21COE, University of Tokyo

MMRC Discussion Paper No. 112

MMRC-F-112

A combined model of segregation and culturaldissemination models:
Searching for conditions of successful nonterritorial
offices
Graduate school of Economics, University of Tokyo
Nobuyuki Inamizu
February 2007

21COE, University of Tokyo

MMRC Discussion Paper No. 112

A combined model of segregation and culturaldissemination models:
Searching for conditions of successful nonterritorial
offices
Graduate school of Economics, University of Tokyo
Nobuyuki Inamizu
February 2007
Abstract
This paper develops a new simulation model by combining the two typical models of social
differentiation: Cultural dissemination model and segregation model. In this combined model, theagents can move around and communicate with one another on a space of non-partition andfree-address setting. Non-partition and free-address setting is called nonterritorial office in officemanagement. Nonterritorial offices have been adopted by many Japanese firms in recent years. This
paper searches successful nonterritorial offices by using the combined simulation model and two casestudies of Japanese firms. This paper suggests that "moderate" office density is a condition forsuccessful nonterritorial offices. This paper also suggests that nonterritorial offices are likely to failunder “high” or “low” office density.

Keywords
Multi-agent simulation; Office management; Cultural dissemination model; Segregation model;
Nonterritorial office; Office density
1Nobuyuki Inamizu

1. Introduction
This paper develops a new model of social differentiation by combining the two existing models.
This combined model not only will be a general model covering the two, but also will offer a newlogic of social differentiation. The results of this model are supported by the cases of two Japanesefirms introducing nonterritorial offices.
There are two typical simulation models dealing with social differentiation: “Cultural
Dissemination Model (CDM)” developed by Axelrod (1997)

and “Segregation Model (SM)”proposed by Schelling (1971). In both models, the agents interact with one another on a space being a
two-dimensional coordinated lattice. Though CDM is a cellular automaton in which agents are fixedin particular locations, SM is a basic multi-agent model in which agents can move around.
These two models explain social differentiation in different spatial settings and rules of agents.
A feature of spatial settings of CDM is non-partition, in which there are no physical barriers thathinder the agents from communicating with others around them. The communication rule of CDM isthat neighboring agents communicate and become even more similar to one another withprobabilities depended on their degree of similarity. The result is that the agents split into several
stable clusters having the same character, and that no more communication across different clusters
occurs. That is, the differences among the agents’ characters do not disappear as a whole. A feature of
spatial settings of SM is free-address, in which all agents have no fixed locations and can movearound freely. The movement rule of SM is that agents move to be near others who are similar tothemselves. This result is that the clusters of the agents having the same character emerge, and social
differentiation becomes increasingly prominent.
These models leave the problem outstanding whether the agents can retain their differences
under non-partition and free-address setting, in which they can move around freely and communicate
with many others easily. The agents of CDM may retain their differences because of not movingaround. On the other hand, the agents of SM may retain their differences because of notcommunicating with one another. We can tackle the problem by combining the two models.
In the combined model, the agents can retain their differences while moving around andcommunicating with one another though some conditions should be satisfied. One condition is“moderate” spatial density. When spatial density is “high,” the agents cannot move around freely.
When spatial density is “low,” the agents split into several clusters. The agents do not move aroundand do not communicate across the clusters.
These results have a suggestion for office management studies. In office management,2

A combined model of segregation and cultural dissemination models

non-partition and free-address setting is called nonterritorial office. Allen and Gerstberger (1973)
conduct an experiment with an R&D organization, in which one or two people were assigned to eachof the several desks or rooms surrounded by partitions. They removed all physical barriers(non-partition setting) and enabled employees to work anywhere (free-address setting), and theycalled this arrangement nonterritorial office.
The nonterritorial office seems to encourage employees to move around and to communicate
with colleagues. Allen and Gerstberger (1973) studied how long each employee spent at a single
place and clarified that, rather than staying in any one specific place, the employees preferred tomove around. They also recorded each employee’s interactions during a day chosen at random every
week and clarified that the number of individuals with whom each employee communicated as wellas the amount of communication increased after the experiment. These results are interpreted asfollows: “The best explanation for this finding probably is that each employee’s neighbors changed
from time to time, and employees tended to talk to their more numerous neighbors, especially thosewith whom they were relatively unacquainted” (Sundstrom and Sundstrom 1986, p. 268).
The nonterritorial office would be a driver of knowledge creation if the employees can retain the
differences of their thoughts while behaving as reported by Allen and Gerstberger (1973). It is
assumed that moving around in an office enhances the possibility of meeting a variety of people (e.g.,
Becker and Steele 1995). Previous studies show that frequent contact with many colleagues having
different thoughts is related to generating, sharing, and assessing new ideas (Peltz and Andrews 1966,
Allen 1977, Katz 1982). Some other researchers suggest that interaction with various people
stimulates knowledge creation (e.g., Nonaka and Takeuchi 1995, Wenger et al. 2002). Kujirai (2005)
sees the nonterritorial office as a place for knowledge creation and points out the effectiveness of thenonterritorial office. Becker and Steele (1995) refer to cases where companies introduce
nonterritorial offices not for cost reduction but for lively communication and organization reforms.
Therefore, we can say that nonterritorial offices are successful when the employees move around,communicate with many others, and can retain their differences of their thoughts.
As the new combined model suggested, nonterritorial offices with “moderate” office density
would be successful. This is supported by the cases of two Japanese firms. The first firm’s
nonterritorial office performed well. This office is so ingenious that the density is appropriate. The
second firm’s nonterritorial office worked well in the initial phase. In the second phase, however, thecompany outgrew its office, and the nonterritorial office worked less than it used to because of“high” office density. Although the company moved to a large nonterritorial office in the third phase,
3

Nobuyuki Inamizu

the new office wasn’t effective either because of “low” office density.

2. Two Typical models of social differentiation
2.1. Cultural Dissemination Model proposed by Axelrod (1997)
At a micro level, this model assumes that each agent has a common tendency to become similar
to each other through communication with neighbors.

Initial setting.
(1) Each agent is placed on a fixed lattice (there is no vacant site). There are no physical barriers thathinder the agents from interacting with one another (non-partition setting).
(2) Each agent holds “culture” represented in a character string. This “culture” is determined
randomly. If “culture” has five features (“width of culture” is 5) with 10 possible traits in eachfeature (“depth of culture” is 10), an agent’s culture could be “18943,” for example.

Rule.
(1) An agent is picked up at random and becomes active.
(2) The agent picks up one of its neighbors and calculates cultural similarity (CS). CS is the
proportion of the number of common features in the “width of culture.” For example, the agent
whose “culture” is “18943,” shares three features with its neighbor whose culture is “19743”(first, fourth, and fifth feature), the CS is 60 percent.
(3) The probability that the agent communicates with the neighbor is equal to the CS between the two
agents. Once communication between them has been established, the agent picks up one of its
cultural features and changes its trait to that of the neighbor. In the previous example, theprobability that the agent communicates with its neighbor is 60 percent, and may change theculture to “19943” if it picks up the second feature. If two agents share no cultural features (CS is0), they do not interact. If two agents have the same “culture” (CS is 1), their “culture” do notchange, although they always interact.
(4) The simulation ends if any agent does not change its “culture.”
At a macro level, the agents split into several stable cultural groups, and no morecommunications across different cultural groups occur though we tend to consider, from the tendencyof convergence at micro level, that all the agents have the same “culture.”

4

A combined model of segregation and cultural dissemination models

2.2. Segregation Model proposed by Schelling (1971)
At a micro level, this model assumes that each agent follows a rule such as “If few members of
the same group are my neighbors, I will move.”

Initial setting.
(1) Each agent is placed randomly on a fixed lattice (there are some vacant sites). This does not mean
the agents are fixed in these locations (free-address setting).
(2) Each agent is a member of one or another group and has a threshold for moving. This threshold isthe minimum proportion of the agent’s neighbors who are in the same group.

Rule.
(1) The agent calculates the proportion of neighbors who are in the same group.
(2) If this number is greater than or equal to the threshold, the agent satisfies it, in which case end;
else continue.
(3) The agent looks for the nearest unoccupied site that satisfies its threshold and moves there.
(4) The simulation ends if all agents satisfy and do not move.
At a macro level, segregated settlement patterns emerge from this rule. The agents aresegregated into groups and eventually stop moving around. This occurs even if the thresholds of eachagent are not very high though we tend to consider that social differentiation does not become
prominent in this case.

3. Combining the two models
Initial setting(1) Each agent is placed randomly on a fixed lattice (there are some vacant sites). There are no
physical barriers (non-partition). The agents are not fixed in particular locations (free-address).
(2) Each agent has the same “culture” as CDM and the same threshold as SM. They have also “Moverange” and “Vision.” “Move range” means the distance each agent can move around. This is set
at 1; that is, each agent can move within one site. “Vision” means the distance each agent cancommunicate. This is set at 2; that is, each agent can communicate with an agent within twosites 1.

1

The range within eyeshot or earshot is wider than the range we can move about.
5

Nobuyuki Inamizu

Circles in some sites represent agents.

D

B
A

C

The agent (red circle) calculates culturalsimilarities (CS) by the same rule of CDM about eachneighbor within “View.” “Vision” is a range painted
on gray in the left-hand side figure. Then, it obtains
the mean value of each CS.
e.g., Culture of red circle is “18943.”
Culture of “A” is “19743.”
Culture of “B” is “76511.”
Culture of “C” is “18943.”
CS with “A” is 0.6, CS with “B” is 0, and CS
with “C” is 1. CS with “D” does not calculate since“D” is outside “View.” Therefore, their mean value
is 0.53.

The mean value ＜ Threshold

The mean value ＞ Threshold

D

D

B

B

A

A

C
The agent looks for a vacant site within“Move Range” and moves there. (“Move range”
is a range painted on grey in the above picture.)C
The agent randomly picks up one of its neighbors
within “View” and communicates with it.
1) If the agent picks up “A,” it communicateswith “A” with a probability of 60% and maychange its culture to “19943” if it picks up thesecond feature.
2) If the agent picks up “B,” it cannot
communicate with “B” since CS with “B” is 0.
3) If the agent picks up “C,” it can always
communicate with “C” since CS with “C” is 1.
However, it does not change its culture.

Figure 1: Rules of the Combined Model6A combined model of segregation and cultural dissemination models

Table 1: Input parameters and output data(a) Input parameters
Notation

Definition

Range of setting

THRESHOLD

Threshold to move

From 0.1 to 0.9

SIZE

Size of space

From 100 sites (10 × 10) to 400 sites (20 × 20)

W-CUL

Width of culture

From 1 to 9

= Number of features each culture has.
D-CUL

Depth of culture

From 1 to 9

= Number of possible traits in each feature.

(b) Output data
Notation

Definition

NOTMOVE

Number of agents who cannot move because there are no vacant sites in the neighboring area.

MOVE

Number of agents who find an unoccupied site and move there.

COM

Number of agents who can communicate with other agents and change own culture.

DIV

Diversity of culture of the agents, obtained from subtracting the total mean value of CSs
calculated for each agent from 100.

Note: Number of agents = 100.

Rule(1) An agent becomes active 2.
(2) The agent calculates CS using the same rule of CDM about each neighbor within “Vision.” Then,it obtains the mean value of each CS.
(3-a) If this mean value is less than the threshold, the agent looks for a vacant site within “MoveRange” and moves there 3.
(3-b) If the mean value of each CS is greater than the threshold, the agent randomly picks up one of2

The order to become active is determined at random. A new period does not start until all the agents’ trialends.
3
If there are some vacant sites, the agent picks up one of them randomly and moves there. Schelling moves
agents to the nearest satisfactory site, whereas the agents of this paper simply select an acceptable site at
random. Epstein and Axtell (1996) show the same result as Schelling's from the same rule as ours (Epstein and
Axtell 1996, p. 165–170).
7

Nobuyuki Inamizu

its neighbors within “View” and communicates with them. The communication rule is the sameas the CDM.
Input parameters and output data are summarized in Table 1. Input parameters are
THRESHOLD, SIZE, W-CUL (the width of culture), and D-CUL (the depth of culture). Changing
the SIZE means changing the space density, because the number of agents is always 100. Output data
are NOTMOVE, MOVE, COM, and DIV.

4. Results of the combined modelThis paper will tackle the problem whether the agents can retain their differences though theykeep moving around freely and communicating with one another. According to the combined model,
this non-convergent state can be interpreted as follows:
Criterion 1: NOTMOVE is 0 or almost 0. If this is not the case, the agent cannot move around freely.
If the state where NOTMOVE is greater than 5 continues for ten periods, the run ends.
Criterion 2: MOVE is more than 0. If MOVE is 0, this indicates the agents do not move around. If
the state where MOVE is less than 5 continues for ten periods, the run ends.
Criterion 3: COM is more than 0. If this is not the case, the agents do not communicate with various
others. If the state where COM is less than 5 continues for ten periods, the run ends.
Criterion 4: The state where the above three criteria are satisfied, continues for 8000 periods. Axelrod(1997) reports that it takes about 800 periods to reach an equilibrium (the state where the agentsstop communicating with others) in the case of W-CUL = 5, D-CUL = 10, and the number of
agents = 100. Then, we can consider that the agents continue to move around and communicate
with others, if 8000 periods (ten times more than the report of Axelrod (1997)) can pass.
As inferred from the rules of the model, DIV is kept high when MOVE and COM are more thanzero.
We have to run more than 10000 patterns of settings to test all combinations of the fourparameters (THRESHOLD, SIZE, W-CUL, and D-CUL). Because of limited time, as a preliminary
test, I selected parameter settings randomly and conducted a few runs for each. As a result, I realized
there is a correlation between THRESHOLD and D-CUL. Therefore, I decided to hold
THRESHOLD at 0.25 and change the others. I conducted 50 runs for each combination of the threeparameters and confirmed whether there was a case, in which all the four criteria were satisfied.
I found that, when SIZE is 12 × 12, W-CUL is 3, and D-CUL is 5 (hereafter called Successful-Case),
the four criteria are satisfied. Of the 50 runs, 29 continued to satisfy the first three criteria even after8

A combined model of segregation and cultural dissemination models

8000 periods 4. Figure 2, which is the result of a run, shows that MOVE is kept about 40 and COM is
kept about 15 for 8000 periods. Therefore, the agents move freely and communicate with various
others in this case.

100
80
60
40
20

20
0
80
0
14
00
20
00
26
00
32
00
38
00
44
00
50
00
56
00
62
00
68
00
74
00
80
00

0

Periods
MOVE

COM

DIV

Figure 2: Output data of a Successful-Case. When SIZE is 12 × 12, W-CUL is 3, and
D-CUL is 5, MOVE, COM, and DIV are remained fairly constant for 8000 periods.

We tend to consider from the two models (SM and CDM) that the agents have a tendency todevelop some cultural groups over time, if MOVE and COM are kept at more than 0. However, DIV
is kept around 70 in that case (Figure 2), indicating that the tendency cannot be observed. To confirm
this, I pictured an initial arrangement of the agents (Figure 3 (a)) and the one after the 8000 periods(Figure 3 (b)). These pictures show that there are no distinct cultural groups even after 8000 periods.
When SIZE is smaller than that of the Successful-Case, Criterion 1 is not satisfied. The case of
SIZE = 10 × 10 is similar to CDM. The agent does not move as in CDM, and therefore the run ends
at ten periods (see Table 2 (a)). When SIZE is 11 × 11, only 21 sites are vacant. As shown in Figure 4,
many agents have no vacant sites within their “Move range.” Therefore, NOTMOVE is more than 5
and the run ends immediately.
4

When continued, 13 of the 29 runs do not reach equilibrium after 16000 periods (two times more than
Criterion 4).
9Nobuyuki Inamizu(a) An initial arrangement(b) After 8000 periods

Figure 3: Agents’ locations and cultures of a Successful-Case. The number in eachcell represents the agent’s “culture.” These pictures show that the agents do not split into any culturalgroups.

Figure 4: Result of Small SIZE. The number in each cell represents the agent’s “culture.” This
figure shows many agents have few vacant sites to move.
10

A combined model of segregation and cultural dissemination models

Table 2: The effects of SIZE, W-CUL, and D-CUL(a) The effects of SIZE
W-CUL

D-CUL

SIZE

3
3
3
3
3
3
3
3
3
3
3

5
5
5
5
5
5
5
5
5
5
5

10 × 10
11 × 11
12 × 12
13 × 13
14 × 1415 × 15
16 × 16
17 × 1718 × 18
19 × 19
20 × 20

Periods to exit*

Criteria to exit

10.00
12.64
>8000.00
1159.12454.30248.92178.80125.02105.62
80.54
67.00

1
1
4
2
2
2
2
2
2
2
2

Note: The mean value of 50 runs.
(b) The effects of W-CUL
W-CUL

D-CUL

SIZE

1
2
3
4
5
6
7
8
9

5
5
5
5
5
5
5
5
5

12 × 1212 × 1212 × 1212 × 1212 × 1212 × 1212 × 1212 × 1212 × 12Periods to exit
10.00
165.92>8000.00
1892.282383.68
1109.50427.76376.04
31.56

Criteria to exit
3242 (in many runs)
2 (in many runs)
3 (in many runs)
3 (in many runs)
3 (in many runs)
3(c) The effects of D-CUL
W-CUL

D-CUL

SIZE

3
3
3
3
3
3
3
3
3

1
2
3
4
5
6
7
8
9

12 × 1212 × 1212 × 1212 × 1212 × 1212 × 1212 × 1212 × 1212 × 12Periods to exit

Criteria to exit

10.00
10.00
67.86
1631.44>8000.00
16.00
10.54
10.00
10.00

2 and 32 and 3
2
2
4
3
3
3
3

11

Nobuyuki Inamizu

When SIZE is larger than that of the Successful-Case, Criterion 2 is not satisfied. In this case,although the agents move around and communicate with the others at first, they gradually split into
groups with same culture and eventually stop moving. As shown in Figure 5, the agents are separated
into cultural groups.

Figure 5: Result of Large SIZE. The number in each cell represents the agent’s “culture.”
Heavy lines are the boundaries of the agent groups having the same culture. This picture showsagents separating into cultural groups.

When W-CUL is narrower than that of the Successful-Case, Criterion 3 is not satisfied (seeTable 2 (b)). The case of W-CUL = 1 is similar to SM. Each agent is a member of a cultural group.
Therefore, the agents move around but do not communicate with others. When W-CUL is 4 or 5,
many runs do not satisfy Criterion 2. The results of these cases are similar to that of the large SIZE.
The agents split into several cultural groups and eventually do not move. When W-CUL is more than5, many runs do not satisfy Criterion 3. In these cases, the agents move around but cannot
communicate with the others because of high mutual differences.
When D-CUL is shallower than that of the Successful-Case, Criterion 2 is not satisfied in manycases (see Table 2 (c)). The agents split into cultural groups and end up not moving because of the
low mutual difference (DIV= 49.0 at the start in the case of D-CUL = 2). When D-CUL is deeper
than that of the Successful-Case, Criterion 3 is not satisfied. As in the case of quite wide W-CUL, theagents cannot communicate because of the high mutual difference (DIV = 87.39 at the start in the12A combined model of segregation and cultural dissemination models

case of D-CUL = 8).
In sum, the combined model shows that the agents move around freely, communicate with one
another easily, and retains differences between them under the conditions: SIZE = 144, W-CUL = 3,
and D-CUL = 5. As the number of agent is constant (=100), SIZE of 144 means the spatial density of
69.4 percent (= 100/144). This condition of spatial density is a discovery not having been pointed out
by the existing two models.

5. Two Japanese firms’ cases
I will describe the cases of two Japanese firms introducing nonterritorial offices, focusing on
their office density. From the results of the combined model, we can consider nonterritorial offices
are successful when the employees move around freely and communicate with various others. I
consider office density from two perspectives. The first is, as usual, the number of employees present
within a given space (Szilagyi and Holland 1980). The second is the proportion of the number ofoccupied seats to the total number of seats.

5.1. The successful nonterritorial office and “moderate” office density
The first case is of a company in the telecommunications industry, which I refer to as “X.” Thecompany’s corporate marketing division originally assigned one desk to each employee and usedpartitions to hinder the line of vision. In 2001, the division moved to a nonterritorial office. Althoughseveral years have passed, it still performed well as a nonterritorial office.
This case is based on interviews, observations of that division’s office, and a simple
questionnaire survey. I interviewed the executive in charge of the office relocation (the interview
lasted for two hours on June 4, 2004), as well as a general manager and two managers of thecorporate marketing division (one hour on December 7, 2004). I was allowed to observe the office on
the days I interviewed. In addition, I conducted a simple questionnaire survey, consisting of 9
multiple-choice questions on daily behavior in the office and 21 “yes or no” type questions on
employees’ attitudes 5.

5.1.1. Employees’ behavior in the nonterritorial office.
This study clarified that the employees move around daily and communicate with various
5This survey was conducted on the web site from August 25 to September 9, 2005. I circulated the survey toabout 100 employees of a section of that division, of which 43 responded; 86 percent of them were male, andabout 80 percent of them were engaged in sales. Most of them had been in that division for several years.
13

Nobuyuki Inamizu

colleagues. I will show this by focusing on the results of the following five questions in myquestionnaire survey:
XQ1: Compared with two days before, did you change your seating position yesterday?
XQ2: Compared with two days before, do you think the people who sat next to you yesterdaychanged?
XQ3: Why do you and your neighbors sit next to each other?
XQ4: Do you think that the office members with whom you had discussions changed?
XQ5: Does the atmosphere enable you to consult a member of another group (divisions or units)
about problems in your business?
Most of the employees engage in sales and do work outside the office; the proportion of
employees remaining in the office on a typical day is between 40 percent and 50 percent. Therefore,
only 15 percent to 25 percent of the employees stay in the office for two successive days. As a result,only 13 respondents answered XQ1, XQ2, and XQ3. However, we can draw conclusions from thesequestions because they are supported by other questions, interviews, and the observations in theoffice.
First, the results of the study suggest that the employees move around in the office daily. Abouthalf of the respondents to XQ1 said that they changed their seating positions. The executive said thatwithin three or six months after the move, employees started to position themselves wherever they
could work effectively, rather than remaining in the same seat. During the observation of the office,some employees said that they relocated every day.
Second, the results of the study suggest that the employees communicate with various
colleagues. To XQ2, about a half of the respondents said that the people sitting next to them changed.
For XQ3, about a half of the respondents answered that it was by chance that they and theirneighbors sat next to each other. That is, the probability of the employees meeting various others ismany, whether they intend or not. Besides, for XQ4, 62.8 percent of the respondents answered thatthe people with whom they had discussions changed. For XQ5, 90.3 percent of the respondents
answered that the atmosphere enabled them to consult with members of other groups. That is, theemployees feel that they can communicate with a variety of colleagues rather than being limited to a
specific group. These results are supported by the interviews. The employees in the office ofCompany “X” move about freely and communicate with various other members, as Allen and
Gerstberger (1973) report.
The office density is adjusted appropriately in this office. Only 40 percent or 50 percent of the14

A combined model of segregation and cultural dissemination models

employees stays in the office because many employees spend most of their time outside the office. At
first glance, it might seem that the office density is low. However, this office is so ingenious that it
can increase its density, according to the executive I interviewed. The first idea is to reduce thenumber of desks in the office to 70 percent of all employees. If the proportion of employees staying
at the office is 42 percent, the proportion of occupied desks becomes 60 percent by dividing 0.42 by
0.70. In a similar way, the proportion of occupied desks becomes 70 percent if the proportion of
employees staying at the office is 49 percent. The idea is to adjust the proportion of occupied desks;
that is, the office density to 60 percent or 70 percent. The second idea was to remove the employees’
personal cabinets beside their desks, to give employees an appropriate feeling of crowding. Removalof the cabinets shortens the distance to the next desk from 240 to 210 cm, which is enough to see theneighbor’s personal computer screen, and this promotes discussion between them.

5.2. The failure of the nonterritorial office and inappropriate office density
The second case is of a venture company in the telecommunications industry, which I refer to as“Y.” The company’s office was nonterritorial, with no one having a particular desk, and almost no
partitions could be seen (the first phase). However, by October 2004, the nonterritorial office ceased
to work well (the second phase). Although the company moved to a new nonterritorial office inNovember 2004, the new office also eventually ceased to work well (the third phase).
This case is based on simple questionnaire surveys, some interviews, and observations of thecompany’s office. At first, I conducted questionnaire surveys about two weeks before the move
(mid-October, 2004), and again about three months after the move (end of January 2005). The
questionnaires were identical, with 65 “yes or no” type questions on the atmosphere and behavior in
the office 6. I also conducted 20 interviews with 11 people (45 minutes to one hour each) from
September 2004 to November 2005 7. In these interviews, I asked about their work patterns and theirattitudes in the office. In addition, I observed the employees’ behavior in the office about twice aweek from October 2004 to March 2005.

5.2.1. The first phase: Employees’ behavior in the office until the summer of 2004.
6

I administered the pre-move survey to 51 employees and obtained 48 respondents; and post-move survey to
50 employees and obtained 41 respondents. 86 percent of the respondents were male. About 60 percent of them
are engineers. About 60 percent of them are regular staff. There was no significant difference between the
proportions in the pre-move survey and those in the post-move survey.
7
From the point of status, the interviewees are executives, general managers, managers, or ordinary employees.
From the point of affiliation, they belong to sales, engineering, or administrative affairs.
15

Nobuyuki Inamizu

At Venture Company “Y,” it was the top management that decided to introduce a nonterritorial
office. According to interviews with a company executive and the company secretary in September
2004, it was necessary as a top management to offer an environment, in which employees were able
to work comfortably and freely. Therefore, right from the time when the company was established,
they distributed a notebook computer and a cellular phone to each employee, and enabled theemployees to work anywhere. They showed me their office, in which no one has a specific desk andno walls or partitions could be seen. When I told them about the office of Company “X,” they said
the office was similar to their own.
The nonterritorial office of Company “Y” seemed to work well until the summer of 2004. As thenumber of employees was about 30 in the spring of 2004, and as there were vacant seats and plentyof spaces, the employees were able to move and work anywhere they liked. They also communicatedwith a variety of members. Indeed, in the interviews, a manager said that when he joined thecompany in January 2004 he was told to change his seating position daily, work near various
employees and learn how they did their job. Another employee said that, as Company “Y” had an
atmosphere similar to group activities at school, the employees got together and dispersed flexibly ineach project, and communicated with one another while developing their projects. Therefore, theemployees’ behavior in the office at the time corresponds to the report of Allen and Gerstberger(1973).

5.2.2. The second phase: Employees’ behavior in the office in October 2004.
The company had outgrown its office by October 2004. The number of employees in the officeincreased to about 50 by October, and the office density became too high. The high office density
restricted the employees’ freedom of movement. This is shown in the questionnaire survey (see Table3). I asked the respondents whether they thought it was difficult to stand up and move around in theoffice (YQ1), to which 23.4 percent answered yes, although no one was expected to answer yes tothis question. I also asked whether there was enough space to gather together at once if necessary(YQ2), to which 66.0 percent of the respondents answered no. These results are supported by theinterviews and observations of the office at the time. In the interviews, an employee said that he andhis project members had to go to a restaurant outside the office to discuss, because there was little
space to gather in the office. In the observations at the time, employees coming to work late had few
alternatives of seating position. Therefore, each employee thought it difficult to move around freely
in the office in October 2004.
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A combined model of segregation and cultural dissemination models

Table 3：Questionnaire survey results of the employees in Company “Y”(a)
YQ1: Do you feel it difficult to stand up and move around in
the office?
Yes
Pre-move

No

Total

11

36

(23.4)(76.6)

Post-move
Total

47

4

37

(9.8)

(90.2)

41

15

83

88

χ² = 2.885, Cramer’s V = 0.181†(b)
YQ2: Is there enough space to gather at once if necessary?
Yes
Pre-move
Post-move
Total

No

Total

16

31

(34.0)(66.0)

365(87.8)(12.2)

52

36

47
41
88

χ² =26.183, Cramer’s V = 0.545**(c)
YQ3: Is the atmosphere helping you to consult a member ofanother group (divisions or units) about problems inyour business?
Yes
Pre-move
Post-move
Total

No

Total

42

6

(87.5)(12.5)

25

16(61.0)(39.0)

52

36

47
41
88

χ² = 8.360, Cramer’s V = −0.306**
Note: † p< .1; * p < .05; ** p < .001

5.2.3. The third phase: Employees’ behavior in the new office since November 2004.
Because of the scarcity of space in the previous office, the company moved to a new office on
November 1, 2004. Although the new office is similar to the previous one in terms of its

17

Nobuyuki Inamizu

nonterritorial setting, it is different in its large space. This is shown in the results of the post-movequestionnaire survey (see Table 3). For YQ1, only 10 percent of the respondents answered yes, andthis shows a significant decrease at the 10 percent level with the pre-move survey. For YQ2, 90
percent of the respondents answered yes, and this shows a significant increase at the 1 percent level.
The observations of the new office in November 2004 revealed that the employees used only half theoffice space.
The new nonterritorial office, however, has failed in the employees’ movement According to theobservations, the employees tended to establish their own seats and workspaces more than everbefore. They drew up a seating chart, which means each of them had their own desk. They also madetheir own workspace comfortable at their own judgment. For example, some employees boughtliquid-crystal displays with their own funds and put them on their desk, whereas before the movethey had had nothing on their desks apart from their notebook computers. Because the displays are
immovable, no one else could use their desks.
The new nonterritorial office has also failed in the employees’ communication. According to thequestionnaire surveys, the employees tended not to communicate across work groups. For YQ3,
about 40 percent answered no, and this shows a significant increase at the 1 percent level from theresults of the pre-move survey (see Table 3). This is supported by the interviews, in which I heardthat the office became too large for the employees to get a glimpse of others at work and to hearuseful information (see Appendix). Besides, the comments suggesting that each work group has
evolved its own rule or pace were heard in the interviews (see Appendix). When I put thesecomments together, the large office space would promote each group’s development of rules or pace,and once each team has its own rules or pace, employees found it difficult to communicate across thegroups.

6. Discussion: implications of the combined model for office management
From the combined model and the cases of the two firms, we can draw a suggestion;
nonterritorial offices succeed under “moderate” office density (69.4 percent) and fail under extremely“high” or “low” office density. The optimum office density of 69.4 percent offers practicalsuggestions for nonterritorial office design and management. If only half of the employees stay at theoffice, we should achieve the optimum density either by using a small office or by creating a closeseating arrangement. If all employees stay at the office, we should use an office that is 1.5 times
larger than the existing one. In this case, introducing a nonterritorial office leads to an increased18

A combined model of segregation and cultural dissemination models

facility cost in the short run.
This paper is one of the few studies to consider the effects of office density on human behaviors
in nonterritorial offices. The office density has been considered as a factor influencing humanbehaviors in offices. Many studies on the effect of the office density on communications in a
non-partition setting can be seen. For example, Szilagyi and Holland (1980) report that, in a
non-partition office, high office density increases the chance to communicate with neighbors.
Oldham (1988) reports that, in a non-partition office, low office density limit interactions withneighbors. However, there are few studies on the effects of the office density on not only employees'
communications but also their movements in nonterritorial offices (non-partition and free-address
setting).
Several limitations of this study must be mentioned. First, this paper focuses on the movements
and communications of employees, and does not consider the effects of their privacy, identity, job
satisfaction, etc. Some previous studies on the non-partition setting suggested that these factors haveeffects on employees’ behaviors (Oldham and Brass 1979, Hedge 1982). Second, the agents of themodel in this paper have the same rules, and the effects of types of work are not considered. Some
previous studies on open-plan setting insist that differential effects across types of work,organizational positions, and job complexity can be observed (Hedge 1982, Sundstrom et al. 1982,
Zalesny and Farace 1987, Carlopio and Gardner 1992).

7. Conclusion
The combined model of this paper offers a new explanation of social differentiation. The model
was developed by combining the two typical models of social differentiation: CDM and SM. Thismodel has a space of non-partition and free-address setting and has rules of communication andmovement. Though these settings and rules tend to lead convergence, the agents of this model canretain their differences while moving around and communicating with one another under someconditions. One condition is the spatial density of 69.4 percent. When spatial density is higher, theagents cannot move around freely. When spatial density is lower, the agents split into several stableclusters. The agents do not move around and do not communicate across the clusters. The existing
two models have not pointed out the spatial density as a factor behind social differentiation.
These results of the combined model are supported by the cases of the two Japanese firms
introducing nonterritorial offices. In office management, a non-partition and free-address setting iscalled nonterritorial office. Nonterritorial offices are considered to be successful if the employees
19Nobuyuki Inamizu

keep moving around and communicating with many others and retain the differences of theirthoughts, because their introduction is for knowledge creation. The first firm’s nonterritorial office
performed well. Its office is so ingenious that the density is appropriate. The second firm’s
nonterritorial office worked well in the first phase. In the second phase, however, the company
outgrew its office, and the nonterritorial office worked less than it used to. The employees could not
move around freely in the high-density office. Although the company moved to a large nonterritorial
office in the third phase, the new office was not effective either. The employees split into several
groups, did not move around, and did not communicate across the groups very well in the
low-density office.

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A combined model of segregation and cultural dissemination models

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Appendix
The results of the questinnaire surveys at Company “Y” show that the employees tended not tocommunicate across work groups. This is supported by the interviews, in which I heard the following
comments.
Comment 1: “In the previous office, I knew instantly what incidents occurred in other groups
because I could see how others were working. In addition, I was aware, however vaguely,of how other projects were progressing because discussions from other groups could beoverheard. However, it became difficult now to see what others were doing and to hear
what others were discussing.”
Comment 2: “I cannot see what problems other groups faced with.”
Comment 3: “The office became quiet after the move.”
Comment 4: “In the previous office, I could see other peoples’ painstaking ways of working, anda healthy rivalry was stirred up. However, in the new office, I was unable to see those withwhom I possess a sense of rivalry.”
These comments suggest that the office became too large for the employees to get a glimpse ofothers at work and to hear useful information.
Other interesting comments were heard in the interviews. These comments suggest that eachwork group has evolved its own rule or pace.
Comment 5: “In the previous office, employees never thought help from another project team asinterrupting. In the new office, however, each team developed its own rules and employees
started to feel that help from other groups was bothersome because it did not follow theirown rules.”Comment 6: “I went to lunch with members of other workgroups in the previous office. Afterthe office move, each group works at its own pace. As a result, I go to lunch with themembers of my own group when I reach a stage where we can take a rest.”
These comments suggest that each team has evolved its own rule or pace. When we put the first
four comments together, the large office space could be seen as promoting each group’s developmentof rules or pace. Once each team has its own rules or pace, employees would find it difficult tocommunicate across the groups.

23