Structural Inertia and Organizational Change Revisited III: The

RESEARCH PAPER NO. 1734

Structural Inertia and Organizational Change Revisited III: The Evolution of Organizational Inertia* Michael T. Hannan László Pólos Glenn R. Carroll

April 2002

RESEARCH PAPER SERIES

GRADUATE SCHOOL OF BUSINESS STANFORD UNIVERSITY

Research Paper 1734

Structural Inertia and Organizational Change Revisited III: The Evolution of Organizational Inertia∗ Michael T. Hannan†, L´aszl´o P´olos‡, Glenn R. Carroll§ April 29, 2002

Abstract Building on a formal theory of the structural aspects of organizational change initiated in Hannan, P´ olos, and Carroll (2002a, 2002b), this paper focuses on structural inertia. We define inertia as a persistent organizational resistance to changing architectural features. We examine the evolutionary consequences of architectural inertia. The main theorem holds that selection favors architectural inertia in the sense that the median level of inertia in cohort of organizations presumably increases over time. A second theorem holds that the selection intensity favoring architectural inertia is greater when foresight about the consequences of changes is more limited. According to the prior theory of Hannan, P´ olos, and Carroll (2002a, 2002b), foresight is limited by complexity and opacity. Thus it follows that the selection intensity favoring architectural inertia is stronger in populations composed of complex and opaque organizations than in those composed of simple and transparent ones. ∗

This research was supported by fellowships from the Netherlands Institute for Advanced Study and by the Stanford Graduate School of Business Trust, ERIM at Erasmus University, and the Centre for Formal Studies in the Social Sciences at Lorand E¨ otv¨ os University. We benefited from the comments of Jim Baron, Dave Barron, G´ abor P´eli, Joel Podolny, and the participants in the workshop of the Nagymaros Group on Organizational Ecology and in the Stanford Strategy Conference. † Stanford University ‡ Lor´ and E¨ otv¨ os University, Budapest and Erasmus University, Rotterdam § Stanford University

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1

Introduction

Social scientists have increasingly recognized that organizations and other social structures display powerful tendencies of inertia. That is, these entities tend to resist efforts to transform them and attempts to do so can lead to deleterious consequences. Yet, at the same time social scientists encounter, and frequently feature in their analyses, those organizations and other structures that undergo successful significant structural transformation. How might these two views of inertia be possibly reconciled? A first answer, dominant in the contemporary literature, says that randomness or chance makes it possible for a few organizations (out of multitudes) to escape the pressures of inertia and the dangers of transformation. A second answer, of the type, which we develop at length here, discriminates analytically among organizations and other social structures based on certain general characteristics. By this view, some kinds of organizations experience greater inertia pressures and some are more likely to suffer deleterious outcomes if they undertake structural transformations. These views are not necessarily contradictory. Among organizations with particular characteristics making them less susceptible to inertia, randomness may well determine individual fates. Likewise, from a research-design point of view, a sample of successful organizations is still highly biased as a statistical foundation from which to draw inference–except that the inference problems with respect to those characteristics disassociated with inertia may be lessened, Our goal here is to move the theoretical analysis of inertia in this direction. Toward that end, we follow Hannan, P´ olos, and Carroll (2002a, 2002b, hereafter HPCa, HPCb) and focus on the general organizational characteristics of complexity and opacity and their implications for successful organizational transformation. Both complexity and opacity limit foresight in organizations and this limitation plays a crucial role in the potentially destabilizing effects of significant changes. Complexity involves limits on the calculative capacity of the actors relative to the number of connections that must be considered in analyzing the likely impacts of architectural changes. In this model, the actors can foresee all of the consequences of a change as long as the number of units whose features will be in violation of new architectural codes falls below the number that specifies the upper limit on calculative capacity. We define an organization as complex if architectural changes generally produce cascades of changes that exceed the calculative capacity of the agents. 2

Opacity stems from the presence of inscrutable units. Such enclaves, as we define them, are teams whose information structures are hard to penetrate, either because the boundaries around the units are impermeable or because the languages used within the units differs greatly from the languages used elsewhere in the organization. When a unit is an enclave, then the consequences of some architectural changes for it might be “hidden” from the perspective of those in other parts of the organization. When arbitrary architectural changes normally have hidden consequences for at least one unit, the organization as a whole can be said to be opaque. Opacity normally hampers foresight under all conditions. Reduced foresight matters because it produces a systematic tendency to underestimate the length of reorganization periods and thus to underestimate the costs of change. Given such systematic underestimation, actors can easily choose to enter into changes that cost far more than the expected benefits of successfully completing the change. The theory also has implications concerning the effect of structural change on mortality hazards. The key theorem of HPCb holds that magnitude of the effect of change on the hazard increases with the architectural/cultural significance of the change and with the organization’s complexity and opacity. In this paper, we turn attention to structural inertia.1 We define inertia as a persistent organizational resistance to changing architecture (given expected costs and benefits of changes). We define the selection intensity favoring architectural inertia in an organizational population as the increase in the average (median) level of inertia for the population at the start of a time interval and for the survivors at the end of the interval. (This part of the argument shifts from the organization-level to the population-level.) Our theory implies that this selection intensity is positive, that selection favors inertia. It also follows that the selective advantage of inertia is greater for complex organizations than for simple ones and for opaque organizations than for transparent ones. According to these results, selection processes produce a positive correlation between complexity and inertia and between opacity and inertia among surviving organizations in populations subject to strong selection. We follow HPCa,b in developing formal representations of the argument and in using a nonmonotonic logic. Such a formal approach is valuable for making precise the connections among the facets of the general argu1 We describe the main findings of HPCa and HPCb but we do not reproduce their formal structure here. Interested readers are referred to the original papers. We do present formal descriptions here of the aspects of the theory developed anew in this paper.

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ment and for facilitating integration with other theoretical developments in organizational ecology. The nonmonotonic logic and its advantages for developing sociological theory are sketched in the Appendix and explained more fully in P´ olos and Hannan (2001, 2002).

2

Architecture and Culture

HPCa model organizations as consisting of architectures and cultures. Architecture refers to the formal specifications of an organization and its governance. Culture governs the processes by which transactions actually get completed. The notion of culture includes both tacit knowledge of the details of the work process (including locally generated knowledge and craft/professional knowledge generated outside the organization) and norms encoding the informal understandings and practices for interaction, authority, and so forth. HPCa model architectures and cultures as collections of sentences pertaining to ontology (e.g., definitions of the units in an architecture) and rules (e.g., statements of which units have authority over which other units). We regard such sentences as codes. As explained in P´ olos, Hannan, and Carroll (2002), the notion of code can be understood as both (1) a set of specifications in a blueprint, as in the genetic code, and (2) a set of rules of conduct, as in the penal code. Our use of the term code reflects both meanings. Some organizational codes are held strongly in the sense that violations get punished more severely, somewhat analogous to the distinction between felonies and misdemeanors. The theory is restricted to apply to “serious” codes. Henceforth, when we refer to architectural and cultural codes, we always mean only the serious ones, those for which observable violations bring strong sanctions. The relevant literature treats inertia as a persistent organizational resistance to change. One form is architectural: architectural inertia involves some kind of built-in resistance to changing architectures akin to risk aversion of individual agents. We believe that these inertial forces vary widely across organizational forms. Churches, universities, and governmental agencies, for instance, appear to be much more resistant to architectural change than high-technology companies. Nonetheless, even within a form, there appear to be inertial differences, arising perhaps from founding conditions. For instance, we believe that high-technology firms founded initially with highly developed organizational structures are more likely to be inertial than those that later develop them.

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Suppose we define the expected benefit of an architectural change purely in “objective” terms, ignoring any possible valuation of the architecture and culture per se. (This might be the kind of evaluation that an outsider, with no investment in the organization, might make.) Then inertia is reflected in an ordering of organizations with respect to the likelihood of making an arbitrary architectural change, net of these objective benefits. At one extreme, there is no investment at all in the current organization and the objective benefits carry all of the weight. At the other extreme—the case of an intensely institutionalized organization, the objective benefits get no weight. In Selznick’s (1948) terms, the architecture of such an organization has become “infused with moral value.” Given the same calculations of the “objective” costs and benefits that forecast that some architectural change has some positive net benefit, an organization with sufficiently high inertia will forego the change while one with lower inertia will undertake it. Let
b(x, t, αi:j ) be the expected net “objective” benefit (that is, the foreseen objective benefit net of all foreseen costs with no valuation placed on the architecture and culture) to x of initiating the change αi:j at t. We define architectural inertia, inert(x) using the nonmonotonic quantifier N (see the Appendix). Formulæ quantified by N state what state of affairs ought to be expected to hold “normally” (in the absence of more specific information that overrules the normal state of affairs). Definition 2.1 (Architectural inertia) Architectural inertia is a function mapping from organizations to the non-negative real numbers that satisfies the following constraints: c(x, s, αi:j ) =
c(y, t, αk:l )) −→ inert(x) > inert(y) ←→ N s, t, αi:j , αk:l [(
b(y, t, αk:l )) → ¬∆(x, s, αi:j ) ∧ ∆(y, t, αk:l )∧ ∃b[(b =
b(x, s, αi:j ) =
b(x, s, αi:j ) =
b(y, t, αk:l ))) → ∀b [(b < b) ∧ ((b =
¬(∆(x, s, αi:j )) ∨ (∆(y, t, αk:l ))]]]. [Read as: organization x has stronger architectural inertia than organization y if it is normally the case for any pair of architectural changes of equal cost that there is a level of benefit b such that (1) if the benefit to each organization falls below b that neither organization will undertake the change and (2) if the benefit equals b for each organization that x will undertake the change but y will not.]

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3

Significance, Complexity, and Opacity

Architecture (or culture) creates connections between units. Two units are connected in an architectural (cultural) sense if architectural (or cultural) rules govern and constrain the interactions between them. Consider an adjacency matrix in which each cell equals 1 if the architecture (culture) specifies that unit on the associated row constrains unit on the associated column and equals zero otherwise. HPCa propose an eignenvalue measure of a unit’s centrality in the architecture (culture) such that a unit is central to the extent that it constrains units that are themselves central. That is, a unit’s architectural (cultural) centrality is given by a function that maps from units and time points to the non-negative reals and that is proportional to its corresponding entry in the eigenvector associated with the principal eigenvalue of the adjacency matrix expressing the asymmetric inter-unit constraints specified by the architecture (culture). By this construction, the architectural (cultural) significance of change in a subset of elements of the architecture is given by the sum of the architectural (cultural) centrality scores of the units that are constrained either by the code that is replaced or by the replacement code. Now consider what happens when there is an architectural change to a unit: all of the units constrained by it might need to make changes as well, then those constrained in turn by these units might need to change, and so forth. In other words, a cascade of adjustments follow the initial change in architecture. HPCa propose that the reorganization following an architectural change runs from the initiation of the change to the earliest subsequent time at which the organization has eliminated all nonconformity of organizational features to the newly added architectural code and has adopted feature values that are compatible with these codes. That is, it is the time during which the cascade of adjustments to the change play out. Therefore, a change in a set of architectural codes initiates a period of reorganization of length recorded by the function dur(x, t, αi:j ), which equals the duration between the initiation of the change and the earliest subsequent time at which none of the units feature values violate newly added architectural codes or to infinity, if the violations cannot be eliminated for one or more units. HPCa focus on periods of reorganization because devoting attention, time, and energy to reorganization (adjusting codes to eliminate violations) diverts members of an organization from the tasks that generate revenues, as we argued above. It seems unproblematic to assume that the opportunity cost associated with change rises monotonically with the length of the pe6

riod of reorganization. So, the length of a period of reorganization initiated by a change normally increases with the number of units that violate newly added architectural codes; and the opportunity cost of changing a set of architectural elements normally increases with the length of the reorganization period. The final component of the first part of the theory links significance of changes to the danger of attempting them. We sketch a generalized version of this argument below, after introducing issues of limited foresight.

Limited Foresight HPCb introduce issues related to limited foresight about the consequences of architectural change. Lack of foresight surely complicates planning for reorganization. If the actors can foresee which units will be affected by an architectural change, then they can plan actions and adjustments that deal with the full scope of the direct and indirect effects of the change. But, if limited foresight precludes such broad vision, then any plans must be incomplete. At best, the actors can plan adjustments for the units that they foresee as being affected by the architectural change. Then, indirect (induced) effects on units outside the foreseen scope will appear—come into clear sight—only after reorganization has begun. So, if the actual number of units whose features violate newly added architectural codes exceeds the foreseen number, then the actual length of a period of reorganization normally exceeds the foreseen length. A key part of the argument assumes that an excess of violations over the limits on foresight normally lengthen actual periods of reorganization. As we noted above, when violations cannot be foreseen, agents cannot plan comprehensively for reorganization and cannot undertake as many adjustments in parallel. The fact that the unforeseen violations show up in mid-change slows the process of reorganization, thereby lengthening actual periods of reorganization. This observation implies that, the actual period of reorganization normally increases with the number of unforeseen violations (for a given level of actual violations of new architectural code). HPCb argue that organizations have a limited computational capacity or intelligence and represented this tendency by assuming that each organization can only foresee code violations for a given number of units. As long as the number falls below this capacity, then the situation can be foreseen in its entirety. Otherwise, decision makers envision the situation through a window that restricts the view to some proper subset of the units affected. Complexity means that the number of connections to be considered ex7

ceeds the number that the agents can visualize simultaneously in considering the possible impacts of changes. This problem stems not from a lack of information; indeed it often takes the form of information overload. If the number of units and the density of their interconnections are both high and the pattern of inter-unit ties lack a simple structure (such as hierarchy), then the analytical problem overwhelms the cognitive capacity of the agents, individually and collectively. In such circumstances, agents normally break the analytical problem into pieces that they can envision and analyze. As long as they focus on one piece, other aspects of the implications of change fall outside their field of vision. We define complexity at the organizational level by abstracting from the details of particular changes. Therefore, we define an organization as complex if arbitrary, minimally significant architectural changes generally overwhelm foresight. Specifically, organizational complexity, cpx(x, t), is a (binary) function defined on organizations and time points that equals 1 for an organization if architectural changes normally generate a number of unit violations that exceed its computational capability and equals 0 otherwise. If the limits are purely computational, then improved computational ability would eliminate the problem of limited foresight. In contrast, some kinds of limits on foresight are structural. Here we have in mind situations in which information about some parts of an organization are unavailable in other parts, in which the structure creates limits on what can be known. Sometimes the lack of transparency arises because the languages used in different parts of the organization differ such that those outside the unit cannot interpret a full-disclosure description of the activities in an organizational unit. Other times, lack of transparency arises due to strategic withholding of information. We treat issues of structural limits on foresight by introducing notion of opacity. We first define enclaves, transaction units that are inscrutable to the rest of the organization. Enclaves are partially informationally isolated. Given such isolation, agents in one part of an organization might not be able to see the consequences of an action in other parts. The consequences of the architectural change for unit are said to be hidden if (1) the unit’s feature values do not conform to the newly added architectural code, and (2) this violation is not foreseen. So, opacity, op(x, t), is a (binary) function defined on organizations and time points that equals 1 for an organization if architectural changes normally generate (initially) hidden violations for at least one unit and equals 0 otherwise.

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4

Mortality During Reorganization

Greater complexity and opacity normally mean longer periods of reorganization for changes of a given level of significance. This is because the agents cannot know a priori all of the adjustments required to eliminate code violations in a complex or opaque organization. As a result, not all changes can be done in parallel. Only when a cascade of adjustments within one part of the organization has played itself out can a “downstream” enclave begin to undertake adjustments to those changes. The model in HPCb yields the following key theorems:2 Theorem 4.1 A complex or opaque organization presumably foresees a shorter reorganization period for a given change. [T5.2 in HPCb] Theorem 4.2 The length of the actual period of reorganization normally increases with an organization’s complexity and opacity, as well as with the architectural and cultural significance of the elements being changed. [T5.3 in HPCb] Theorem 4.3 The total cost of a change presumably increases with an organization’s complexity and opacity, as well as with the architectural and cultural significance of the change. [T5.4 in HPCb] What do these arguments imply about the risks of change? Following Hannan and Freeman’s (1984) theory, we assume that organizations generally miss opportunities for expanding their resources and do more poorly at protecting the resources they do command during periods in which they experience code violations. According to our definition of reorganization, organizations experience violations of newly added code during reorganization periods but not after reorganization ends. Thus it follows that an organization’s stock of resources presumably shrinks during periods of reorganization. Adopting now standard arguments, we also assume that organizations with access to greater resources can better withstand life-threatening environmental shocks (Carroll and Hannan 2000). Specifically, we assume that an organization’s hazard of mortality normally declines monotonically with its level of resources. 2

These theorems are stated in nonmonotonic logic rather than the more familiar firstorder logic. The Appendix describes this methodology and its rationale.

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Now it is straightforward to derive conclusions about mortality during the reorganization process. Consider several insightful scenarios. First, consider two organizations with equal resources at the start of a time interval. If one has more code violations during the interval, then its hazard of mortality is presumably higher. Second, consider two organizations with equal resources at the start of a time interval. If one experiences reorganization during an interval and the other does not, then the resources of the nonreorganizer presumably exceed those of the reorganizer during that interval. Third, consider two organizations with equal resources at the start of a time interval. When one experiences reorganization during an interval and the other does not, then the hazard of mortality for the reorganizer presumably exceeds that of the non-reorganizer during that interval. From these assumptions, HPCb derive a theorem about mortality and reorganization: Theorem 4.4 An organization’s hazard of mortality presumably rises monotonically over a period of reorganization. [T7.2 in HPCa] The theorems in HPCa and HPCb with greatest substantive import concern the rise in the hazard of mortality due to structural change. They rely on differences in lengths of periods of reorganization implied by differences in significance, complexity, and opacity to establish periods over which mortality hazards will be rising for one and not the other entity being compared. So, Theorem 4.5 The increase in the hazard of mortality due to an architectural change presumably increases with its architectural and cultural significance and with the organization’s complexity and opacity. [T6.4 in HPCb] Figure 1 summarizes the flow of the argument in HPCb.

Architectural Inertia and Mortality Now we develop the connections between inertia and mortality. To do so, we need a few more predicates and functions. First, we want to ensure that the comparisons made between organizations are meaningful in the sense that they are exposed to the same flow of external shocks, opportunities, and events that might stimulate change. Restricting comparisons to those within populations of organizations helps in this matter. Yet, there still might be local variations that need be considered to guarantee comparability. (This is, of course, a matter of central importance in the empirical research on 10

Number of units with unforeseen architectural code violations + Complexity/opacity + Number of units with unforeseen code incompatibilities

+

+

+

Length of reorganization

-

+

Resources

Indirect costs

+

Opportunity cost

+

Mortality hazard

Figure 1: Overview of the argument linking architectural and cultural significance of a change to the hazard of organizational mortality this problem.) To represent this consideration explicitly, we first introduce a two-place function. Let opp(x, t) denote the set of opportunities available to organization x at time t. Now we are ready to define the three-place similarity predicate SIM(x, y, t) Definition 4.1 (Organizational similarity) Organization x is similar to organization y at time t if (1) they belong to the same population of organizations, (2) the same set of opportunities available to both organizations, and (3) they are equally complex, equally opaque, and have access to the same level of resources. SIM(x, y, t) ←→ O(x, p) ∧ O(y, p ) ∧ p = p ∧ opp(x, t) = opp(y, t)∧ op(x, t) = op(y, t) ∧ cpx(x, t) = cpx(y, t) ∧ res(x, t) = res(y, t)) We also introduce a function, N∆(x,s,t) , mapping from organizations and time intervals to the natural numbers, that records the number of architectural changes  initiated by organization x over the interval [s, t) and another function, dur (x, s, t), mapping from organizations and time periods to the non-negative real line, that gives the sum of the lengths of all reorganization periods for organization x during the interval (s, t]. Assumption 4.1 If neither of a pair of similar organizations is in structural 11

reorganization at a given time, then for any difference in their levels of architectural inertia there exists a period (starting at that time) such that the organization with lower inertia does initiate a structural change but the other does not. N x, y, s[(¬RE(x, s, s) ∧ ¬(RE(y, s, s)) → (∀δ[(δ = inert(x) − inert(y)) → ∃ ∀t, u[( ≤ t − s) ∧ (s < u < t) ∧ SIM(x, y, u)] → N∆(x,s,t) < N∆(x,s,t) )]]] It seems intuitively obvious that if (1) one set of organizations normally spends more time in reorganization than another, and (2) the hazard of mortality during reorganizations exceeds that hazard outside of reorganization, then the reorganizers normally have a higher cumulative hazard of mortality. However, we do not yet have in place all that is needed to derive this intuition. There is a complication due to the result (T4.4) that an organization’s hazard of mortality rises monotonically during periods of reorganization. Without further assumption, we cannot rule out the following scenario: one set of organizations spends less total time in reorganization than another but has one or more longer spells of reorganization. According to T4.4, the cumulative hazard for one long spell of reorganization might be higher than for a set of shorter spells of longer combined duration. This could happen if the function relating duration to the hazard rises slowly initially and then accelerates. We think that this situation is highly unlikely when the comparisons are restricted to similar organizations. The theory in HPCa yields a theorem that changes of given significance (either architectural or cultural) presumably yield reorganization periods of equal length for organizations in the same population with equal resources, complexity, and opacity. Now we need to “average” over the significance of changes, because we want to characterize a set of changes over some period. We assume that the expected duration of reorganization within the specified set of organizations (and the time period) is the same, regardless of the details of the architectural changes, as long as attention is restricted to comparable organizations. In taking this perspective, we regard dur as a random variable. Let E(dur) denote its mathematical expectation. Assumption 4.2 The expected duration of reorganization following any (minimally significant) architectural change is normally the same for all organizations in a population in a given time period with equal resources, complexity, opacity, and comparable opportunities. N x, y, t[SIM(x, y, t) −→ ∀αi:j , αk:l [E(dur(x, t, αi:j )) = E(dur(y, t, αk:l ))]]. 12

If the expected durations do not differ for members of a set of organizations and if one organization in the set undertakes more changes than another, then it presumably follows that there is a positive monotonic relationship between number of changes and total duration of reorganizations over a period. In the nonmonotonic logic, provisional theorems (those that depend upon causal stories, formulæ quantified by N) are expressed using the quantifier P, which states what is “presumably” the case. (The Appendix explains why a separate quantifier is needed.) In a formulation in nonmonotonic logic, all premises must be considered in checking proofs, because different parts of the argumentation might clash in their implications. However, we do not have such clashes in the argument presented in this paper. We note following each theorem (or lemma) the premises that comprise the rule chain used in the proof. Lemma 4.1 The time spent in reorganization during a period presumably declines monotonically with the number of changes undertaken. [from A4.1 and A4.2] P x, y, s, [¬RE(x, s, s)¬ ∧ RE(y, s, s)) ∧ ∀u[(s ≤ u ≤ t) → SIM(x, y, u)] −→ (N∆(s,t) ↑ Σdur(s,t) )]. [Note: if the antecedent in this formula holds, then the organizations being compared have identical expected durations. Then the consequent holds as a basic result in probability rather than as a provisional result. So the “presumably” part of the lemma concerns the relationship between the antecedent and the expected durations.] Lemma 4.2 If a pair of organizations (not currently in reorganization) experience the same set of opportunities to change their architectures during a period, then the one with stronger architectural inertia presumably spends less time in reorganization during that period. [from D4.1, A4.1, and L4.1] P x, y, s[(¬RE(x, s, s) ∧ ¬RE(y, s, s)) → (∀δ[(δ = inert(x) − inert(y)) → ∃ ∀t, u[( ≤ t−s)∧(s < u < t)∧SIM(x, y, u)] −→ Σdur(x,s,t) < Σdur(y,s,t) )]]]. The δ– construction guarantees that the period in consideration is long enough to contain an opportunity to reorganize that only the organization with lower architectural inertia will find attractive.

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5

Mortality After Reorganization

Decision makers normally intend to improve organizational performance (and increase inflows of resources) when they change architectures. If such intentions become realized, then an organizations is better off after it completes the architectural change than it was ex ante. Hannan and Freeman’s (1984) formulation allowed for this possibility: it holds that the hazard of mortality jumps with the onset of change, increases during the period of reorganization, and then declines afterwards, possibly eventually falling below the hazard of an otherwise identical organization that did not change Surely some architectural changes do improve performance and thereby reduce mortality hazards. Just as surely, others have the opposite effect. Should we assume that the beneficial case as a default? We think not. Whether replacing one architecture with another will improve performance or degrade it depends upon organization-specific contingencies that are generally very difficult to assess a priori. These contingencies make the consequences of any significant change in architecture highly uncertain. (Our theory implies that complexity and opacity magnify such uncertainty (HPCb).) Moreover, much recent research shows that some architectural redesigns spread among organizations in a population by contagion; fads and fashions generally hold sway under uncertainty. When redesign reflects simple imitation of other organizations rather than sound analysis of organizational specific conditions, then potential benefits likely prove elusive. Finally, significant architectural changes generally produce cascades of unforeseen and unintended consequences. (The part of the theory presented in HPCa) concentrates on importance of such cascades in destabilizing organizations.) We see no reason for assuming that such unintended consequences normally prove to be beneficial. These considerations prompt us to follow the spirit of the nonmonotonic approach, to admit that we lack enough information to make a claim about this matter with enough certainty to make the claim a permanent part of the theory. Instead, we make a weaker, more justifiable, assumption as the default. We assume, in the absence of more specific information, that completed architectural changes are generally neutral with respect to the hazard of mortality. Think of a distribution of outcomes to architectural change, ranging from disastrous to highly beneficial. Our default assumption builds on the idea that this distribution is symmetric and centered at zero, that changes are as likely to increase mortality as to decrease it. The nonmonotonic logic is very important here. More specific information about the type of change or the contingencies facing the organization might 14

override this default assumption in many cases. According to Corollary 7.1 in HPCa, if one of a pair of equally resourcerich organizations changes its architecture and the other does not, then the resources of the reorganizer fall below those of the non-reorganizer at all time points within the period of the reorganization. It follows (in the absence of more specific information to the contrary) that the reorganizer has a smaller stock of resources than the non-reorganizer when it completes the change. The key question is what to assume about the period after reorganization has been completed. Our reasoning that change is normally neutral in its impact on resource flows leads us to assume that changers normally do not catch up with (otherwise identical) non-changers.3 The predicate ∆(x, t, αi:j ) means that “organization x initiated the architectural code change αi:j at time t,” where αi:j denotes that the architectural codes αi were replaced by the codes αj . The state of reorganization is the time during the interval that begins with an architectural change and ends when the period of reorganization ends. Then we can define the state of reorganization as follows: Definition 5.1 An organization experiences reorganization during a time interval if (1) the reorganization begins within the interval, or (2) the reorganization begins before the interval and ends after the start of the interval. RE(x, s, t) ←→ O(x, p) ∧ ∃αi:j , u, v[∆(x, u, αi:j ) ∧ (dur(x, u, αi:j ) = v) ∧ ((s ≤ u ≤ t) ∨ (u < s ∧ u + v ≥ s))]. We implement the key assumption that organizations normally do not recover the full cost of architectural change using the function res(x, t), mapping from organizations and time points to the real line, that gives the level of resources available to an organization at a point in time. Assumption 5.1 Organizations normally do not recoup the full costs of significant architectural change. N p, x, y, s, t, v, u, α i:j [O(x, p) ∧ O(y, p ) ∧ p = p ∧ (res(x, s) = res(y, s)) ∧ ∆(x, s, αi:j ) ∧ (dur(x, s, αi:j ) = t) ∧ ∀u[s ≤ u ≤ s + t → ¬RE(y, t, u)]∧ ∀v[v > s+t → ¬(RE(x, s+π, u)∨RE(y, s+π, u))] −→ res(x, v) < res(y, v)], 3 In expressing this assumption formally, we restrict the scope to identical time periods for the organizations being compared. We do so because we expect that environmental variations over time affect resource flows for all organizations in a population.

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Selection Favors Architectural Inertia Now consider architectural inertia again, focusing on its evolutionary implications. If organizations with weak architectural inertia normally spend more time reorganizing during a time interval, then they presumably get exposed to a higher risk of mortality (due to reorganization) over that interval. According to A5.1, changers do not normally experience gains from reorganizing once they complete the changes that offset the costs to reorganizing. Therefore, it follows that the organizations with low inertia are exposed to greater risk. We specify this conclusion in terms of the cumulative hazard of morality experienced over a period: Definition 5.2 (Cumulative hazard of mortality)  t haz(x, u)du, t > s ≥ 0. Haz(x, s, t) = s

Theorem 5.1 If a pair of organizations (not in reorganization) experience the same set of opportunities during a period, then the one with stronger architectural inertia presumably experiences lower cumulative risk of mortality over that period. [from D5.1, D5.2, A4.1, and L4.2] P x, y, s[(¬RE(x, s, s) ∧ ¬RE(y, s, s)) → (∀δ[(δ = inert(x) − inert(y)) → ∃ ∀t, u[( ≤ t−s)∧(s < u < t)∧SIM(x, y, u)] −→ Haz(x, s, t) > Haz(y, s, t))]]]. Following P´eli, P´ olos, and Hannan (2000), we want to characterize the distributions of relevant characteristics for the organizations that escape mortality over a period, the survivors. This requires a focus on the population as the unit of analysis. Such a focus motivates explicit reliance on the probabilistic structure of hazard analysis. We define risk(x, s) as a binary function mapping from organizations and time points that equals 1 if x is at risk of mortality (and, therefore, has not yet experienced mortality) at s and equals 0 otherwise. In the language of hazard analysis, a value of 1 for this function indicates that x is a member of the “risk set” at s. We also define a binary function, surv(x, s, t) that takes the value 1 if the entity survived over an interval of risk [s, t) and equals 0 otherwise. Formally,  1 if ∀u[u ∈ [s, t) −→ risk(x, u) = 1, surv(x, s, t) = 0 otherwise. [Note that it must be the case that ∀x, s[surv(x, s, s) = 1]. We can define the probability of survival over an interval as follows: 16

Definition 5.3 (Survival probability)    t haz(x, u)du G(x, s, t) = Pr{surv(x, s, t) = 1} = exp − s

= exp (Haz(x, s, t)) . This definition is a basic result in the mathematics of survival analysis (Cox and Oakes 1982). If selection favors a characteristic, then the frequency of this characteristic increases. We have come to the point in the theory where we can derive theorems that pertain to such selective advantage. We find it natural to express them in terms of changes in average levels of architectural inertia in a comparable subset of a population over an interval, expressed in terms of medians. We focus on medians to avoid having to make precise assumptions about distributions. As we see it, the current state of empirical and theoretical knowledge does not warrant strong distributional assumptions. Definition 5.4 (Selection intensity) The selection intensity for architec−−→ tural inertia, inert(p, s, t), equals the median level of architectural inertia for the surviving members of a cohort minus the median defined over all members of the cohort at the start of the interval. In formal terms: 1. If any members of a cohort have survived over [s, t), then −−→ inert(p, s, t) = median(inert(p, t) | surv(x, s, t)) − median(inert(p, s) | surv(x, s, s)); −−→ 2. otherwise, inert(p, s, t) is not defined. The core of the evolutionary argument is represented in the following theorem: Theorem 5.2 (Selection favors architectural inertia) The average level of architectural inertia of the surviving members of a cohort of comparable organizations presumably exceeds the average level in the whole initial cohort (when calculated over a sufficiently long period).   −−→ P p, s, t ∃λ λ < (t − s) −→ inert(p, s, t) > 0 .

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Proof: 1. With | · | denoting the cardinality of a set (the number of distinct elements), the expected number of survivors over an interval in a set of entities at risk of mortality at risk at the start of the interval can be written as: N (p, s, t) = E (|{x : O(x, p) ∧ surv(x, s, t) = 1}|) G(x, s, t), = x∈z(s)

where z(s) = {x : O(x, p) ∧ risk(x, s) = 1}. Let N + (p, s, t) denote the expected number of survivors in the set of organizations whose architectural inertia exceeds the median in the population at risk at t and N − (p, s, t) denote the expected number of survivors for the set at or below the median level of architectural inertia. G(x, s, t), N + (p, s, t) = x∈z+

z+ = {x : O(x, p) ∧ (risk(x, s) = 1) ∧ inert(x) > median(inert(p, s))}, G(x, s, t), N − (p, s, t) = x∈z− −

z = {x : O(x, p) ∧ (risk(x, s) = 1) ∧ inert(x) ≤ median(inert(p, s))}.

2. According to T4.1, each entity in the set of those with above-median levels of architectural inertia presumably experiences a lower cumulative hazard of mortality over an a sufficiently long interval than each entity in the belowmedian group. Given the definition of the survivor probability (D5.3), if G = 0, then Np = ln(M ). Because the logarithm is a monotonic function, the most specific rule chain (under the conditions stated in T4.1) concludes with the conclusion: N + (p, s, t) > N − (p, s, t). 3. Given that values of inert(x) are assumed to be fixed for all x and given the definition of the median, it follows that greater mortality in the set below the median forces the median to increase. QED 18

Variations Due to Complexity and Opacity The theory developed in the foregoing sections also has more specific implications for selective advantage. We have noted at various points that architectural change proves to be especially problematic when decision makers cannot foresee some of the consequences of an architectural change. If this argument is correct, then it follows that architectural inertia is favored most strongly among organizations whose properties make it hard to foresee the consequences of change. We have argued that opacity is one such property. Yet, even fully transparent organizations generate problems of limited foresight when the scale of consequences of changes exceeds their computational capacities. We will treat the transparent case in terms of complexity. We use the following notational convention to express “subgroup” changes −−→ in medians. inert(p, s, t) ξ denotes the change in the median level of architectural inertia over the interval (s, t] for the set of organizations that satisfy −−→ the condition ξ. For instance, inert(p, s, t) cpx∧op denotes the change in the median level of architectural inertia over the interval (s, t] for the set of organizations that meet the condition cpx(x, s) ∧ op(x, s). We need to take account of the distribution of architectural inertia within subgroups. Definition 5.5 (Conditional distribution function) Finertp (t) (y | ξ) = Pr{inert(p, t) ≤ y | ξ}. Now we can state the second of the central theorems. Theorem 5.3 The selective intensity favoring architectural inertia is presumably stronger for complex and transparent organizations than for simple (noncomplex) and transparent ones. 

P p, t, u ∃λ λ < (t−s) −→ Finertp (t) (y | cpx∧¬op) = Finertp (t) (y | ¬cpx∧¬op) 

−−→ −−→ −→ inert(p, t, u) |cpx∧¬op > inert(p, t, u) |¬cpx∧¬op . The proof follows the lines of the proof of the preceding theorem but also uses T4.5. Figure 2 illustrates the implications of the theorem for the simple case in which the median level of inertia among survivors increases linearly over time.

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Median architectural inertia among survivors

Cohort of complex/opaque organizations

Cohort of simple/transparant organizations

Time

Figure 2: Illustration of empirical implications of the theory for variations in the selection intensity favoring architectural inertia

Discussion Hannan and Freeman (1984) developed a theory of structural inertia with two main parts. The first part derived the claim that social selection processes favor organizational inertia from arguments about reliability and accountability. The core insight is that the very properties (reliability and accountability) that make organizations valued social actors have the unintended consequence of making them resistant to change. This argument has ´ Nuall´ been controversial. P´eli, Bruggeman, Masuch, and O ain (1994) formalized it in first-order logic and translated the conclusion (selection favors inertia) into a formula that states that if an organization has high inertia then it is favored. With this translation, the argument does not go through. P´eli et al. (1994) proposed a weakening of the premises that preserves the argument. P´eli, P´ olos, and Hannan (2000) argue that this translation of the conclusion of the argument does not fit the argument. They argue instead that a faithful formal rendering of the conclusion should reverse an implication in the P´eli et al. (1994) translation. With this revision, they show that the argument is logically sound as originally stated when posed either at the level of organizations or at the level of properties. The second part of the Hannan–Freeman theory implies a different process by which inertia might proliferate in the organizational world. It holds that

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change in core features of organizations set off processes of reorganization that expose organizations to a high risk of mortality and that old age and high complexity exacerbate the problem by lengthening periods of reorganization. This part of the theory has been used mainly as a framework for analyzing the effects of structural change of life chances of organizations (see Barnett and Carroll (1995) and Carroll and Hannan (2000) for reviews). But, it also has implications for the evolution of inertia. If a cohort of organizations differs in inertia (making some less likely to undertake changes) and change raises the risk of mortality, then over time there should be a greater tendency for the change-prone organizations to fail. Such a failure process yields an increase in the prevalence of inertia over time—selection favors inertia. This paper develops this implication systematically by using a more elaborated theory of structural change. In a pair of papers, we have presented a theory that incorporates the main insights of Hannan and Freeman (1984) but embeds the argument on a more detailed and specific model of organization. The first paper (HPCa) proposed an alternative way of specifying which organizational changes are weighty and potentially hazardous. It defines the significance of changes in terms of an organization’s architecture and culture, each defined as a code system. Broadly speaking, a change is significant to the degree that it sets off cascades of other changes. The second paper (HPCb) argues that foresight is generally limited in organizations and that such limits are potentially important in destabilizing organizational structures. It concludes that organizational change is more precarious when organizations are either complex or opaque or both. Here we analyzed inertia and its consequences. Previous analyses often cast the issues in terms of particular organizational properties that are associated with inertia and themselves directly favored by selection. Selection in this kind of context yields an increasing prevalence of inertia as a byproduct of the favor shown to the other organizational properties. We have no reason to doubt that this kind of story makes sense of important processes in the organizational world. But, we wanted to develop the second story in which inertia plays a more active role. We argue here, instead, that a built-in reluctance to modify architecture is neither favored nor disfavored by itself. However, such reluctance constrains organizations and sometimes prevents them from undertaking changes whose unforeseen consequences might destroy the organization. Because change-prone organizations generally make more changes, they expose themselves to risk. Unless change is generally extremely beneficial once completed, systematic benefits do not offset this additional risk. We argue that 21

there is no reason to suppose that the benefits of architectural changes generally exceed the costs and risks of change. If this is so, then the level of architectural inertia will presumably rise over time in a population of similar organizations. In other words, selection favors architectural inertia. This conclusion holds more strongly the more risky is architectural change. According to our formulation, the mortality risk due to change increases with the number of unforeseen violations that are generated. Because complexity and opacity limit foresight, change is presumably riskier for more complex and more opaque organizations. As a result, the selective intensity favoring architectural inertia works more powerfully in populations of complex and opaque organizations.

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Appendix: Methodology To represent the propositions and theorems in the arguments, we employ the nonmonotonic logic developed by P´ olos (see P´olos and Hannan 2001; 2002). In logic, monotonicity means that the set of conclusions derivable from a set of premises grows monotonically as premises are added. In contrast, nonmonotonic logics (NMLs) allow the addition of new premises (reflecting new knowledge) to overturn existing conclusions. In such logics, introducing premises that would result in contradictions according to classical first-order logic do not necessarily create inconsistency. Switches between explanatory principles follow a generic guideline: (1) when different principles give conflicting results, inferences should be based on the most specific principles that apply; and (2) when conflicting principles do not differ in specificity, no inference should be drawn. Consider a famous example of simple inference pattern in which monotonicity fails.4 Premise 1. Birds fly. Premise 2. Tweety is a bird. Proposition Tweety flies. Suppose we add three new premises: Premise 3. All penguins are birds. Premise 4. Penguins do not fly. Premise 5. Tweety is a penguin. What happens to the conclusion that seemed justified based on the first two premises alone? Not only does it now seem unjustified, but we are tempted to derive the opposite conclusion: “Tweety does not fly.” What is going on here? Compare the two possible arguments about flying. One builds on a premise about birds; the other builds on a premise about penguins. Tweety is both a bird and a penguin; so both premises apply. But, the premise about penguins seems to be more relevant for Tweety than the premise about birds. The premise about penguins seems to be more specific than the premise about birds. This difference in the specificity of the premises accounts for the difference in the relevance of the 4

This stylized example and the Nixon Diamond (discussed below) are ubiquitous in the technical literature.

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arguments. We want to use the most relevant arguments available. So, we go for the conclusion: “Tweety does not fly.” What is the source of this (implicit) specificity ordering? We argue that it is the third premise “All penguins are birds.” One might object that the presence/absence of this premise should not matter much, because our common background knowledge holds that penguins are birds. Yet, another of the logicians’ favorite examples—the Nixon Diamond—shows that common background knowledge does not always clarify inferences, Premise 1. Quakers are doves. Premise 2. Republicans are hawks. Premise 3. Dick is a Republican. Premise 4. Dick is a Quaker. Proposition ??? Our background knowledge tells us that no one can be both a hawk and a dove. Indeed, the argumentation implicitly assumes that “x is a hawk” is the negation of “x is a dove.” But, background knowledge does not inform us about the specificity of the premises. Lacking a dependable specificity order, we cannot conclude either that “Dick is a dove” or that “Dick is a hawk.” During the last 15 years, logicians working on applications in computer science designed and studied many NMLs.5 Given their typical computerscience motivation, most of these logics are suitable tools for studying reasoning in databases but they are much less useful for studying patterns of argumentation in theory building. There are two key differences. First, it obviously matters for representing theoretical arguments whether the “rules” are definitions, universally quantified propositions, metaprinciples, or insightful causal stories. These distinctions ought to be marked in the syntax used to represent a theory. However, because these distinctions are not important in modeling computer-science applications, they do not appear in the syntaxes developed in this approach. Second, the database approach treats old information as less valid than new information: one normally updates an entry in a database to override old information that has been found to be incorrect. But, argumentation patterns usually differ—updates add 5

Standard technical references on the subject include: McCarty (1980), Makinson (1994), and Veltman (1996); Brewka, Dix, and Konolige (1997) provide an accessible overview of the field of NML.

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new information but do not vitiate existing information (P´ olos and Hannan 2002). Only Veltman (1996) rigorously maintains the desired distinctions (among the different kinds of elements that comprise an argument) in designing his nonmonotonic language for update semantics. P´ olos and Hannan (2002) followed Veltman in formulating their approach. Nonetheless, they altered a number of features of his update semantics to fit the representation of social-science argumentation. This required construction of a new NML. (The details are spelled out in P´ olos and Hannan (2001).) Explanatory principles are the key substantive ingredients of theory, the specific causal explanations. So we call them causal stories. Causal stories differ from classical first-order (universal) principles in two ways. First, causal stories are more stable than classical principles, which get overturned by a single counterexample. Specifically, causal stories should be treated as informationally stable: they ought not to be withdrawn even when their first-order consequences get falsified. Instead, the effects of the causal stories are controlled by more specific arguments. Second, the grammatical surface of a causal story typically takes the form of what linguists call bare plural sentences. The normal interpretation of such linguistic forms is as generic sentences (Krifka et al. 1995), which express general, but not universal, ideas. Their truth conditions of a generic sentence cannot be expressed in terms of particular cases. In other words, causal stories are default rules, rules (with exceptions) that tell what ought to be expected under normal conditions. As a theory develops, the only thing that can happen to a causal story is that new insights restrict its domain of application, if knowledge about exceptions develops. Even new knowledge should not lead us to discard a causal story. Instead, we add new rules to the body of knowledge; and we allow the new, more specific rules to override older, more general rules. Suppose that new knowledge casts serious doubt on a causal story. Then discarding it might be exactly the right thing to do. Yet, doing so means that the theory is changed so fundamentally that we should regard the old theory as having been ended and a new theory begun. The P´ olos–Hannan approach differs from previous developments in nonmonotonic logic in how the specificity orderings of arguments are defined. In formal terms, it builds formal models of arguments in terms of sequences of the intensions of open formulæ. It employs two formal languages. The first, the language of working theory, is used to represent causal stories. It introduces a new kind of quantifier, denoted by N. Formulæ quantified by N state what is expected to “normally” be the case according to a causal 25

story. As noted above, the normal case is a default, what we assume to be the case if we lack more specific information that overrules the default. The use of default reasoning plays a very crucial role in our reasoning about change and mortality. The second language, the language of theory testing, is used to represent so-called provisional theorems, the logical consequences of a stage of a theory. Provisional theorems have a haphazard existence: what can be derived at one stage, might not be derivable in a later stage. So the status of a provisional theorem differs from that of a causal story. The syntax of the second language codes this difference. It introduces a “presumably” quantifier, denoted by P. Sentences quantified by P are provisional theorems at a stage of a theory if they follow from the premises at that stage. Finally, the new methodology designs formal machinery for testing what follows from the premises in a stage of a theory. Such testing operates on representations of arguments in the form of rule chains. The links in these chains are strict rules and/or causal stories. The chains start with the subject of the argument and terminate with the purported conclusion (the consequence to be derived). In nonmonotonic inference, different rule chains— each representing an argument embodied in the state of the theory—might lead to opposing conclusions. The testing procedure determines whether any inference can be drawn at all and, if so, which one. Such testing requires standards for assessing whether a pair of relevant rule chains is comparable in specificity and for determining specificity differences for comparable chains. It thus provides a method of constructing proofs of the claims of a theory. It does not require expertise in logic to realize that all of the theorems offered in this paper would be derivable in classical first-order logic, had the assumptions (causal stories) been presented as universally quantified axioms. We still insist on using a non-monotonic approach not because classical logic is not powerful enough but because it is too powerful. We argue in the body of the paper that in higher is the architectural significance of an organizational feature affected by a change the longer the reorganization period happens to be, and we also argue that the higher the cultural significance of a change the longer the reorganization period. In other words, this part of the argument contains follows the pattern of a Nixon Diamond. In a classical setup these two principles are sufficient to show that it is impossible that the same change has higher architectural significance and lower cultural significance in one organization, and lower architectural significance and higher cultural significance in an other organization. To avoid such immature conclusions non-monotonic logic serve us well. Neither of the two 26

arguments is more specific then the other. If the architectural and cultural significance of a given change are both greater than that of another, then our theory makes a prediction. But, if one dimension is higher and the other is lower (the Nixon Diamond), then no prediction is made. Although Nixon Diamonds proliferate the argument, Tweety patterns do not arise here (as they do in the formalization of age dependence (P´ olos and Hannan 2002)). This means that the proofs are simple and straightforward. We indicate in the display of each theorem the premises that make up the shortest rule chain that generates the proof.

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