organization, emotion and performance...

ORGANIZATION, EMOTION AND PERFORMANCE:

INTERACTIONS BETWEEN FORMAL AND INFORMAL STRUCTURES.

R. COWAN† AND N. JONARD‡

Abstract. Organizations are composed of interdependent design elements, including both for-mal and informal structures and processes, whose interaction and alignment determine perfor-mance. This paper addresses two aspects of organization alignment: formal structures and theenvironment; informal structures and formal structures. The formal structure determines workflows (who can pass work to whom); the informal structure supports the social transmission ofstress. Social dynamics of stress and effects of stress on productivity are well-documented inthe psychology literature. Using a computational model we examine the effects of alignmenton organization performance in the presence of varying degrees of environmental turbulence,and intra-organizational social stress dynamics. Alignment between the formal organizationand its environment is always good for performance, but when stress is present in the modeltwo regimes (corresponding to high and low stress) can emerge, and they present very differentlevels of productivity. The higher the quantity and quality of social interaction, the strongerthe difference in the two regimes. Stronger alignment between formal and informal structuresdecreases performance, whether or not the organization is aligned with its environment. Gen-erally, higher quantity and quality of social interaction produces more unpredictability in theperformance of the organization. Organizations can improve performance by improving qualityof social interaction (through human resource management for example), but at the cost of lesspredictability. Similarly, cutting fat as a strategy for improving efficiency may be self-defeatingas it reduces opportunities for social interaction to mitigate high stress-low productivity situa-tions.

†BETA, University of Strasbourg, Institut Universitaire de France, and UNU-MERIT Maas-tricht University‡University of Luxembourg.

keywords: stress, emotional contagion, social networks, formal organization, informal socialstructure

Date: May 12, 2015.We gratefully acknowledge the very helpful comments to two anonymous referees. We also thank Tim Folta forvery insightful conversations regarding the model, and Rifka Weehuizen for her very valuable insights into socialstress dynamics. Research assistance was provided by Francois Lafond.

1. Introduction

Organizations are composed of interdependent design elements, including both formal and

informal structures and processes, whose interaction and alignment determine performance. In-

vestigations of the past 60 years lead to the strong conclusion that the relationship between

design and performance is a complex one. The consensus in the literature is that no general the-

ory of design exists, but rather that the “right” design for any organization depends heavily on

a variety of contingencies (Mintzberg 1980). Contingencies that have been explored include the

nature of technology (Woodward 1965), task interdependencies (Thompson 1967), information

processing (Galbraith 1973; Tushman and Nadler 1978), environmental turbulence (Lawrence

and Lorsch 1967), environmental complexity and decomposability (Siggelkow and Rivkin 2003)

and so on.1 Nadler and Tushman (1980:43) formulate this very generally when saying that “...an

organization is most effective when its strategy is consistent with its environment (in light of

organizational resources and history) and when the organization components are congruent with

the tasks necessary to implement that strategy.” Congruence refers to how well components

fit together: how well task assignment fits peoples’ expertise; organization structure fits envi-

ronmental demands; information processing capacities fit information processing requirements;

informal and formal structures support or impede each other.

Empirical studies have examined various types of congruence, but currently few formal analyt-

ical framework exists with which to organize the results and intuitions. In this paper we present

a computational model of two types of congruence: the organization with its environment, and

formal and informal structures within the organization. We use this model to show how the

two congruencies interact to determine organization performance. When complex components

interact, such a numerical model is very useful in tracing the effects of changes or variations

in one or another part of the organization. Our concern has to do with complex interactions

1For example, one dimension of structure is the extent to which the organziation is hierarchical. The associationbetween a flat (rather than tall) hierarchy and performance is found to be positive by Worthy (1950) in a largedepartment store (Sears Roebuck) as well as by Ivancevich and Donnelly (1975) for salespersons, but negativeby Meltzer and Salter (1962) for physiologists and by Blau (1968) for government agencies; Mackenzie (1978)and Roberts (1990) argue that a high degree of hierarchy increases performance and reliability, but Jablin et al.(1986) and March and Simon (1958) invoke a loss of information stemming from condensation and uncertaintyabsorption to argue the opposite — different contexts, conceptualizations and metrics yielding conclusions thatare hard if not impossible to generalize (see also the comprehensive survey by Anderson and Brown 2012).

2 COWAN AND JONARD

among variables which are difficult to access empirically, and whose interactions are difficult to

sort out empirically (particularly those governing the social dynamics of stress, or measures of

environmental fit that are independent of performance). By adopting a simulation approach we

are able to address these interactions in a controlled manner and thoroughly investigate their

consequences, unconstrained by the difficulties often encountered in empirical investigations of

these types of issues.2 A second contribution of the model has to do with terminology. Much of

the literature seems to employ a terminology that borders on tautology. “Fit”, “congruence” or

“alignment” often seem to have no clear definition independent of firm performance. Therefore

to use any of these terms as explanans for firm performance runs a big risk of circularity. In

this paper, while we do discuss fit or alignment, we employ a measure which is defined indepen-

dently of firm performance (concretely the measure we use is the correlation between networks).

This will enrich both theoretically and empirically the discussion of the congruence of different

aspects of organizational structure.

We use well-established results from psychology to examine how the interaction of formal

and informal networks in the organization affect individual performance and ultimately organi-

zational outcomes. Formal organizational elements in the broad sense refer to the structures,

processes and methods intentionally created in order to distribute tasks and coordinate the

actions of individuals in pursuing organization goals. Standard examples would be organiza-

tional charts, formal workflows and procedures, authority and approval relationships, all of

which result from explicit design efforts to align the organization with its strategy and business

environment, and to optimize its processes (see for instance March and Simon 1958; Burns

and Stalker 1961; Lawrence and Lorsch 1967; Thompson 1967 or Galbraith 1973; Nadler and

Tushman 1980, 1999). Informal elements, on the other hand, are emerging arrangements such

as friendship relations, advice networks, information-seeking routines and in general processes

and structures that do not follow from intentional design at the level of the organization but

rather have formed from the interactions among members of the organization (Krackhardt and

Hanson 1993; Krackhardt 1994; Gibbons 2004; Gulati and Puranam 2009).

While it is widely believed that organizations rely on both formal and informal elements to

coordinate task roles in order to reach collective objectives, the joint effects and coevolution

of formal and informal elements have remained relatively unexplored in the literature. It is

explicit in Nadler and Tushman’s research on congruence, but the formal/informal distinction

was already clear in the work of Van de Ven et al (1976) or Thompson (1967) on the relationship

between coordination modes (going from impersonal to personal to group) and task uncertainty

2See Burton and Obel (1995) for a full discussion of the value of simulation in organization science.

ORGANIZATIONS AND EMOTIONS 3

or interdependence,3 and strongly suggested in March and Simon’s (1958) decomposition of

coordination in terms of programming and feedback or mutual adjustment. However, McEvily

et al. (2014:299) argue in a recent survey that over the past two decades a disproportionate

focus of research on (informal) social networks “...has left a disconnect between the literatures on

formal organization and informal social structure such that crucial questions at the intersection

of the two streams of research have been neglected.”

In this paper we take up the challenge laid out by McEvily et al. and develop a model incor-

porating both formal and informal structures. In the model members of the organization are

embedded in two distinct networks that guide and constrain both their behaviors and the flow of

organizational resources. Together, these two networks, the formal and the informal, form the

organizational architecture (Nadler, Tushman and Nadler 1997) in which actors are embedded.

Firm performance is the ultimate concern, and formal structures (hierarchies, teams) are known

to have contingent effects on performance. Our model is consistent with those effects, but adds

two things. First is an examination of the “fit” between formal and informal structures. Second

is the dynamics of individuals’ stress and its effects on performance. Individual stress affects

individual productivity, and stress is affected by both formal and informal interactions. Thus

the general issue we address is the conditions under which the informal structure exacerbates

or moderates the stressors arising from formal interactions.

The formal part of network architecture in the model summarizes the workflows (seen as

flowcharts) and procedures that regulate work, connecting task roles with one another. We

map roles one-to-one with organizational members, so that the formal, workflow network is

an actor-to-actor network in which two employees are connected by a directed link when one

provides resources (information, work, materials, supervision, task-related knowledge,...) to the

other. This allows us for instance to capture Thompson’s (1967:54-65) flows of work, materials

and objects between personnel — pooled or parallel, sequential and reciprocal. Although the

formal network connects people, it is worth recognizing that the connection between two people

is about the task roles they perform, not about the persons they are. The persons they are will

be relevant to the informal network.

3Although there were formal and informal elements (in the sense of designed and spontaneous), the divide wasnot between these but rather in terms of the amount of autonomy and information needed to function. InVan de Ven et al. (1976:323), the impersonal mode consisting of “...the use of pre-established plans, schedules,forecasts, formalized rules, policies and procedures, and standardized information and communication systems...”,all mechanisms for which “...a codified blueprint of action is impersonnally specified...” and whose “...use requiresminimal verbal communication between task performers” has informal elements to it, while the personal mode inwhich “...individual role occupants serve as the mechanism for making mutual task adjustments through eithervertical or horizontal channels of communication” has many formal elements to it.

4 COWAN AND JONARD

The informal part of network architecture in the model focuses on affect and social support.

In the recent literature (Gibbons 2004; Casciaro and Lobo 2008) the informal network has cov-

ered two major notions: task-related relations between advisors and advisees on the one hand,

and the much more task-independent affect relations between friends on the other hand. The

advice network, closely related to organizational power and status (Ibarra and Andrews 1993;

Krackhardt 1990), is the substrate individuals tap to accomplish their work, independently from

what the formal organization workflows and procedures suggest. The friendship network, on

the other hand, being “...based on personal attraction and mutual positive affect...” (Gibbons

2004), conveys shared understandings and trust. It has been shown to be linked with com-

mitment to the organization (Morrisson 2002) and resource sharing during crisis (Krackhardt

and Stern 1988) among other things. The literature suggests an important overlap between

advice and friendship networks (Ibarra 1992). At the same time, the two networks do differ in

terms of their consequences (on people’s values for instance, as shown in Gibbons 2004). But

the two networks have also been shown to interact: Casciaro and Lobo (2008:655) remark that

task-related networks in organizations reflect the trade-offs made by people when combining in-

strumentality (in the sense of competence and intellectual desirability) and affect (in the sense

of liking and social desirability) in interpersonal evaluations, observing that affect is a strong

moderator of task competence.4

In the model our informal structure is taken as a friendship network. While informal structure

in the organization can concern many things, friendship is certainly a large aspect of it, and

friendship links are typically more important carriers of affect than other kinds of relations.

Affect, as we argue below, can be extremely important in individual motivation or productivity,

so this focus captures an extremely important role of the informal network.

The paper most closely related to this one is Soda and Zaher’s (2012) empirical study of a

financial services firm, in which they find that iso-morphism between formal and informal net-

works is good for firm performance. While they also view the organization as two interacting

networks (the formal and informal structures) their informal network is the advice rather than

the friendship network. Thus what their informal network transmits (namely information on

how to do a job or solve a problem) is directly relevant to the task role of the individual and

ultimately to organizational outcomes. Our informal network transmits affect, which is relevant

to individual performance, but only indirectly. As our focus is on a different function of infor-

mal networks our findings differ, and we find value in independence rather than isomorphism.

4Some research also compresses the two networks into a single one: Shah’s (2000) paper on layoff survivorsexamines how downsizing, by disrupting existing advice and friendship networks in the organization, revealsnegative reactions to the loss of friends in the organization but positive reactions to the loss of coworkers insimilar structural positions (a non-friend with whom many friends are shared).


However the framework we provide can be generalized to include different types of informal

interactions, which will, by their different natures generate different types of value or effects on

productivity.

In our model, the formal and informal networks interact to determine individual productivity

levels, and the intervening variable is individual stress. We base our model on well-established

evidence from social psychology, referring to phenomena which jointly create complex individual

and organizational performance dynamics. It is worth emphasizing that although we have chosen

to frame the issue in terms of stress, the point is more general and our model can capture and

analyze any phenomenon involving attributes or features of individuals which respond to changes

in workflow and social interaction. Because of the existence of an abundant literature on stress,

with well identified effects, we have taken stress as our specific application, but individual

commitment, intrinsic motivation, or identification with the organization could equally likely

be at the centre of the analysis.5

Psychologists have identified three aspects of social stress dynamics and the effects of stress

on productivity.

First, experienced stress influences the ability to perform given tasks. The original purpose

of stress is to trigger coping behavior — a form of resource deployment by the agent — which,

when effective, reduces or eliminates the stressors (Seyle 1956; Cox 1978). High levels of stress

however imply deteriorated judgement, misdirected behavior and a reduced ability at effective

coping (McEwen and Sapolsky 1995; Sapolsky 2004) so stressors will not be reduced, agent

response will keep deteriorating, stress will increase further and effective coping decrease further

(Hobfoll 1989).6

Second, workload can be a major source of an individual’s experienced stress. In the well-

known Demand-Control model (Karasek 1979), stress results from discrepancies between the

demands dictated by the structural or organizational aspects of the work environment and the

capacity to deal with them (lack of control in terms of planning, regulating, (self-)managing,

decision-making,...). This misalignment renders the agent unable to cope effectively, yielding

withdrawal, reduced motivation and commitment, and further stress accumulation (Karasek and

5We are grateful to a referee for pointing this out.6Kahneman’s (1973) view on attention and effort is related: human beings make use of a scarce resource —cognitive energy — in information processing and decision-making. The provision and allocation of cognitiveenergy is determined by the perceived importance of tasks and ultimately determines the speed and quality ofcognitive performance. More stress implies more energy mobilized from a limited and rapidly consumed reservoir,limiting task performance and coping ability. Cognitive scarcity and effort have been the focus of many studiesin psychology and economics (Simon 1982; Conlisk 1996; Prelec and Herrnstein 1991), serving as a basis for thenotion of bounded rationality.

6 COWAN AND JONARD

Theorell 1990).7 Gilboa et al. (2008) find that a long list of stressors (including role ambiguity,

role conflict, role overload, job insecurity, work-family conflict, environmental uncertainty and

situational constraint) all have a negative effect on job performance. Distinguishing hindrance

(organizational politics, red tape, role ambiguity, job insecurity) and challenge stressors (work-

load, time pressure, job scope and responsibility), LePine et al. (2005) use strain and motivation

as mediating variables to find that hindrance stressors have a negative effect on performance

both directly and indirectly through strain and motivation, whereas challenge stressors have a

positive direct effect on performance and offsetting positive and negative effects via motivation

and strain.

Third, social interactions can both increase and decrease the stress level of the individuals

involved in them. Besides (autonomous) coping, involvement in social relationships is gener-

ally beneficial, increasing well-being and reducing stress through buffering effects. Social sup-

port from spouses, friends, colleagues and family helps reduce stress and psychological strain

(Glowinkowski and Cooper 1985) and is one of the main mechanisms of buffering (Cohen and

Wills 1985; Lepore 1992; Florian et al. 2002). However, as good as buffering may sound, be-

ing used as a buffer is somehow less attractive. Crossover is the process occurring when the

psychological strain experienced by one person affects the level of strain of another person in

the same social environment (Westman 2001; Westman and Etzion 1995; Hatfield et al. 1994

for a survey). An analogous phenomenon is contagion, the process by which one individual’s

mood and/or perceptions seem to spread to those in close proximity. Social interaction thus

tends to promote stress convergence, but not necessarily stress elimination. Both social support

and crossover follow patterns of affiliation or responsiveness, and their intensity depends on the

strength of the affiliation, or agents’ affinity with each other (see Gump and Kuliks 1997; Bena-

zon and Coyne 2000). In turn, the quality and amount of social support a person is able to give

is negatively affected by the person’s own stress level (Procidano and Smith 1997; Silverstein

et al. 1996; Repetti 1989; Repetti and Wood 1997).

In the next sections, we incorporate these effects into a simple model of an organization that

coordinates the work of its employees towards accomplishing collective tasks. In the model we

develop, tasks in the organization’s environment, consist of several sub-tasks. Each agent in

the organization has expertise that is suitable for one specific sub-task, so completing a task

implies passing it among different agents in the organization. The formal organization structure

7Van der Doef and Maes (1999) and Hausser et al. (2010) have reviewed the past 30 years of empirical researchon the Demand-Control(-Support) model (20 year coverage for the former, and the subsequent 10 years for thelatter) and come to the robust conclusion that individuals in high strain jobs are more likely to suffer mental orphysical illness and reduced well-being, though control moderates these effects in some circumstances, as does,importantly, social support.


determines how task-passing can take place, that is, who can pass work, material, information

and other task-related resources to whom. As tasks are passed among agents through the

organization, each agent has changing numbers of tasks awaiting his or her attention. These

changes in workload affect agents’ stress levels and consequently their abilities to perform their

sub-tasks. On top of these effects, informal social interactions also influence agents’ stress levels

through the effects of coping and buffering as discussed above.

Though the informal and formal structures can have any form of relation (from isomorphism

to independence) they jointly determine the psycho-affective state of agents, their performance

and ultimately organizational outcomes. Central to an organization’s success, then, is its ability

to coordinate and efficiently transmit tasks among agents, but also to manage the alignment of

the formal and informal components of its network architecture. In such a context, we are inter-

ested in understanding which structural attributes of the formal and informal organization affect

its performance, and how they interact. As the model combines results of social psychology re-

search on stress with insights from modern theories of organizational behaviour, it provides an

integrated understanding of how social, psychological and structural factors jointly affect the

workings and performance of organizations. We find that agents’ embeddedness in multiple

relations (the formal, workflow and informal, friendship networks) yields complex effects. De-

pending on the alignment of formal and informal elements, social interaction is capable both of

amplifying and of undoing the effects of organizational design. This has important implications

for organizational design as well as for the management of slack in the organization.

2. The model

Following the discussion above, the model we develop has two parts: the operation of the

organization, and social interaction among its members.

We characterise the goal of the organisation as the efficient completion of tasks, and we will

measure an organization’s effectiveness by the number of tasks it completes in a given time.

Each task consists of a list of sub-tasks of particular types which must be done in a given order.

Each member of the organisation is specialized in one type of sub-task, thus for a task to be

completed, it must be passed among members of the organisation so each of the sub-tasks can

be addressed by the agent who has the appropriate expertise. In this sense, the organization

coordinates task roles in the presence of specialization (Thompson 1967; Van de Ven et al. 1976;

Nadler and Tushman 1980; Levitt et al. 1999; Garricano 2000).

Different organisations might have different structures, and so different workflows (who can

pass work to whom). In a pure and strict hierarchy for example, work can only be passed

8 COWAN AND JONARD

down, and within a branch of the hierarchy; by contrast in a perfectly flat organization, the

task-passing network can appear random, as anyone can pass work to anyone else.

When all sub-tasks in a given task are completed, the task is finished and leaves the organi-

sation. We assume that at any time the organization is processing the same number of tasks, so

a new task arrives only when a task is completed. Agents have a fixed processing capacity, so

can work on at most one task per period. At any point in time, any agent in the organisation

will have some number of sub-tasks awaiting his attention. The extent to which these are piling

up on his or her desk affects the agent’s stress level, and thus productivity, broadly defined, as

discussed above.8 The lower the agent’s productivity, the longer it takes him or her to pass the

task to the next agent. Finally, agents interact socially with each other, and are thus subject to

social dynamics of stress. Within this general framework, we are not interested in specific types

of organization (hierarchy, team, etc.) but rather in two types of alignment or congruency: the

fit between the formal organization structure and its external environment; and the fit between

formal and informal structures within the organization.

In the sections below, we give the details of each element of the model.

2.1. The environment: tasks and subtasks. The environment in the model consists of the

population of tasks that the organization will face over its lifetime. A task t is an ordered

sequence of ` sub-tasks, t = (t1, . . . , t`), and there is a finite set N of types of sub-tasks,

N = {1, 2, 3, . . . , n}. To generate the task population we proceed as follows. First an initial

task set S is constructed by forming vectors of length ` with random draws from the set N . We

add randomly created tasks to this task set until each sub-task-type appears at least once in the

task set. Then, with this task set in hand, we create an (ordered) list of all future tasks: the task

population. This we do by sampling with replacement the task set for a very large number of

tasks. This task population constitutes the environment of the organization. To illustrate, in an

environment in which the set of possible sub-tasks is N = {1, 2, . . . , 8} and tasks are of length

` = 5, a possible initial task set is provided by S = {(2, 5, 1, 8, 6), (4, 7, 8, 2, 4), (3, 1, 2, 5, 7)}.

Sampling (with replacement) this initial set of 3 tasks would yield an environment for the

organization.

2.2. Organizational, formal structure. As the environment confronts the firm with tasks

involving all existing sub-task-types in N, it is reasonable that all least one member of the or-

ganization is able to address any sub-task. For simplicity, we assume a specialized organization

such that each agent has a unique expertise and we index agents so that agent i can address

8We abstract here from other sources of stress.


sub-tasks of type i, for all i ∈ N .9 Tasks being ordered lists of sub-tasks, we also need com-

munication patterns between agents. An organisation thus consists of a set of agents and a set

of pairwise links among them, together forming a directed network in which the links indicate

communication or work-flow patterns. Specifically, a link from agent i to agent j implies that

i can communicate with or pass work to j.

Is there an intuitive way to create the best-aligned organization? To complete a task the

organization must structure its work flow such that any task that enters can be successfully

transmitted among those who will complete the sub-tasks. This is clearly possible if in the

organization, anyone can pass tasks to anyone else. But such an organization is likely to have

very many transmission channels that are never used. By contrast, the best-aligned orga-

nizational structure will concentrate flow where transmissions between sub-tasks take place.

In the simple example considered above, communication must be active between the ordered

pairs that appear in the tasks. So it must be possible to transmit tasks between agent-pairs

(2, 5), (5, 1), (1, 8), (8, 6), (4, 7) and so on. This way, each task can be completed with only 4

transmissions. Following this logic we construct a transmission matrix T , where each element

in the matrix, Tij , is an indicator (1 or 0) of the presence or absence of the transmission from

sub-task i to sub-task j in the task set S. No other potential transmission channel between

two agents should be allocated transmission capacity, as it will always be idle. This creates

an asymmetric, binary matrix describing the work flow that an organization will face, given its

task environment.

One final issue remains, namely that the previous binary structure prevents the completion

of any unforeseen transmission (nothing flows along a link of weight 0). To permit exception

handling, we allow a (small) amount of reverse flow on any existing link, thus making the

organization “quasi-symmetric”. For any Tij = 1 we assign also a small positive weight to Tji,

Tji = ε � 1 (in practice we set ε = .05). The transmission matrix T can now be seen as a

weighted adjacency matrix which describes the network structure of the organization.10

To ensure that organizations are comparable in their ability to transmit information and

govern workflow, we normalize the entries so that the sum of weights in T is equal to n − 1.

For the example given above, with 8 individuals in the organization and the task set S of three

9Since no two members of the organization have the same specialty, no coordination issue can arise in theworkflow; in that respect the fit between individuals and tasks is as good as can be.10As an observation, we point out that the matrix T can be used to investigate modularity. It is analogous to forexample, the matrices in Figure 1 of Ethiraj et al. 2008. See also Baldwin and Clark (2000). Here modularitywould exist in the population of tasks — can their sub-tasks be arranged in a modular way? This providesanother axis which could interact with alignments: does the value of alignment (of either type) vary with thedegree of modularity in the task population. We leave this for further work.

10 COWAN AND JONARD

tasks, the organizational structure would be described by the final weighted adjacency matrix

T below:

T =(8− 1)

11(1 + ε)×

· 1 ε 0 ε 0 0 1

ε · 0 1 1 0 ε 0

1 0 · 0 0 0 0 0

0 ε 0 · 0 0 1 0

1 ε 0 0 · 0 1 0

0 0 0 0 0 · 0 ε

0 0 0 ε ε 0 · 1

ε 1 0 0 0 1 ε ·

where the first term is the normalization factor.11

With T , we have created an organization that is perfectly ‘fit’, in the sense of being aligned

with its environment. But for this to be a reasonable way to create the formal workflow struc-

ture, one must assume that a firm can read its environment, form a valid idea of the type of

tasks it faces, and incorporate this knowledge into its strategic architecture and organizational

design (so the usual sequence from environment to strategy to organization, see for instance

Nadler and Tushman 1999). Perhaps this is possible in some instances, but in general this

level of perfection in fit seems unlikely. Indeed, depending on the degree of turbulence in the

environment, a firm will be able to do this to a greater or lesser extent. We would expect

that as turbulence increases, firms will be less and less able to create a structure that mimics

the structure of tasks they face. To capture varying degrees of environmental turbulence and

the consequent (in)ability of organizations to align with their environments, we take things the

other way around and perturb the previous organizational structure. With tunable probability

p we rewire each link of the fit structure.12 To measure this alignment between the formal

organizational structure and its external environment, we record the correlation between the

adjacency matrices of the fit and rewired structures.

2.3. Workflow. A task t = (t1, t2, . . . , t`), enters the organisation directly onto the desk of

agent t1. When agent t1 has completed sub-task t1, he or she attempts to pass the work

11One could also imagine that more frequent transmissions in the intial task set (such as the transmission from 2to 5 occuring twice in our example) have larger transmission channel than the others, or that the flow capacity isthe relative frequency of transmissions in the task population rather than the initial task set, all variants whichdo not alter significantly our findings.12“Rewiring” implies that for any pair ij such that Tij = w > 0, with probability p set Tij = 0 and either Tik = wor Tkj = w for a randomly chosen k. Thus p can be seen as implicitly reflecting environmental turbulence: whenp = 0 the environment is entirely predictable and the organization can be perfectly aligned with it; when p = 1turbulence is so high that the organization cannot predict anything about the nature of future jobs, and so cannotalign in any meaningful way the organization structure with its environment.


to agent t2. If there is a direct connection from t1 to t2 the work is passed directly. If no

direct connection exists, then agent t1 needs to pass the work to a different agent. We assume

that members of the organization are knowledgeable about the formal structure, so know the

shortest (weighted) paths from themselves to any other agent in the organisation. So agent t1

will pass the work to the first agent on the shortest path to agent t2. This is repeated until t2

is reached, after which t2 completes its sub-task and attempts to transmit the work to agent t3

for completion of sub-task t3. Again the same principle applies and eventually the work reaches

agent t`. When agent t` finishes his sub-task, the task is passed out of the organisation and at

that point is considered completed.

From the above it is important to see that although a task involves exactly the completion

of ` sub-tasks by ` agents it will, depending on the distribution of flow in the organization

(what we refer to as the organization’s formal structure) possibly involve many more agents

and many more transmissions (if no direct connection exists between two consecutive sub-tasks

ti and ti+1 in t). In other words, a misaligned structure will impose for a task t many extra

transmissions between agents who are not part of t (or are part of t but need to intervene also

as pure transmitters) and therefore a much longer completion time for the overall task.

Sub-task completion is probabilistic: the lower an agent’s stress level, the more productive

her or she is and the faster he or she will compete the sub-task. This is modelled simply as the

probability of completing a subtask in any period, t, is

(1) pi = 0.5/z2i ,

where zi is agent i’s stress level in that period.

Work-passing, or transmission, is also probabilistic. It depends on the flow capacity of the

link between the two agents involved, and on the stress levels of the two agents involved. In

general, transmission from agent i to agent j succeeds with probability

(2) pi,j = Ti,j/(zi × zj)2.

Transmission is more likely to succeed as the strength of the communication channel, Ti,j ,

increases, and as the stress levels, zi and zj , of the agents involved in the transmission decrease

(we describe below how stress is determined). Suppose for a moment that agent ti succeeds in

transmitting the task. Then i is free to address attention to another task in the next period. If

he fails to transmit, he tries again in the next period. So an agent’s capacity in each period is

used up by one attempt at transmitting, whether the attempt succeeds or fails. At any point

in time, any agent has a (possibly empty) queue of partly completed tasks on his or her desk.

12 COWAN AND JONARD

Partly completed tasks are treated according to a first-in-first-out principle: the oldest task on

any agent’s desk is always treated first, whether it is for completing a sub-task, transmitting

a task for which the agent’s sub-task is complete, or acting as a pure transmitter on the path

between two sub-tasks.

2.4. Social, Informal structure. Beside the formal network over which agents can pass tasks,

there is a network which structures agents informal interactions within the organization. Part

of our interest is whether alignment (or in this case iso-morphism) between formal and informal

structures is beneficial or detrimental to firm performance.

To control this informal network we proceed as follows. Our tuning parameter is pISO ∈ [0, 1].

We start with a social network that is isomorphic to the workflow network, with links unweighted

and undirected (we assume that communication in the social network is symmetric and of

uniform intensity) — the weighted adjacency matrix T describing organizational structure is

simply made symmetric and binary. Then with probability pISO we rewire one of the endpoints

of each link uniformly randomly to new agent in the network. When pISO = 1 the resulting

network is totally uncorrelated with organizational structure: any pair of agents is equally likely

to be connected, regardless of whether that pair is connected in the formal structure or not.

This algorithm does not completely cover the space of possible informal structures. Thus we

add a second part in which we do effectively the reverse. Here we start by constructing a social

network that is the mirror image of the workflow network with undirected, unweighted links.

Then we remove enough links to ensure that this complementary network has the same number

of links as the isomorphic network. By construction none of the links in this network exists

in the organizational network. Then, again, with probability pISO we rewire each link in this

network. With this double algorithm we span an entire family of informal networks that range

between perfect alignment (in the sense of isomorphism) and perfect complementarity (or anti-

isomorphism) with the organizational structure. This way we can test whether alignment of

these two components of organizational architecture is desirable, and more generally answer the

question of the joint effects of formal and informal structure on performance. To measure this

alignment between the formal, organizational structure and the informal, friendship structure,

we record the correlation between their adjacency matrices.

2.5. Stress dynamics. Agents in the model have distinct roles and occupy distinct positions

in two networks: they pass and receive work in the formal, organizational network, as well

as transmitting affect in the informal, friendship network. Regarding the latter, social effects

obviously go much beyond the boundaries of the organization, including spousal, family and

friends interactions, and broader, even society-level effects. While acknowledging that such


effects are at work and can play an important part in the fluctuations of individual stress levels,

our focus here is only on social interactions among members of the organization. For that reason

it might be useful to conceive of these interactions as taking place around the coffee machine

or in the cafeteria.

Because of double network membership, each agent is subject to two sources of stress dy-

namics: changes in his or her workload; and social interaction with co-workers, and each source

of stress can conduce towards high or low stress levels.

The formal network captures the workflow and therefore dictates the workload of any agent.

As mentioned above, at any point in time any agent has a (possibly empty) queue of partly

completed tasks on his or her desk. The number of tasks in the queue determines the agent’s

work stress: a longer queue implies higher work stress. This is modelled very simply as

(3) zworki =

z if qi ≤ θwork,

z otherwise,

where qi is the number of tasks awaiting attention on i’s desk and z > z.

The informal network controls the flow of affect, and therefore the social stress of any agent.

Cowan et al. (2011) present a model of stress dynamics which mimics closely the discussion in

Section 1 (p. 5). That model shows how individual and aggregate stress levels co-evolve, but

also clearly demonstrates the possibility of multiple equilibria: a single organization can, under

slightly different circumstances, stabilize on either a high or a low aggregate stress level. In the

current paper we adopt a discrete, reduced form version of that model.13 Each period a number

of agents, m, is randomly drawn to engage in social interaction. Each of those agents engages

with all of his direct neighbours in the social network. Social stress levels follow a principle

similar to work stress: more high stress neighbours in the friendship network implies higher

social stress. This is modelled very simply as

(4) zsociali =

z if hi ≥ θsocial,

z otherwise,

where hi is the number of agents in the high stress state z in the (friendship) neighbourhood of

i augmented with i himself.

An agent’s overall stress level is determined jointly by work and social stress. If both work

and social stress are high (low) then the agent’s overall stress level is high (low). If work and

13Implementing the current model using exactly the stress dynamics of Cowan et al. (2011) produces littlequalitative change, which suggests the more parsimonious model of adoption of the majority stress state isadequate. We have not presented that here simply for reasons of simplicity — the added complexity of theirstress model does not increase the insight to be gained here.

14 COWAN AND JONARD

social stress “disagree” then the agent’s overall stress level is set according to

(5) zi =

zsociali with probability α,

zworki with probability 1− α.

with α, referred to as “affinity”. The parameter α is a control parameter in the simulation

which captures the extent to which agents are sensitive to each others’ stress levels, and thus

subject to the forces described on p. 5. In other words, α can be interpreted as a measure of

the strength of affiliation or affinity among agents. The value of α can be seen as the result

of the socialization efforts of the firm: different strategies to human resource management, and

more generally to corporate culture, will yield different amounts of affinity among colleagues.

In some firms every promotion is a cut-throat competition among colleagues; and this can be

captured by a very low α. By contrast, a company whose culture demands that employees view

themselves as part of a larger family, and display care and empathy for each other, is one with

large α.

The aggregate stress level of an agent affects his or her ability both to complete the sub-tasks

in which he or she is specialized, and to pass tasks to the appropriate next agent. One comment

here is that we are effectively compounding two different sources of stress via the strength of

affinity α. The human stress system being non specific, stress easily transfers from one role to

another, for example stress created in the home environment spills over to stress or performance

in the work environment (Bolger et al. 1989; Ginn and Sandell 1997; Repetti 1989; Stephens et

al. 1997). We have kept the representation of work and social stress simple by using a binary

form which allows us to combine the two sources of stress into one level of experienced stress

simply, and then to let this level of aggregate stress be the moderator of productivity.

The precise timing of when social interaction takes place (at the start, the end or in the

middle of the period) does not affect the results, so we have opted for a timing which allows

a simple story to be told. The social network, or cafeteria interactions take place at the end

of a period, after a round of task–completing activity. People enter the cafeteria carrying their

current aggregate stress levels. A total of m agents interact with their direct social connections,

and the social stress levels of those m change according to Equation 4, and the day ends.

Overnight completed tasks leave the organization, and are replaced by new ones. When the

new day begins, agents arrive carrying the social stress levels arising from the most recent social

interactions. These are combined with the stress levels determined by the (new) pile of tasks

they find on their desks in the morning, as described in Equation 5, to generate an agent’s


overall stress level, zi. This overall stress level determines their productivities (Equations 1 and

2) in completing and passing tasks.

Intuitively, if things go “well”, the cafeteria acts as a cooling device and the joint effect of

coping and buffering exceeds the effect of crossovers, yielding overall stress reduction. However,

as casual observation suggests, the cafeteria can also be a place in which agents feed each

others’ stress. The total amount of stress in the system snowballs as agents amplify each

others’ emotions and eventually all leave the place with an even lower efficiency in the next

period. The possibility of multiple stress equilibria in the social network has been explicitly

designed into the model, based on the results of Cowan et al. (2011). Whether aggregate stress

(and thus productivity) is high or low in the system depends on the interaction of the dynamics

of emotional contagion in the social network on the one hand, and the fluctuations of workload

induced by the arrival of tasks in specific organizational designs on the other. Organizational

design then plays an essential part in selecting either the high or the low stress equilibrium.

3. Implementation

3.1. Experimental design. The model we have developed represents a complex dynamic sys-

tem which we study numerically. To remove as many spurious effects as possible the following

experimental design is followed. We create the environment first, i.e., the task set as described

in Section 2.1 and an (ordered) list of all possible future tasks by uniformly sampling the task

set. This environment remains fixed for the entire experiment. We then create an organization

— the formal network — whose fit to the environment can be tuned via the probability p, and

a friendship network — the informal network — whose alignment to the organization can be

tuned via the parameter pISO (according to the details in Section 2.4).

With these aspects fixed, we compare across two main factors: the amount of social interaction

(m) and the degree of affinity among agents (α). There are 6 levels for the first factor, intensity

of social interaction: m = −1, 0, 10, 20, 50, 100; and 4 levels for the second factor, affinity:

α = .6, .7, .8, .9. Each combination of factor levels (m,α) is considered in turn, and we let

the organization operate on the ordered task list for 1,500 periods (this duration guarantees

that organizations never run out of tasks to do). As a measure of performance we record the

total number of tasks completed by the organization over that time. Having run through all

level combinations for these two factors, we start again with a new organizational structure and

informal network.

16 COWAN AND JONARD

The simulations have been conducted in parallel on 50 cores of a computing cluster, on the

same task environment but in otherwise independent replications which are then aggregated

and analyzed to yield the results analyzed below.

3.2. Parameter settings and effects. Several parameters need to be set, which we do now

and briefly comment upon.

We set the organization size and number of sub-task types to be identical and equal to

n = 100. We assume that members of the organization are specialized; each able to do one

specific sub-task type. We fix all tasks to have exactly ` = 10 sub-tasks, a value large enough

to guarantee that long chains of transmission can occur in misaligned organizations, and small

enough to ensure many tasks can be completed over the simulation horizon so that performance

displays enough variation.

The capacity of the organization is set to 200 tasks. At the end of each period, the task

which have been completed exit the organization and are replaced by the next ones on the task

list. Because tasks are groups of random sub-tasks, tasks will pile up unevenly on agents desks,

though at any point in time the average individual deskpile is 200/100 = 2 tasks high.

The work stress threshold is set to θwork = 5 so an agent who has 6 tasks or more on

his desk awaiting attention is in high stress. Given the average workload is 2, θwork is the

average workload plus 3 and so work stress should remain low for most of the people in the

organization. Unless θwork is unreasonably high (so that no one ever experiences high work

stress) or unreasonably low (so that everyone always experiences high work stress) the results

are qualitatively unaffected. We set the social stress threshold to θsocial = 3 so an agent is in

high stress if his neigbourhood including himself includes at least 3 individuals in the high stress

state. As for the previous threshold, extreme values should be avoided but intermediate values

make no significant difference to the patterns we find. Any agent’s stress level is always either

low or high, and we set the level of low stress to be z = 1 and the high stress level to be z = 2.

Agent i’s aggregate stress level, si, affects his or her productivity at completing sub-tasks

and passing work. The probability of completing a sub-task of type i in a period is .5/z2i ; the

probability of agent i passing a task to the appropriate next agent j (either the next agent who

can work on the task or the first agent in the shortest path to that agent) is Ti,j/(zi × zj)2.

Stress is raised to the power 2 so that the effect of being in high stress is strong.

4. Results

We have designed a model of organizational behavior and outcomes in which the organization

completes groups of sub-tasks — tasks — that need to follow a given order. The rate of


task completion depends on two aspects of the alignment of organizational components: the

classic alignment of formal organizational structure with the environment; and the less-classic

alignment of formal and informal organizational structures.

Agents in the organization both work on the sub-tasks for which they possess expert knowl-

edge, and help manage the general work flow by sending any pending task to the next relevant

agent. Agents’ abilities to do the previous two jobs are moderated by their stress levels, in a

way consistent with empirical findings in psychology and organization studies. Stress fluctuates

with an agent’s workload which results from organizational structure (and its fit to environ-

mental conditions). Stress also responds to patterns of affiliation and social interactions which

are constrained by the informal network.

We begin the next subsection by briefly discussing the congruence of organizational structure

and the environment, first ignoring any stress effects and then in the presence of stress but

without social interaction. Our findings are in line with intuition and with the literature:

structural misalignment and stress both lower organizational performance. We then introduce

social interaction, showing that the negative effects of work stress can be overcome by the

positive effects of social interaction, provided affinity is strong enough. However, when affinity

is strong, social interaction is also a source of multiple equilibria. The potential benefits from

social interaction are thus mitigated by the additional increase in the variance of organizational

performance. Finally, we explore architectural alignment, which we define as the alignment

of the formal and informal networks. We find that architectural alignment is not a desirable

feature — isomorphism between the friendship and workflow networks is the worst possible

situation.

4.1. Organizational structure, stress and environmental fit.

4.1.1. The effects of formal structures, and of work stress. When we suppress all stress dynam-

ics, organizational structure is the only source of performance variation. Indeed, absent job

stress, fluctuations in workload have no effect on individuals’ capacity to process, that is, com-

plete or transmit sub-tasks. The absence of stress implies that at any moment, total potential

flow of work is identical across all organizations.14 All organizations therefore have the same

total task processing capacity embedded in their workforce and structure.

Organizational structure affects the distribution of sub-tasks over individuals by changing

effective workflow. An organization “tuned” to its environment, (if that can be done), will

be efficient in moving sub-tasks among the people needed to complete them. This will reduce

14This follows from the way total carrying capacity in the formal network has been normalized in the organizationconstruction.

18 COWAN AND JONARD

transmission time of a task through the organization, less time spent transiting through the

organization implying faster task completion rates and better performance.

When we introduce stress, it operates through two channels: workload and interpersonal

dynamics. Initially we consider only the former. Any agent in the organization is subject to job

stress, which mounts as the number of sub-tasks on his desk awaiting completion or transmission

increases. Mounting job stress implies that the agent spends more mental energy managing his

stress and less on his work. Formally, as stress increases, the agent is less successful in completing

sub-tasks and transmitting work, that is, the probabilities of completion, and transmission to

the next agent are lower.

0.0 0.2 0.4 0.6 0.8 1.0

100

300

500

700

0.0 0.2 0.4 0.6 0.8 1.0

Alignment of structure to environment

Num

ber

of ta

sks

com

plet

ed

Figure 1. The value of structural alignment with (right panel) and without(left panel) stress. Alignment between the organization and its environment(abscissa) is measured as the correlation between T and the re-wired organiza-tion. A correlation of 1 implies that the organization is perfectly aligned withthe environment: all tasks can be passed directly from sub-task to sub-task. Acorrelation of zero implies that almost all tasks take a circuitous route throughthe organization.

Figure 1 shows the relationship between organization performance (measured by tasks com-

pleted over 1,500 periods) and the degree of alignment between the organization’s formal struc-

ture and the environment (measured by the correlation of organizational structure with the

best-aligned structure as described in Section 2.2). Reassuringly we find that structural align-

ment, in the sense of designing a structure which fits well the demands placed on it by the

environment, matters (left panel of Figure 1). The more misaligned an organization is with its

environment the more poorly it performs. This was explicitly designed into the model, so should


not be seen as a result, but rather as a check. More interesting is that this relationship also

holds in the presence of stress (right panel). Stress degrades individual, and as a consequence

organizational, performance significantly but the value of alignment between formal structures

and environment is preserved.

4.1.2. Adding social stress dynamics. In addition to job stress, agents are subject to stress

buffering and spillovers, which take place during social interaction. We explore two dimensions

of social interaction: quantity and quality. Quantity is measured by the number of social

interactions that take place each period, m, ranging from zero to one hundred. (When m =

100 the system will move very close to an equilibrium each period.) Quality of interaction is

controlled by α, 0 ≤ α ≤ 1, which captures the extent to which one agent is affected by another’s

stress level.

We present the results in a multi-panel plot, which deserves a word of explanation. The

key performance measure is the number of tasks an organization completes over the entire

history. We plot this against our measure of environmental fit, the correlation of organizational

structure with the best-aligned structure. In each panel, one point represents one organization’s

performance over 1,500 periods, on the sequence of tasks which arrive at its door. Each panel

represents one level of social interaction, m crossed with one level of affinity, α. Reading across

a row of panels, the amount of social interaction increases from zero to 100 interactions per

period. Reading up a column of panels, affinity increases from weak (0.5) to strong (0.9). The

experiment has been constructed so that each of the points in any panel has a counterpart in

every other panel. Here we are not yet concerned with the effects of formal/informal alignment

so we have simply used a random social interaction structure, having no correlation with the

formal structure of the organization.15 This issue we take up explicitly below.

Figure 2 shows the effects of the strength of affinity and the intensity of social interaction

on organizational performance. The patterns seen in the absence of stress (Figure 1) carry

over in the presence of informal (social) interaction. Again remarking that we have assumed

that there is no correlation between the formal and informal networks, aligning the structure

to the environment is always performance-improving. However, increasing this alignment not

only increases the average number of tasks completed, but it also increases the variation in

performance, and this increase is large when social interaction is very intense (m = 100 in the

last column).

Increasing quantity (moving left to right along any row) or quality (moving up any column) of

social interactions has ambiguous effects on performance. On average, both effects are positive:

15This assumption is not crucial. Running this experiment using a social network that has a high correlation tothe formal structure produces the same patterns, possibly slightly amplified.

20 COWAN AND JONARD

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Num

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sks

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0.6

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tren

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ffini

ty

Figure 2. The value of structural alignment (correlation between environment,i.e, general task structure, and organization structure) when the informal (social)network is random. Darker greys indicate higher average stress levels of agentsin the organization.

for any degree of structural alignment, expected performance increases as quantity and/or qual-

ity of social interaction increase. As interaction increases, buffering dominates the interactions

and stress is dissipated; agents who are less stressed on average complete more tasks.16 How-

ever, when interactions are strong in these senses, averages are misleading: with the increase

in expected performance comes an increase in the variance of performance — another instance

of the classic risk-return trade-off. When both quantity and quality of social interaction are

strong (m ≥ 20 and α ≥ 0.8), we observe two regimes emerging. In the first one most agents

are in low stress, and the organization performs very well. These are the lighter grey points

in Figure 2. Here social interaction acts as a cooling device. The joint effects of coping and

buffering exceed the effect of crossovers, yielding overall stress reduction. Average stress levels

in the organization are low, and productivity is high. In the other regime most agents suffer

high stress and performance is poor (darker grey points in Figure 2). Here, while in the cafe-

teria agents feed one another’s stress, amplify one another’s emotions and eventually leave the

place in worse rather than better mental shape. We can also observe that while the average

performance for any degree of structural alignment increases as quality and quantity of interac-

tion increase, the high stress regime yields an aggregate performance that is noticeably poorer

16Note that here that there is no cost of informal time. That is, spending “time” socializing does not reduce theamount of “time” spent working.


than performance when either there is less social interaction or when agents feel less affinity for

each other. So in increasing quantity or quality of social interaction to extreme values increases

payoffs on average, but the risk of getting a worse payoff increases. An organization can be

lucky, in which case social interaction raises productivity significantly relative to its absence, or

it can be unlucky, when social interaction generates lower productivity.

A final comment about Figure 2 is that when affinity is low, (α ≤ 0.7) increasing the quantity

of social interaction (reading left to right along the row of panels) has a non-monotonic effect on

average output. Initially, increasing the amount of social interaction increases performance (as

m increases from zero to m = 20, for α = 0.7; or to m = 50 for α = 0.6) performance increases.

Beyond that amount of social interaction though, average performance seems to decrease again.

Two regimes are present, with the low stress regime continuing to provide improved performance,

but in the average, this appears to be dominated by the high-stress-low-performance regime.

4.2. Aligning the formal and informal networks. In this section we examine how features

of the social network affect task completing activity, and in particular whether aligning the

formal and informal structures is beneficial as theory would suggest (Nadler and Tushman 1980

and 1999 for instance). Soda and Zaheer (2012) find alignment (or coherence as they call it) of

the formal and informal networks to be desirable. Their informal network, however, is an advice

network, whereas we consider the friendship network which conveys affect rather than expertise.

Based on the outcome of the previous subsection, in this section we examine only organizations

that are perfectly aligned with their environments (in the way described in Section 2.2 above)

and focus attention on the effect of formal/informal alignment.

As described in Section 2.4, we control the social network with the parameter pISO. To

recall, we start with a social network that is isomorphic to the formal network and rewire it,

pISO controlling the extent of re-wiring. But because rewiring is a random process, a single

value of pISO can produce social networks that are aligned with the formal network to different

extents. Thus the variable we report on the abscissa is the correlation between the isomorphic

social network and the re-wired, implemented social network.

Figure 3 uses the same conditioning plot format as Figure 2. The performance metric is again

the number of tasks an organization completes over the entire history. It is plotted against our

measure of architectural fit, the correlation of organizational (formal) structure with social

(informal) structure. Each point in each panel represents one organization’s performance over

1,500 periods, on the sequence of tasks which arrive at its door, and each panel represents one

level of social interaction (m) crossed with one level of affinity (α).

22 COWAN AND JONARD

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Alignment of architectural components

Num

ber

of ta

sks

com

plet

ed10

2050

100


0.6

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0.9

Giv

en: s

tren

gth

of a

ffini

ty

Figure 3. Tasks completed over 1500 periods as a function of architecturalalignment (degree of alignment between formal and informal structures), condi-tioned on the intensity of social interaction and the strength of affinity. Orga-nizations are perfectly aligned with their environments. Darker grey indicateshigher average stress levels in the organization.

The major finding is that architectural alignment matters (by alignment here we mean extent

of isomorphism). For any combination of the amount of informal interaction and the strength

of affinity, increasing the correlation between formal and informal structure on average lowers

organizational performance. This occurs in two ways: observing the panels to the left (and

bottom) of the plot, we see a mass of points presenting a clear negative relationship between

performance and alignment. There is a second source of a negative relationship on average

though, which is that when affinity increases and/or amount of interaction increases a second,

low-stress-high-performance regime appears. But this appears to a very great extent only when

there is strong mis-alignment between informal and formal structures. That is if either affinity

is high, or there is a considerable amount of social interaction, performance can be strikingly

good, if the informal, social, network is not aligned (correlation of less than roughly 0.4) with

the formal structure of the organization. But when architectural alignment becomes too strong,

the possibility of reaching an organization-wide low stress-high performance regime essentially

vanishes.

Figure 3 presented results based on an organization which was perfectly aligned with its en-

vironment. Here we look at the opposite extreme: an organization facing an overly turbulent

environment in which the alignment of structure is impossible. Perhaps the set of tasks faced is


unknown, or perhaps their frequencies are impossible to estimate, in any case the organization

is structurally misaligned. We capture this situation by simply focussing on rewired organiza-

tional structures that are as far as can be from the ideal structure (so p = 1 in the previous

subsection).17

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ffini

ty

Figure 4. Tasks completed over 1500 periods as a function of architecturalalignment, conditioned on the intensity of social interaction and the strengthof affinity. Organizations are assumed not to be able to align formal structureswith the environment.

Figure 4 shows the effect of alignment between formal and informal structures on these

environmental misfits. The patterns here have more variance, though the average effects are

similar: alignment between formal and informal structures is bad for performance. Again

though, as in the case where aligning formal structures with the environment is possible, here

when there is considerable social interaction and/or high affinity, some very good outcomes

can emerge. While in general the pattern is less clear in this case, these very good outcomes

are more likely to emerge when formal and informal structure are “mis-aligned” (more to the

left in any panel). At the same time as social interaction increases (in either dimension), poor

outcomes become poorer. Increasing social interaction again increases variance of performance.

Whether average performance increases with social interaction is unclear, however it does seem

clear both that poor performances gets poorer, and that good performances get better.

17As an alternative we tried sampling uniformly the interval p ∈ [0, 1] but the results were very similar to thosereported here.

24 COWAN AND JONARD

4.3. Environment and architectural alignment together. Two types of alignment have

been discussed here and in the literature more generally as important in determining organiza-

tion performance. The previous subsections have discussed each of these types of fit separately.

Here we present the results in a different way, to show the joint effect. Figure 5 is a filled

contour plot of total problems solved against the fit between formal structures and the environ-

ment (on the horizontal axis), and the fit between formal and informal structures (on the vertical

axis). Note that in this figure the grey scale has changed meaning. Here darker greys indicate

more problems solved. In the figure quantity and quality of social interaction have been frozen

(m = 20; α = 0.7). As expected given the results presented above, Figure 5 clearly shows that

best performance occurs when the organization is strongly aligned with the environment and

informal and formal structures are strongly mis-aligned. Environmentally aligned organizations

waste little time passing tasks, and so distracting those who are passing tasks from working on

tasks for which they have relevant expertise. Architecturally mis-aligned organizations “never”

suffer from high-stress spillovers which poison particular transmissions from both receiving and

transmitting ends at the same time.

0.0 0.2 0.4 0.6 0.8 1.0

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0.8

Organizational performance


Alig

nmen

t of a

rchi

tect

ural

com

pone

nts

80

100

120

140

160

180

Figure 5. Problems solved versus structural alignment and architectural align-ment. Darker greys indicate more problems solved.


4.4. A comment. Important in the results of the model is the way two colleagues interact.

One can think of a perfectly separable system as one in which each operation is isolated from

every other operation. Or more relevant in this case, the productivity of one operation does not

affect the productivity of another. To a great extent this is true in our model: the probability of

i completing a sub-task is not affected by the productivity of j. (Recall that both productivities

are determined by the agents’ individual stress levels.) However, the act of task transmission is

not separable in that sense. The productivity of i in transmitting is affected by the productivity

of j in receiving. Productivities in general scale as z−2i , where zi is the stress level of the

agent. In a separable system, average productivity would be roughly the average of individual

productivity or 1/z2. This is true of task completion in our model. However it is not true of task

transmission/receipt. There the productivity scales with (zizj)−2. To illustrate, suppose low

stress is z = 1 and high stress z = 2. Consider a case where there are two potential transmissions:

i → j and k → l, and all agents are in low stress. The average transmission time, the inverse

of transmission probability, will be 1 period. Now suppose i becomes highly stressed, and that

spills over to one of his “friends”. If the informal network is iso-morphic to the formal network

he will diffuse high stress to j. Now the i→ j transmission has probability (1/2× 1/2)2 = 1/16

and the expected transmission time is 16 periods. The expected k → l transmission times

remains at 1, for an average transmission time of 8.5 periods. But now suppose i diffuses his

high stress to k instead. Here the i→ j transmission probability is (1/2×1)2 = 1/4 so expected

transmission time is 4 periods. Similarly for the k → l transmission, so average transmission

time is only 4 periods. This is higher than the case when all were in low stress, but lower

than the case when i diffuses to j. If this interaction between sender and receiver were absent,

then no matter who i diffuses his stress to, the average transmission productivity will be the

same.18 What this points to is the importance of the nature of the interaction between the

two networks. In our case, there is a very direct connection through which productivity effects

are felt through the informal network and those effects are multiplicative. In a more general

setting, one could imagine that whole groups of agents who work together but also socialize

together can talk themselves into very low, or very high, productivity for the group as a whole.

If working and socializing as a group, has not only individual but also group-level effects, then

an informal network that is iso-morphic to the formal network can be very dangerous for the

organization’s overall productivity. If group-level effects are absent, the risk is much reduced.

18If for example the productivity of transmission were (1/z2i + 1/z2j )/2 then the average productivity of the two

transmissions after i diffuses his high stress would be (1/22 + 12 + 1/22 + 12)/2 no matter to whom he diffuses it.

26 COWAN AND JONARD

5. Discussion and conclusion

The model presented above captures several important aspects of organizational “alignment”.

The literature has stressed the importance of alignment between formal organizational structures

and environment, and between formal and informal structures within the organization. It is

relatively rare, though, to see them addressed together, and that is what we have done here. In

contrast to much of the literature on informal aspects of organizations, in our model informal

interactions serve to transmit psycho-social affect, and in the transmission either increasing or

diminishing it. We have focussed on stress as the main variable, but the mechanisms could as

easily apply to any sort of affective state that has an effect on individual performance. One

reason to focus on stress is that its social dynamics have been well-studied, and the mechanisms

of transmission relatively well-understood.

On the issue of alignment between formal structures and the environment, our model mimics

standard results in the literature. Aligning the organization with the environment improves

performance. “Alignment”, here refers to whether or not organizational structures reflect the

work-flow structures imposed on it by the nature of the tasks it will receive. Here we should

observe that in one sense the organization is very passive. It cannot control the nature of the

task flow, selecting and rejecting tasks depending on whether or not they fit the organization.

We have assumed that the nature of the firm’s business determines the type of environment in

which it operates, and that it cannot affect it. Certainly in reality firms do attempt to change

their environments, by for example specializing (or diversifying) in specific areas which are

perhaps easier to predict, and certainly there is a relationship between organizational structure

and a firm’s ability to make such adaptations. That, however, is outside the realm of our

study here. We have assumed that to be in business, the firm must process whatever tasks

the environment delivers. And when that is the case, not surprisingly, alignment is good for

performance.

More interesting is the relationship between formal and informal structures, and presenting a

formal model that treats them as interacting networks is one of the contributions of the paper.

Soda and Zaheer (2012), using a similar approach, find that increasing iso-morphism between

formal and informal structures improves performance. This contrasts with our model which

finds that mis-alignment is typically good and sometimes great, for organization performance.

The difference lies in what is being transmitted across the links in the informal network. For

Soda and Zaheer the informal network transmits advice and information (p. 756). By contrast,

our informal network transmits affect. It seems quite reasonable that informally transmitting

information and advice about our tasks to close colleagues (with whom we might even explicitly


collaborate) will make us more efficient. On the other hand, transmitting a high stress state

to a collaborator will reduce his or her efficiency, and possibly, when we need to do something

jointly, may have an joint effect on the two of us that is bigger than the sum of the parts. This

is what drives the results in our model — diffusing high stress to collaborators (in the task

transmission process) makes it difficult to make a transmission from one colleague to the next.

In a different context, Gulati and Puranam (2009) also find that mis-alignment is good

for performance. Their study focuses on the mis-alignment that occurs following a firm’s re-

organization. A major re-organization will have the effect of divorcing the informal network

(assuming that before the re-organization it had developed some iso-morphism with the formal

network) from the formal network. Gulati and Puranam argue is that this mis-alignment can

have the effect of permitting the firm to pursue two apparently conflicting goals, one being ex-

plicitly arranged through the formal network, the other happening more spontaneously through

the informal network. This mechanism is very different from that present in our model.19 For

us the mis-alignment prevents the spread of low productivity in a way that amplifies its effects.

In our organization there is no issue of multiple goals. Thus what we observe here is a second

and probably orthogonal mechanism by which (mis-)alignment can affect performance.

Our results are based on a particular assumption regarding the relationship between stress

and productivity, namely that increases in an individual’s stress reduces his productivity. One

must interpret that with some caution, on account of what is know as the Yerkes-Dodson law.

This empirical generalization states that there is an inverted-U relationship between stimulus

(which can be interpreted as stress) and performance. It could be possible that in some cases,

workers are on the left side of this relationship, and so a little increase in stress, induced in the

model through social interactions, would be good for performance. This is not included in the

model since it seems unlikely that it would apply to many organizations. It is something that

could usefully be explored further however.

A second issue that could be further explored is the cost of social interactions. In the model,

there is no cost — social interaction does not take time away from work. Some interaction does,

and some does not reduce the time agents have available to address their tasks. Introducing this

into the model could change the dynamics, and the effects of social interaction on productivity. It

would also permit a further more detailed exploration of the optimal amount of social interaction

for given organizational structures under different environmental stress conditions.

19They too present a formal mathematical model, and but their goal is to “...ask under what conditions aninconsistent organizational architecture can exist stably.” (p.430). One of their propositions addresses theinefficiencies associated with inconsistent architectures, but this is not the main focus of their formalism. Weshould also point out that while Gulati and Puranam define fit in a positive sense (a firm has a fit if it performeswell), they explicitly discuss “consistency” between the formal and the informal, which is very akin to our use of“iso-morphism”.

28 COWAN AND JONARD

The model has focussed on the value of social interaction. Psychology has found that social

interaction, through buffering effects, is in general good for keeping stress down. This result

materializes in our model, but it is contingent upon quality and quantity of social interaction.

When quality and quantity are relatively low, the model yields clear-cut predictions about the

effect and value of social interaction. But the situation is less predictable as quantity and

quality are both high. All else equal, tiny random shocks taking the form of different sequences

of task arrival (all drawn for the same distribution) translate into big differences in terms of

organizational performance. Two otherwise identical organizations can end up in very different

stress states and therefore display persistent differences in behavior and performance. This

brings us back to two practical implications of the model. Different organizations have different

attitudes towards internal relations among employees. Some encourage employees to compete

with each other, some actively encourage employees to collaborate and support each other. This

is captured in our model with the parameter we call “affinity”. As we have seen, affinity can

have an important effect, and by increasing the extent to which its employees respond to each

other’s psycho-social states (or affect) can have effects on performance. In the context of our

model, in general more affinity seems better, but this increased performance would come with

a risk, namely that the variation in performance also increases. In the right context (employees

are generally relaxed and not too susceptible to stress) higher amounts of affinity will be very

good for quickly dispersing whatever incidents of high stress might occur. On the other hand, if

employees general stress levels are higher, or they are more susceptible, then higher affinity will

have the opposite effect — magnifying instances of higher stress, and decreasing performance.

Thus manipulation of affinity within the organization must be done carefully. Finally, there

are often discussions about organizations “cutting fat”. Cutting fat has been a common way of

stream-lining organizations to increase productivity. Fat, in an organization, is often thought to

be present when employees spend less than their entire working day engaged in task-completion

or problem-solving. Social interactions in the workplace are often seen as evidence of the kind

of fat that can be safely cut. What the model here argues is that such a line can be quite wrong.

It is well-established both that social interactions can affect group and individual stress levels,

and that stress levels affect productivity. Thus cutting fat to the point of eliminating social

interactions can have unexpected effects on overall production efficiency of the organization.


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