THE GEOMETRY OF ORGANIZATIONAL ADAPTATION: DRIFT, INERTIA, AND VIABILITY GAËL LE MENS, MICHAEL T. HANNAN, AND LÁSZLÓ PÓLOS 1. Introduction Why do organizations generally lose their competitive edge as they get older? Recent theory and research on the dynamics of audiencesand categories in markets shed some new light on issues of organizational obsolescence. ő Inertia and environmental drift lie at the core of theoretical thinking about organizational obsolescence (Barron, West, and Hannan 1994; Hannan 1998; Carroll and Hannan 2000). The basic story holds that environments drift, but aging organizations cannot adapt well to change. As a result, fitness declines with age at some point, and viability then declines with further aging. Prior theoretical work on this issue suffers two important limitations. First, it does not specify clearly what drift means and why it affects fitness. Second, it relies on very strong—possibly unrealistic—assumptions of imprinting and inertia. According to this line of reasoning (Hannan and Freeman 1977, 1989), organi- zations get pre-selected at time of founding to fit to prevailing environmental conditions but have little ability to adapt to changing conditions. We develop a model that seeks to improve these two aspects of the obso- lescence argument. We clarify the notion of drift by building on new thinking about fitness, rooted in a model of what makes an offer appealing to an au- dience. And we relax the strong assumption about organizational inertia. Instead of assuming that organizations can never adapt their core features to changing environments, we propose that organizations do possess some adap- tive capacity but growing inertial pressures degrade this capacity as organiza- tions age. Date: December 8, 2012. 1 THE GEOMETRY OF ORGANIZATIONAL ADAPTATION 2 This paper develops a formal representation of this new view. It builds on recent theory and research on the role of categories in structuring markets (Hannan (2010) and Negro, Koçak, and Hsu (2010) provide reviews). This work treats categories as constructions by audiences. Audience members some- times label certain sets of producers/products and come to some agreement about what these labels mean. These meanings shape tastes and, therefore, the appeal of producers and their offerings to the audience. We emphasize the effects of variations over time in audience tastes and on responses to these changes by producer organizations. In particular we define environmental drift in terms of changes in the meanings that audience members associate with cat- egory labels. We argue that audience member’s tastes tend to shift over time and that aging organizations have trouble adapting their offerings to changes in tastes. This combination creates obsolescence with aging. The model of drifting tastes and producer inertia has a broad range of potential application (discussed in the concluding section). Nonetheless we build a detailed model for only one set of implications by narrowing the focus to organizational viability. Concentrating on a well-studied issue that has already been subject to numerous formalization attempts makes it easy to see how the new model differs from the alternatives advanced previously. In particular, we incorporate ideas about inertia into the framework relating organizational capital and fitness to viability developed by Le Mens, Hannan, and Pólos (2011). This allows us to derive some new predictions about age variations in organizational viability. The theory proposed here builds on previous attempts to unify conflict- ing theories of age dependence (Hannan 1998; Pólos and Hannan 2002, 2004; Hannan, Pólos, and Carroll 2007). This earlier work sought unification by postulating the existence of qualitatively different age periods—marked by a common age of ending of endowment and a common age of the onset of obsolescence—with distinct dynamics. We make the model more realistic by avoiding such assumptions about qualitative phases in the life course. We do not postulate a priori the existence of fixed ages of either the ending of endow- ment or of the onset of an obsolescence. Instead, we conceptualize and model THE GEOMETRY OF ORGANIZATIONAL ADAPTATION 3 the underlying processes that can vary continuously over the organizational life course. The paper has three main parts. The first builds on work on cultural re- sistance to organizational change to construct a model of age variations in adaptive capacity. The second part exposes the implications of this model to empirical test. The third part integrates this model in a broader theory of age dependence. 2. Paths of Organizational Change What matters for obsolescence in changing environments is the ability to keep pace with changing tastes by modifying aspects of offerings, which means adjusting architectures. A highly adaptive producer can alter aspects of its architecture quickly, which allows it to change its offering quickly and main- tain appeal to an audience whose tastes drift. So the concept of adaptive capacity plays a central role in our argument. Because we think of offerings as constrained by organizational arrangements, we begin with issues of speed of organizational change. Measuring the speed of change entails measuring elapsed time and the dis- tance traveled. We define movements by organizations in the space of archi- tectures (or organizational designs). This kind of effort requires attention to the geometry of adaptation, defining an architectural space and the position of a producer in the space. Let vx(t) denote an organization’s actual position in a space of architectural 2 feature values at t; and let df : F −! N be the distance between two posi- tions in the space. As we explain in Section 7, distance in such a space can usefully be regarded as an edit distance (or, more generally, a transformation 0 distance). Let df (v; v ) tell the number of changes of feature values need to convert organization x’s position from v to v0. The pair of the set of posi- tions and this distance function defines a graph space for an organizational architecture. As we explain below, the graph distance considers distance “as the crow files”—it ignores the cultural typography of the space. Just as the shortest THE GEOMETRY OF ORGANIZATIONAL ADAPTATION 4 route in physical space might pass through a mountain, a sequence of organi- zational changes might encounter an analogous roughness (specifically cultural resistance). Actual paths of change might not take the shortest distance (due perhaps to the social typography of the space). A path is a sequence of one-step moves that begins in v and ends in v0. In general more than one path connects any two positions. Some paths involve cycles, e.g., a move from A to B to A to B to C. We are interested in the paths that have the cycles eliminated. Notation (Paths of Change). Let G(v; v0) denote the set of acyclic paths connecting the positions v and v. The component paths, p 2 G(v; v0), are 0 sequences of one-step transitions: p = hv; v1i; hv1; v2i;::: hvk; v i. The length of the path p, in notation jpj, is the number of one-step transitions. Furthermore let δx(p; t) be a real-valued non-negative random variable that tells the length of time it takes the focal organization, x, to transit the path p beginning at time t. Our argument requires long-distance jumps to be ruled out, that organi- zations can change the value of only one feature at a time. We impose this constraint formally in terms of the time it takes to transit a multistep path. In these terms, the constraint that only one feature can be changed at a time can be stated as follows. Auxiliary Assumption 1. Organizations cannot make long-distance jumps in architecture space: the expected duration of the transit of a path is simply the sum of the durations of its one-step transitions. A p; t; v ; v ; x [(p 2 G(v ; v )) ! δ (p; t) = P δ (p ; t)]: 1 2 1 2 x hv3;v4i2p x v3;v4 3. Age and Resistance to Architectural Change A key postulate of Hannan and Freeman’s (1984) theory of structural inertia holds that structural reproducibility increases with age. We now situate this claim in contemporary theoretical arguments. We follow Hannan et al. (2007) (hereafter HPC) in considering the possibility that the members of the internal audience might resist certain transitions that are at odds with the organiza- tional culture. They develop the argument for cascades of induced changes: THE GEOMETRY OF ORGANIZATIONAL ADAPTATION 5 it normally takes longer for a unit to eliminate an induced violation of an ar- chitectural code when cultural resistance is stronger. We broaden the notion here to apply to any kind of attempt at changing any feature of organization. (In the sections that follow we narrow the focus to attempts at moving from one architectural configuration to another.) Cultural Resistance to Change. The core intuition is that cultural resis- tance slows change. A potentially valuable way to formalize this notion em- ploys the language of defaults or taken for granteds. Following prior work, we use a language of modalities to formalize these slippery notions. The key modalities for the present argument concern perception and taken-for- grantedness. We first introduce notations for these two domain-general con- cepts and specify how they relate to each other. Then we make apply them to the specific case of structural configurations. We introduce modal operators that are defined for an (arbitrary) audience member y and a sentence (formula) ' (Polós, Hannan, and Hsu 2010). We use the following notation for these operators: • p y ' stands for “The focal agent y perceives that ' is the case.” • d y ' stands for “The focal agent y takes for granted that ' is the case.” Throughout this section we use 'x(t) to refer some fact (or proposition) about the organization x at time t.