=Paper=
{{Paper
|id=Vol-2387/20190034
|storemode=property
|title=Simulating Pairwise Communication for Studying Its Impact on Macro-Behaviour of Communities
|pdfUrl=https://ceur-ws.org/Vol-2387/20190034.pdf
|volume=Vol-2387
|authors=Grygoriy Zholtkevych,Olena Muradyan,Kostiantyn Ohulchanskyi,Sofiia Shelest
|dblpUrl=https://dblp.org/rec/conf/icteri/ZholtkevychMOS19
}}
==Simulating Pairwise Communication for Studying Its Impact on Macro-Behaviour of Communities==
https://ceur-ws.org/Vol-2387/20190034.pdf
Simulating Pairwise Communication for
Studying Its Impact on Community Public
Opinion
Grygoriy Zholtkevych1 , Olena Muradyan2 , Kostiantyn Ohulchanskyi1 , and
Sofiia Shelest1
1
School of Math and Comp. Sci, V.N. Karazin Kharkiv National University,
4 Svobody Sqr, Kharkiv, 61022, Ukraine; http://math.univer.kharkov.ua
g.zholtkevych@karazin.ua;
spaceiseternal,soniashelest@gmail.com;
2
School of Sociology, V.N. Karazin Kharkiv National University,
4 Svobody Sqr, Kharkiv, 61022, Ukraine; http://sociology.karazin.ua
o.s.muradyan@karazin.ua
Abstract. Communication on the fly made possible by modern informa-
tion and communication technology is a characteristic feature of modern
society. This style of communication significantly changed social life and
provided new ways of public opinion formation. New social practice poses
new challenges for specialists studying social phenomena. One of these
problems is the problem of the reliability of public opinion measure-
ments, which are always based on indirect assessments. Unfortunately,
indirect assessments depend essentially on the suggestions accepted dur-
ing their development. The marked above changes raised by the tech-
nological progress require the new mathematical suggestions lied in the
base of public opinion measurements. This paper is to draw attention to
this situation and to begin the movement toward the rigorous theory of
public opinion measurements basing on social phenomena mathematical
models of adequate to features of modern communication processes. It
seems that authors’ first results are consistent to hypotheses of a number
of sociologists working in this area.
Keywords: public opinion· behaviour· microstate· macrostate· commu-
nication rate· indirect measurement· simulation
1 Introduction
The modern information and communication technology (ICT) has essentially
changed communication processes between communities and their members, gen-
erated new social phenomena. Social networks are of these phenomena. Their
emergence and rapid development have markedly changed the character of com-
munication streams.
In this context, an important point is the effect of a combination of social net-
works and personal telecommunication microelectronic devices (tablets, smart-
phones). This effect significantly speeds up communication, reduces in time and
makes it discrete and as non-linear as possible. The cognitive and motivational
results of such communication are still unknown to sociologists. Nevertheless,
it can be argued that such discrete and nonlinear communication significantly
diversifies the sources of potential influence on the opinion formation of the
of communication participants, and at the same time increases the frequency
of such impact, potentially having a different result. Public opinion formation
becomes the process difficult for predicting because we need to take into ac-
count a significant number of factors than before. At the same time, the effect
of these factors due to the specificity of the new segment of the communicative
space (nonlinearity, discreteness and high communication rate) is characterised
by more and more complex interconnections.
The reliable sociological information about public opinion is especially in
demand in modern society. The reason for this is not to reinforce the need to
effectively predict changes in public opinion (this need has traditionally been
high since the fifties of the twentieth century). The reason is associated with an
increase in such threats to social stability and security as information terrorism,
manipulative technologies affecting society, and the active use of fake-news in
the political sphere. Today public opinion needs not only to predict but also
to protect against the above threats. This, in turn, requires the development of
the technique of sociological measurement based on the dependable quantitative
theory. This necessity is also caused by the high cost of the evidential public
opinion measurements. Improving public opinion measurements by the way of
increasing the frequency of spot measurements as to record in time all possible
deviations and shifts in public opinion seems to be of little prospect due to the
high cost of such measurements and their technical complexity.
Based on the foregoing, it can be said that developing a theory of measur-
ing public opinion to substantiate and improve polling tools aimed at making
it possible to grasp the peculiarities of the formation of public opinion in mod-
ern conditions is a relevant challenge not only for social science but also for
mathematics and computer science.
We believe that simulation of the public opinion formation within the modern
information and communication environment is the origin point for this theory.
This paper is our attempt to attract the attention of researchers in the fields
of ICT, mathematics and sociology to this challenge.
It is needed to stress that the idea to use mathematical modelling as a tool
for studying social processes is not novel. In the middle of the twentieth century,
the use of relational and statistical models for understanding social processes
was proposed by a number of scientists (N. Rashevsky [13], A. Rapoport [12]
and other). The idea was further developed with the inception of network science
(see [1]).
Today there are a lot of works devoted to simulation of social network and
studying social dynamics based on the corresponding methods. But we could
not find a paper that would present a simulation model for studying a public
opinion measurement. This is what caused our research.
2 Model of Communication in Network
In this paper, we consider the special class of homogeneous multicomponent
discrete-time dynamical systems, whose components interact only pairwise via a
network of channels. The components of such a system are entities for modelling
members of the community being studied, and channels are entities for modelling
stable pairwise communications between the members of this community.
2.1 Modelling Assumptions
The goal of this subsection is to formulate explicitly the modelling assumptions.
Assumption 1. A network being simulated is a multicomponent dynamical
system of the discrete time with a constant set of components called members.
Some pairs of components communicate stable and, in this case, we say that
there is an information channel between members of such a pair.
Assumption 2. The property of an information channel to be active is a ran-
dom Boolean variable. Moreover, for different channels, the corresponding vari-
ables are independent.
Assumption 3. Each system component estimates the claim being in the focus
of community interests using an element of the set C = {RED, GREEN, BLUE}
corresponding to either negative, or neutral, or positive estimation respectively.
The mapping associating a claim estimation with each system components is
below called a microstate of the system.
Assumption 4. The personal estimations of a member of a community (a sys-
tem microstate) is not interest and is considered as not available for the direct
observation. Only the occupacy measure of elements of C is available for the
direct observation. The value of this measure for an element of C is a ratio be-
tween the number of community members that have the corresponding opinion
and the total number of community members. This measure is considered below
as a macrostate of the system.
Assumption 5. At each time-point, a member of the community participates
at most in one communication.
2.2 Specification of Network Model
Taking into account Assumption 1, an undirected simple finite graph G = (N, E)
is the most natural mathematical structure for modelling pairwise communica-
tions in a community. The node set N of the graph models members of a com-
munity, and the edge set E of the graph models stable information channels
between ones.
Assumption 2 can be ensured with associating a random Boolean variable
activatede with each edge e ∈ E. To do this it is sufficient to specify a function
activation rate : E → [0, 1] and to think about its value activation rate(e) as
about the activation probability of the channel corresponding the edge e. In
other words, we set activation rate(e) = Pr(activatede = true). Thus, we come
to the following definition.
Definition 1. A network model is a triple hN, E, activation ratei where N and
E are respectively the sets of nodes and edges of some undirected simple finite
graph G = (N, E) and activation rate : E → [0, 1] is the channel activation rate
function.
Assumption 3 causes the following definition of a microstate and micro-
dynamics for the system class being studied.
Definition 2. A node colouring of the graph G in accordance with the colour
set C is a microstate of the system.
Thereby, the system micro-dynamics is a discrete-time stochastic process explain-
ing the observed sequences of system microstates.
Assumption 4 leads us toward the concepts of a macrostate and macro-
dynamics.
Definition 3. Let c : N → C be a microstate of the system then a function
c : C → [0, 1] is the macrostate corresponding to c if for each x ∈ C, it is defined
as follows3
1 X
c(x) = · [c(n) = x] .
|N|
n∈N
Thereby, the system macro-dynamics is a discrete-time stochastic process ex-
plaining the observed sequences of system macrostates.
2.3 Simulation Framework Concept
Based on the above assumptions and definitions, a prototype framework has de-
veloped for simulation of the community dynamics with various kinds of pairwise
communications. The general specification of a simulation process is presented
as a UML activity diagram in Fig. 1. For the realisation of this general specifi-
cation, the language Python 3 [11] and library NetworkX 2.2 [9] have been used.
To construct a framework providing the presented simulation process we
propose the conceptual model shown as a UML class diagram in Fig. 2. This
model based on an undirected simple graph whose nodes are instances of the
class Node and the edges are instances of the class Edge. The attribute estimation
of the class Node is intended for saving the current value of a microstate for the
corresponding node. The association state gives access to the internal description
of a node state. This description is abstract on the framework level. Similarly,
the attribute activation rate of the class Edge is intended for saving the value
activation rate(e) for the Edge-instance that models edge e.
3
In the formula, the Iverson bracket is used (see, for example, [5]). The value of
[c(n) = x] equals 1 if c(n) = x , and otherwise it equals 0 .
[simulation has complete]
Set nodes and Build and save
Build network
edges parameters initial microstate
[otherwise]
Choose Perform Renew
communicated pairs communication protocol microstate
Save macrostate
Fig. 1. General specification of a simulation process
«enumeration»
Colour
RED
GREEN
BLUE
state
Node
1
State
2 setColour(colour: Colour)
getColour() : Coulor
incidence estimate(): Colour
1..*
Edge
activation_rate: Real
weight(colours: Colour[2]): Real[3]
Constraints:
protocol
0 < activation_rate <= 1
forall(c',c'': Colour | 1
weight(c',c'')[0] >= 0 and Protocol
weight(c',c'')[1] >= 0 and communicate(states: State[2]): State[2]
weight(c',c'')[2] >= 0 and
weight(c',c'')[0] + weight(c',c'')[1] +
weight(c',c'')[2] = 1)
Fig. 2. Conceptual model of the simulated net
2.4 Pairwise Communication Model
Above we were focused on modelling the structure of a network, and in this
subsection, we pass to modelling the interaction (or the communication, in the
case of social network) between nodes of the network. The association between
instances of the class Edge and abstract entities classified as Protocol is foreseen
for providing the specification of such interaction (see Fig. 2).
Taking into account that Assumption 5 is accepted we need some method
to form the set of interacting pairs of nodes. We propose to use the method
specified by Algorithm 1.
Algorithm 1: Method for forming communicating pairs
Data: a simple undirected graph G = (N, E)
Result: the subset SELECTED of E representing communicating pairs
/* initialise the target set and auxiliary sets */
1 SELECTED := ∅; AVAILABLE := ∅; FORBIDDEN := ∅;
/* activate communication channels */
2 foreach e ∈ E do
3 choose randomly True or False with probabilities a(e) and 1 − a(e)
respectively;
4 if True is selected then
5 add e into AVAILABLE
6 else
7 add e into FORBIDDEN
8 end
9 end
/* form communicating pairs */
10 while AVAILABLE 6= ∅ do
11 choose randomly an element e ∈ AVAILABLE in accordance with uniform
distribution on AVAILABLE;
12 delete e from AVAILABLE;
13 if for some e0 ∈ SELECTED, e and e0 are incindent then
14 add e into FORBIDDEN
15 else
16 add e into SELECTED
17 end
18 end
The following proposition establishes properties of the method.
Proposition 1. The method presented by Algorithm 1 has properties
1. a computation with respect to Algorithm 1 is halted for any input data after
a finite number of steps;
2. after halting a computation with respect to Algorithm 1, sets SELECTED and
FORBIDDEN are disjoint;
3. after halting a computation with respect to Algorithm 1, set SELECTED does
not contain incident edges;
4. adding to the set SELECTED an edge added to the set FORBIDDEN in loop
10–18 violates the property claimed in item 3.
Proof. The first item of the proposition is true because of the set AVAILABLE
decreases (see, line 12 of Algorithm 1) after each iteration of loop 10–18.
The validity of the second item of the proposition is ensured by branching 13–17.
The validity of the third item of the proposition is ensured by line 14.
The validity of the fourth item of the proposition is ensured by branching 13–
17. t
u
We suggest that any communication protocol can be represented by the UML
sequence diagram as in Fig. 3.
theEdge:Edge theEdge.incidence[0]:Node theEdge.incidence[1]:Node
states[1] = getState()
states[0] = getState()
communicate(states)
newStates
setState(newState[0])
setState(newState[1])
estimate(newStates[0])
estimate(newStates[1])
estimation
estimation
Fig. 3. Model of a pairwise communication protocol
Finally, the method estimate(state: State) of the abstract entity State (see
Fig. 2) is intended to renew the current microstate.
3 Computational Case Studies
In this section, we present and discuss the results of simulation for four kinds of
systems: models A-IR and B-IR, which called below as models of components
with an instant response, and models A-LR and B-LR, which called below as
models of components with a lazy response.
3.1 Realisation of the Method communicate(. . . )
The above classification of the models being studied is based on the general
scheme of the interaction process modelled by the method communicate(. . . ) of
the abstract entity Protocol.
We assume that the communication corresponding to edge e ∈ E is modelled
by the weight function we on C×C and taking random value we (colour0 , colour00 )
in the following outcome set {nobody, first, second}. The outcome is interpreted
as follows
– we (colour0 , colour00 ) = nobody means that participants of the communica-
tion preserve their opinions;
– we (colour0 , colour00 ) = first means that the first participant of the commu-
nication preserves his opinion, but the second one does not preserve;
– we (colour0 , colour00 ) = second means that the second participant of the com-
munication preserves his opinion, but the first one does not preserve.
Based on this assumption, we propose to use the following abstraction spec-
ified by Algorithm 2.
Algorithm 2: The scheme of the method communicate(. . . )
Data: an edge e ∈ E, the weight function we corresponding e
Result: the pair of new node states (newFirstState, newSecondState)
1 firstState := e.incidence[0];
2 secondState := e.incidence[1];
3 choose randomly outcome from {nobody, first, second} in accordance with the
distribution we (firstState.getColour(), secondState.getColour());
4 if outcome = nobody then
5 newFirstState = firstState;
6 newSecondState = secondState
7 else if outcome = first then
8 newFirstState = firstState;
9 create newSecondState in accordance with a concrete algorithm
10 else /* outcome = second */
11 create newFirstState in accordance with a concrete algorithm;
12 newSecondState = secondState
13 end
14 return (newFirstState, newSecondState)
Remark 1. Note that everywhere below we use the weight function defined as
follows
1. we (c, c) = {nobody = 1.0, first = 0.0, second = 0.0} for any c ∈ C ;
2. we (c0 , c00 ) = we (c00 , c0 ) for all c0 , c00 ∈ C ;
3. we (GREEN, c)[nobody] = 0.0 ,
we (GREEN, c)[first] = 0.1 , and
we (GREEN, c)[second] = 0.45 for any c ∈ {first, second} ;
4. we (RED, BLUE)[nobody] = 0.1 ,
we (RED, BLUE)[first] = 0.45 , and
we (RED, BLUE)[second] = 0.45 .
3.2 Systems of Components with Instant Response
The model of a system of components with instant response (below IR-model)
is based on the following model of a state called by SimpleState (see Fig. 4).
«enumeration»
Colour
RED
GREEN
BLUE
SimpleState
colour: Colour
estimate(): Colour
Constrints:
inv: self.estimate() = self.colour State
estimate(): Colour
Fig. 4. Model of a simple state
The IR-model realises items 9 and 11 of Algorithm 2 as follows
if outcome = nobody then
newFirstState = firstState
newSecondState = secondState
if outcome = first then
newFirstState = firstState
newSecondState = firstState
if outcome = second then
newFirstState = secondState
newSecondState = secondState
Simulation Experiment for the IR-model. The simulation experiment
was carried out at the initial macrostate defined as follows c0 (RED) = 0.1 ,
c0 (GREEN) = 0.8 , and c0 (BLUE) = 0.1 . The typical simulation results are
shown in Fig. 5.
1.0
0.8
0.6
0.4
0.2
0.0
0 20 40 60 80 100
Number of iteration
Fig. 5. A typical behaviour of the IR-model
Error Estimation for the IR-Model. We assume that the measurement of
the system is performed sequentially by observing a fixed number of system
components. Thus, the measurement rate depends on the number of observed
components in one step. More precisely, our assumption is that the measurement
procedure under our study is sequential and represented by the Algorithm 3.
We estimate the measurement error by using Kullback-Leibler divergence [7,
6, 3] D(c || c∗ ) where c is the real system macrostate and c∗ is the measured
system macrostste at the end of simulation.
Remind that Kullback-Leibler divergence D is computed by the formula
X c(c)
D(c || c∗ ) = c(c) · log2
c∗ (c)
c∈C
and estimates the minimal information quantity needed to correct an error.
As mentioned above, the measurement speed depends on the number of k
nodes observed during one simulation cycle. A small value of k corresponds to a
slow measurement and a big value of k corresponds to a fast one. In Fig. 6, the
dynamics of error estimation for slow (the blue curve with k = 20) and fast (the
green curve with k = 250) measurements are presented.
Algorithm 3: Measurement procedure
Data: a model of a system, a number k of nodes observed per one simulation
cycle
Result: the measured macrostate c∗
1 N [RED] = N [GREEN] = N [BLUE] = 0;
2 foreach simulation cycle do
3 choose randomly k nodes from the nodes not chosen yet;
4 increase each N [RED], N [GREEN] and N [BLUE] by the number of nodes
from the sample correspondingly coloured
5 end
6 N = N [RED] + N [GREEN] + N [BLUE];
7 c∗ (RED) = N [RED]/N ;
8 c∗ (GREEN) = N [GREEN]/N ;
9 c∗ (BLUE) = N [BLUE]/N ;
10 return c∗
1.0
20
100
250
0.8
0.6
0.4
0.2
0.0
0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0
Relative time
Fig. 6. Error for the measurement with k = 20, for the measurement with k = 100,
and for the measurement with k = 250
Looking in Fig. 6 one can see that the error estimation increases with in-
creasing of the measurement rate. This means that there exists perhaps some
low bound for the precision of a measurement.
3.3 Systems of Components with Lazy Response
The LR-model is based on the following model of a state called by LazyState
(see Fig. 7).
«enumeration»
Colour
RED
GREEN
BLUE
LazyState
colour: Colour
balance: Integer
setColour(colour: Colour)
getColour() : Coulor
estimate(): Colour
State
Constrints:
post: self.colour = self.estimate(balance) setColour(colour: Colour)
inv: self.getColour() = self.colour getColour() : Colour
inv: self.estimate() = self.colour estimate(): Colour
Fig. 7. Model of a lazy state
Unlike the previous model, the model considered in this subsection is more in-
ertial. This is provided by the method estimate(), which uses the function Pm (x) ,
and the field balance, which equals the difference between BLUE-arguments and
RED-arguments (see Fig. 7).
The function Pm (x) is defined as
x3
x
1− if 0 ≤ x < m
Pm (x) = m3 2m
1 + 1 arctan π(x − m) if x ≥ m
2 π m
This function provides model inertness. Its value equals the probability that
the corresponding system node is not green. We assume that the current balance
of the node determines this probability.
The LR-model realises items 9 and 11 of Algorithm 2 as follows
if outcome = nobody then
newFirstState = firstState
newSecondState = secondState
if outcome = first then
newFirstState = firstState
if firstState.colour = RED then
newSecondState.balance = secondState.balance − 1
if firstState.colour = GREEN then
newSecondState.balance = secondState.balance
if firstState.colour = BLUE then
newSecondState.balance = secondState.balance + 1
if outcome = second then
newSecondState = secondState
if secondState.colour = RED then
newFirstState.balance = firstState.balance − 1
if secondState.colour = GREEN then
newFirstState.balance = firstState.balance
if secondState.colour = BLUE then
newFirstState.balance = firstState.balance + 1
The positive parameter m controls the system inertia and in a certain sense
can be considered as a mass. This interpretation is illustrated by Fig 8.
We should mark that the character of the measurement error behaviour is
similar to one for the IR-model. This is a reason to omit the corresponding
illustrating figure.
4 Conclusion
Thus, the paper has proposed a framework for simulating pair-chatting in com-
munities. The simulation results show that our fears associated with a funda-
mental change in social behaviour caused by the widespread use of modern in-
formation and communication technologies are not groundless. Moreover, these
changes have led to a violation of the basic assumptions on which the mathe-
matics of sociological measurements is based. The main argument in favour of
such a conclusion is the observable fact, saying for the existence of a positive
lower bound for measurement errors. The mention of this effect demonstrated
by simulation modelling was described in the works of sociologists devoted to
the survey method. Their reasoning is informal and far from mathematical ones.
In the context of this reasoning, sociologists noted the existence of distortion
effects always present in such measurements. In the context of this reasoning,
sociologists noted the existence of distortion effects always present in such mea-
surements. One can mention, for example, the book of Walter Lippmann [8] and
the article of Pierre Bourdieu [2]. One can also refer to the Noelle-Neumann
hypothesis [10] about the spiral of silence, which illustrates the contradiction of
the internal processes of the functioning of public opinion and the problems of
understanding and overcoming this contradiction by sociological means.
1.0
0.8
0.6
0.4
0.2
0.0
0 200 400 600 800 1000
Number of iteration
a) m = 2
1.0
0.8
0.6
0.4
0.2
0.0
0 200 400 600 800 1000
Number of iteration
b) m = 50
Fig. 8. Behaviours of LR Model
In the case, if this hypothesis is confirmed, we will have to admit that the
assumption of complete observability [4, p. 14] is wrong for intensively commu-
nicating communities. In other words, for studying such communities we need to
use models similar to rather quantum than classical models of physical systems.
Of course, this does not mean that mathematics of quantum theory is adequate
for describing dynamics of intensively communicating communities. Hence, the
challenge to find the adequate mathematical language for studying this class of
systems.
Summing up our discussion, we can formulate the following problems for the
top-priority research
1. conduct a detailed study of the dependence of the behaviour of the LR-model
on the parameter m;
2. establish the dependence of the measurement error on the rate of this mea-
surement;
3. generalise the obtained results for more complicated than pairwise commu-
nications;
4. build a simulation model for communities exposed to external influences;
5. establish the character of the dependencies between parameters of the ex-
ternal influence and the system behaviour;
6. find out whether the community exposed to external influences is a system
managed by these influences.
If all these studies give a positive result then the problem to ensure certain
community behaviour in the presence of limited resources that provide external
influence on the system can be set.
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