of one another. Even a polyarchic system might centralize somewhat if decision-makers are guided by imitation and the choices of others. Errors and actions can bunch and correlate. Moreover, people exist in dimensions that go beyond competency. Economic and political organizations, for one, are not strangers to subversion. ‘Bad’ managers and politicians in this regard will seek to hijack the decisions, projects, and successions to their own personal ends. So to fallibility and uncertainty we might add incentives.

Finally, Stiglitz and Sah highlight that their models ignore the process of ‘natural-selection’ under the economic and political environment. You see, if different architectures aggregate errors differently, then they will also exhibit different “survival probabilities” under different conditions. But as we’ve said before, it is not obvious as to how an ecology of architectures ought to evolve. Here, we might appeal for answers in institutional economics, as with Daren Acemoglu’s work in Why Nations Fail, and evolutionary game theory, as with Robert Axelrod’s in The Evolution of Cooperation. But we will have to leave these topics for another time.

Plato’s aristocracy

In his Socratic dialogue, The Republic, Plato advocated for an aristocracy of valiant philosopher-kings. At the time, he and other Grecian philosophers believed that rule by the carefully selected few is better than rule by majority. But as Stiglitz and Sah show, the manner in which errors are aggregated and perpetuated depend mightily on the choice of architecture and the conditions in which it is embedded. Fallibility, uncertainty, incentives, selection, and frictional costs give rise to complicated trade-offs.

Likewise, history is quick to remind us that democracy and meritocracy can descend just as easily into mob-rule and hereditary-rule. Today, we live amongst a litany of parasitic oligarchs and plodding bureaucracies. But it is not necessarily so dreary. Humanity has made incredible strides in organizational design over the last few millennia—from hunter-gatherer societies to the war machine of Ancient Rome to the market economy of modern times. Perhaps if we remain mindful and lucky, we might someday find better structures that tap truly into the latent wisdom of crowds.

Sources and further reading

Sah, Raaj Kumar., & Stiglitz, Joseph. (1985). Human Fallibility and Economic Organization.
—— (1985). Economics of Committees.
—— (1986). Managerial Quality in Centralized Versus Decentralized Economic Systems.
—— (1988). Committees, Hierarchies, and Polyarchies.