1. RUBENS A. ZIMBRES
PEDRO P.B. DE OLIVEIRA
Dynamics of quality perception in a social
network: A cellular automaton based
model in aesthetics services
Universidade Presbiteriana Mackenzie
São Paulo, SP
Brazil

2. I. INTRODUCTION
 Main goal: simulate interactions between
customers and providers and understand their
rationality using cellular automata.
 First survey Second survey
 Motivation: linear regression models in service
quality literature do not offer a good explanation on
the phenomenom.
 Overall perspective: the process in the service
encounter, regarded as a complex system. 2
rule

3. II. COMPLEX SYSTEMS AND ROLE THEORY
 Commercial system as a complex system
 Clients co-participate in service delivery, influencing
service quality (e.g., self-service restaurant)
 Role theory sees service delivery as a theatrical
metaphor, with actors that act following a script (set
of rules according to the situation)
 Common behaviours = uniform cellular automata
3

4. III. METHODOLOGICAL PROCEDURES:
QUESTIONAIRE DEVELOPMENT
 Qualitative: 6 interviews (3 providers and 3 clients,
in aesthetic services)
 Quantitative:
 Evaluation of each statement: Likert scale with 5 points:
totally disagree, disagree, neither agree nor disagree,
agree, totally agree
 Development of a measurement scale with 74
questions/statements, evaluated by marketing
specialists → 54 were taken
 Quantitative pre-test (variance, correlations, factor
analysis and reliability) → 45 final statements
4

5. IV. QUANTITATIVE RESEARCH
 First survey: 115 clients and 96 providers
 Internal consistency of the questionaire (via
Cronbach's Alpha): 0.937 (clients) and 0.772
(providers) (range from 0 to 1)
 Statistical overall quality estimate: given by linear
regression (R2): 0.760 (clients) and 0.873
(providers), significant at 0.000, with Variance
Inflaction Factor < 10, and normal residues
 Second survey: 4 months later
 36 responses
 Cronbach's Alpha: 0.892 (clients) and 0.631
(providers)
5

6. V. PROPOSED MODEL
o Idea: to predict the evolution of clients-providers
interaction between the two subsequent surveys
o Data of the 1st survey = initial parameters
o Interactions between clients and providers
o Data of the 2nd survey = final condition, for
comparison
o Focus of the analysis between the two surveys:
7 (out of the 45), all related to intangible aspects of
service quality, because they are more relevant to
obtain sustainable competitive advantage 6

7. DETAILS OF THE MODEL
o Lattice = 36 subjects and 7 indicators of service
quality (attention, trust, willingness to help, honesty,
concern, responsibility, and adaptation to client’s
needs)
o Row = indicator, column individual
o No multicollinearity = one-dimensional CA
o 7 CAs, same rule = uniform CA
o Facilitates to unveil the rationale embedded in the
transition table.
7

8. QUESTIONAIRE AND CELULAR AUTOMATA
 Same respondents
 Likert 5 points = CA with 5 states
 CA radius = 1 (nearest left- and right-hand
neighbours)
 Hence:
→ 125 possible rationales (neighbourhoods)
→ 2.35  1087 possible rules
 Search started from the majority rule (herd
behaviour)
8

9. RULE SEARCH
o Initial condition: lattice was ordered according to
the 7th indicator (adaptation to customer needs),
because of its highest variance (higher diversity of
opinions)
 Sampling of the space in blocks of 1500 rules,
picking each one of them with uniformly distributed
random steps in the range from 110 to 1084 (with
occasional smaller ranges for closer inspection):
total of 1.8106 rules were evaluated (200hs of
computer time) 9

10. RULE SEARCH
o Direction of the search:
• Target success rate, measured in terms of the best
possible match between the state values of
corresponding cells in the second survey and the
rule outcome (within 20 iterations).
• Trend to best results with 16 timesteps (4 months
between surveys); thus, 20 iterations
• Success rate at least 70%
• Non-cyclic behaviour
• Variance of the lattice ±0.5 when compared with the
second survey 10

11. LIKERT SCALE AND THE CA STATES
5 = Totally agree that attention is very important in service delivery
4 = Agree
3 = Neither agree nor disagree
2 = Disagree
1 = Totally disagree
PPCPPPCCCCCPPPPPPPPPPPPPPPPPCCCCCCCC
Example: Attention
11
Time t=0
Time t=n

12. RULE RATIONALE
 If a given customer (C) that perceives actual quality
as good (Likert scale value equal to 5 and cell state
equal to 5) evaluates the service quality offered by
one provider (P) as bad (cell state equal to 1) and
the service quality offered by another provider as
good (cell state equal to 5) this could generate a
regular assessment of quality (cell state equal to 2),
which could interfere with future intentions of the
client to remain with the provider, given the
inconsistency of the attitudes.
12
1 5 5
2
P C P

13. RATE OF SUCCESS
 Rule number
2159062512564987644819455219116893945895
9585281520212287057525638079592376559119
50549124 with 73.80 % of success in predicting
the system evolution
0 5 10 15 20
55
60
65
70
75
Cycles
Accuracy
13

14. TRANSITION TABLE FOR THE CHOSEN RULE
14

15. EXPLANATORY POWER
 CA model offers an additional explanatory power of 8.80
percentage points (73.80%−65.00%). Thus, nonlinear effects
appear to contribute with the corresponding gain.
 Sharing only 38.80% in common (intersection) explains
nonlinearity of phenomena, a new perspective of studying
causal relations in management research.
65%
73.80%
73.80%
65%
Linear regression model
Cellular automata model
Linear regression model
Cellular automata model
0% 100%
15

16. EUCLIDEAN DISTANCE
1st survey 2nd survey model outcome
 Consensus (think similarly, intimacy, mutual understanding ): role theory
16

17. EUCLIDEAN DISTANCE FOR THE 7 INDICATORS
Indicator 1 2 3 4 5 6 7
Phase 2 - Phase 1 (c) 5,74 3,31 4,24 4,35 5 4,58 6,55
Simulation - Phase 1 (d) 5,56 3,46 2 3 4 2,44 21,93
Difference c-d 0,18 -0,15 2,24 1,35 1 2,14 -15,38
Euclidean Distances
Highest variance
17
)

18. LATTICE CONFIGURATION ALONG THE RULE
ITERATIONS
18

19. EVOLUTION OF THE INDICATORS
19Interface C-P

20. DISSATISFACTION IN THE NETWORK
 Extremely problematic customers should not be in
contact with each other, otherwise they would
spread the dissatisfaction to everyone they have
contact with, customers or providers.
 Dynamics of opinions, but also and more
importantly, which individuals create dissatisfaction
in a social network. This can enable managers to
identify problematic customers.
 Outbreak of the individuals’ dissatisfaction happens
always in the customer-provider interface.
20

21. TOTAL AVERAGE PER INDICATOR
 If based on averages (as usual in the traditional
literature), and not on a cell-by-cell comparison, the
outcome becomes much higher than the model´s
success rate!!
Indicator 1 2 3 4 5 6 7
Phase 2 - Phase 1 (c) 137 136 140 135 132 138 129
Simulation - Phase 1 (d) 130 135 136 134 127 133 126
Difference c-d 7 1 4 1 5 5 3
Accuracy (%) 94,89% 99,26% 97,14% 99,26% 96,21% 96,38% 97,67%
Total per Indicator
21
)
VARIANCE explanation in literature (average)
Cronin e Taylor (1992) R2 max .47 for SERVPERF and .46 for SERVQUAL.
Elliott (1994) R2 max .65 for SERVPERF and .42 for SERVQUAL.
Lee, Lee, Yoo (2000) R2 max .53 for SERVPERF and .35 for SERVQUAL.

22. RATE OF SUCCESS (CASE BY CASE)
73.80 %
22

23. EFFECTS OF GROUPING INDIVIDUALS WITH
THE SAME OPINION
1 2 3 4
Isolated Group
23
Rebellion

24. ATTEMPTS TO MITIGATE DISSATISFACTION IN A
SOCIAL NETWORK
24
Likert equal to 5
Likert equal to 2
1
1

25. SENSITIVITY TO INITIAL CONDITIONS
25
collide

26. DESCRIPTIVE STATISTICS OF THE DATA: THE
SURVEYS AND THE MODEL
26
Initial Final Simulation
survey survey result
Mean 3.75 3.65 3.67
Variance 0.16 0.25 0.97
Std deviation 0.25 0.37 0.98
Median 4 4 4
Kurtosis 8 11.82 10.84
Skewness -2.21 -2.72 -3.03
Increase in
perception
-0.10 -0.08

27. LATTICE MEANS (SUM OF INDICATORS) OVER
THE 20 TIME STEPS OF THE CA
Cycles
Construct total
27
cause effect
process

28. OSCILLATORY BEHAVIOUR
 First, inconsistencies in mood of customers and
providers, who may perceive the quality of the
relationship differently, according to their emotional
state.
 Second, inconsistencies in the delivery of service
by the provider, who may not always offer the same
service quality.
 Third, there may be a process of mutual adaptation
over the interactions, and the provider cannot
always meet the expectations of customers and
vice versa.
 Intangible aspects of quality and this is probably
due to an affective component, involvement. 28

29. STABILITY
 It might be interesting to increase the interval
between longitudinal surveys to 30 time steps, that
is, 30 weeks or 8 months, so as to verify the
emergence of consensus and stability.
0 10 20 30 40
4.0
4.2
4.4
4.6
4.8
5.0
Cycles
Construtmean
29

30. VARIANCES FOUND IN THE FIRST AND THE
SECOND QUANTITATIVE SURVEYS
30
Indicator
Variance

31. EVOLUTION OF MODEL VARIANCE
0 10 20 30 40
0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Cycles
IndicatorTotal
consensus
31

32. TRANSITION TABLE OF THE CHOSEN RULE
Centre Centre
1 2
1 2 3 4 5 1 2 3 4 5
1 1 5 1 2 5 1 3 1 4 1 2
2 3 2 5 1 5 2 1 2 2 3 3
3 3 1 4 2 2 3 3 2 3 5 2
4 4 1 5 4 5 4 4 2 4 4 3
5 3 4 3 1 5 5 5 3 4 1 3
Centre Centre
3 4
1 2 3 4 5 1 2 3 4 5
1 3 5 3 5 4 1 5 5 2 4 5
2 4 4 5 4 5 2 2 1 1 3 3
3 1 4 5 1 4 3 3 5 2 5 2
4 1 4 1 5 3 4 5 1 1 1 2
5 4 1 1 1 5 5 5 4 1 3 5
Centre Centre
5 Initial state
1 2 3 4 5
1 3 1 1 5 5
2 1 3 3 4 1
3 1 3 2 4 5
4 1 5 5 5 1
5 5 4 5 3 5
RightLeft
Neighbour stateNeighbourstate
Final state of the
central cell
Left
Right LeftLeft
Left
Right
Left
Right
RightRight
32
Nonlinear

33. CONCLUDING REMARKS
 A B B C
 Validation:
Role theory metaphor, Statistical analysis, Careful
implementation, and Reliance on real data.
 Rationality and behaviours to increase satisfaction.
 Management of dissatisfied individuals.
 Linear regression: which indicators and their
magnitudes (cause and effect). CA study nonlinearities
in the process.
 Cellular automata as a complement to helping
management of human behaviour
 Limitation: rule-sample, interpretability of observed
behaviours (cyclic in honesty), initial condition 33
rule rule

34. THANKS!
São Paulo State Foundation for Research
Support: Research grant 2005/04696-3
Mackenzie Research Fund:
Research grant from Edital 2007
Wolfram Research:
Mathematica Academic Grant No. 1149
34National Coordination for the Improvement of
University Level Personel