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DOI: https://doi.org/10.34069/AI/2023.71.11.12
How to Cite:
Samosudov, M.V., Bagrin, P.P., Matyash, A.V., Zuikov, Y.V., & Andreeva, V.A. (2023). The reflection of managerial control
actions in the digital twin of the organization. Amazonia Investiga, 12(71), 138-148. https://doi.org/10.34069/AI/2023.71.11.12
The reflection of managerial control actions in the digital twin of the
organization
Отражение управляющих воздействий руководителей в цифровом двойнике организации
Received: August 9, 2023 Accepted: October 23, 2023
Written by:
Mikhail V. Samosudov1
https://orcid.org/0000-0001-5787-2430
Pavel P. Bagrin2
https://orcid.org/0000-0003-4714-5998
Arseniy V. Matyash3
https://orcid.org/0000-0001-5799-9466
Yan V. Zuikov4
https://orcid.org/0000-0001-6675-9309
Victoria A. Andreeva5
https://orcid.org/0009-0006-4029-9176
Abstract
The work carried out earlier allows us to assert
that a digital twin of an organization can be
created on the basis of a comprehensive agent-
based mathematical model of a social system
functioning in an active environment. Such a
digital twin, consisting of a set of databases for
recording initial data and calculated values of
system parameters, as well as data collection and
processing modules, allows you to automate the
functions of analyzing the activities and the state
of the organization to determine systemic
problems, the causes of the results of activities,
as well as the calculation of control actions and
determining the effect of the control actions of
the head.
The purpose of this work is to determine the
parameters of the control action that need to be
recorded in the digital twin of the organization in
order, using a simulation model, to calculate the
effect of the impact, the dynamics of the social
system in the socio-economic space.
Keywords: digital twin of an organization,
digital twin of a social system, comprehensive
mathematical model of a social system, active
1
Doctor of Science in Economics, leading researcher, The State University of Management, Moscow, Russia. WoS Researcher ID:
JOZ-8239-2023
2
Junior research assistant The State University of Management, Moscow, Russia. WoS Researcher ID: JOZ-8165-2023
3
Junior research assistant The State University of Management, Moscow, Russia. WoS Researcher ID: JHV-1217-2023
4
Master’s degree student The State University of Management, Moscow, Russia. WoS Researcher ID: JOZ-8430-2023
5
Undergraduate student, The State University of Management, Moscow, Russia. WoS Researcher ID: JOZ-8226-2023
Samosudov, M.V., Bagrin, P.P., Matyash, A.V., Zuikov, Y.V., Andreeva, V.A. / Volume 12 - Issue 71: 138-148 /
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system, activeness, organization management,
controlling influence.
Introduction
The term "digital twin" (DT) is often used to refer to a computer model simulating the behavior of a real
object. GOST R 57700.37-2021 defines a DT as "a system consisting of a digital model and bidirectional
information links with the product ... or its ... parts"6. In the context of our objective, it is important to note
that such a model contains information about the values of phase variables at specific points in time and a
module that calculates the system's dynamics based on this data. Strictly speaking, the DT of an object is a
data set (phase variable values) that, using a simulation model, allows for the calculation of the object's
dynamics and changes in its properties (i.e., the nature of the object's interaction with the environment).
Applied to an organization, this involves simulating the movement of a social system in the socio-economic
space (SES), implying the presence of data about the object and its operating environment.
Agent-based models are increasingly being utilized for the modeling of social systems. The development
of such models is outlined in the Fundamental Scientific Research Program until 2030, approved by the
Government of the Russian Federation7. To apply these models practically, there is a need for software and
hardware complexes that implement the model.
Considering the above and the goals of digitizing the economy and society, the digital twin (DT) of the
organization should ensure the recording and processing of data that allow tracking changes in the
organization during the modeling of perturbations, managerial actions, and other influences. The data and
dependencies should consider all significant cause-and-effect relationships, enabling the simulation of the
organization's behavior in the market environment. To achieve this, the DT should allow:
• Recording the organization's state: capture the organization's state and the environment in the form of
phase variable values.
• Recording changes in the organization's state: document changes in the organization's state (values of
phase variables) in response to any events, altered circumstances, or agent actions.
• Calculating changes in the social system: calculate changes in the state and properties of the social
system when modifying the values of phase variables.
The technical implementation of the digital twin (DT) involves a complex of databases and a module (or
modules) for processing real-time values of phase variables to model activeness (processes), the state of
the social system, calculate its behavior, and assess the consequences of management subjects' actions and
the environment.
The aim of the study is to determine the parameters of managerial impacts (MI) by management subjects
that need to be recorded in the DT databases. This information is crucial for assessing the effects resulting
from the implementation of MI.
Literature review
In the literature, there is a lack of comprehensive materials addressing the formalization and calculation of
MI in social systems. Works related to MI in technical systems (see, for example, (Tyunkov & Bocherova,
2012)) provide strict dependencies, describe parameters, and the mechanism of MI. In the context of social
systems, predominantly, individual processes and some influencing factors on the outcome are described.
There are examples of practical implementation, but often these examples and processes are discussed
6 GOST R 57700.37–2021 Computer Models and Simulation: Digital Twins of Products. General Provisions. – Moscow: Russian
Institute of Standardization, 2021.
7 Program of Fundamental Scientific Research in the Russian Federation for the Long Term (2021-2030). Approved by the decree of
the Government of the Russian Federation dated 31.12.2020 No3684-r / https://docs.cntd.ru/document/573319222?marker=64U0IK
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without sufficient reflection on implementation conditions, and the influencing factors are considered in an
abstract manner, without fully disclosing the mechanism of influence.
The management system implies the presence of a control device (or a management subject in a social
system), a managed object, the impact on which alters its functioning, MI, and the result. There should also
be a controlling device or organ that determines the trajectory of movement, final and intermediate goals,
etc.
When performing a management act, the subject influences the object to bring it into a new desired state.
In management, methods are divided into economic (material incentives), organizational and directive
(orders, directives, etc.), and socio-psychological (suggestion, imitation, etc.) (Fundamentals of
management (n.d.)). It is worth noting the inaccuracy of the traditional definition: 'management method is
a set of ways and means of influencing the managing subject on the managed object to achieve ... goals'
(Fundamentals of management (n.d.)) – the right and left parts do not correspond to each other: the right
part can be recognized as a definition of the method of influence (although it is vague), but not every
influence will be management, so it is incorrect to equate the management method with 'a set of ways and
means of influencing...'. The management method is a way of management. In general, there are only three
main ones – without feedback, with feedback on perturbing influence, and with feedback on the result –
and their combinations.
Universal methodology for calculating MI in management has not emerged. This is often explained by the
fact that the impact is realized in a specific situation involving specific individuals under different
conditions. However, the main reason is the lack of a strict theoretical foundation and the associated ability
to reason abstractly. The tasks of automating activeness require the calculation and quantitative assessment
of all influencing factors and unambiguous relationships between variables.
One of the factors is social institutions. Social institutions are often understood as a "stable complex of
formal and informal rules, stereotypes, norms, attitudes, controlling various areas of society's activity and
individual personality, as well as organizing the system of roles and statuses of a person" (Danilova, 2009,
p. 14). While agreeing that formal and informal rules, stereotypes, etc., are social institutions, a stricter
interpretation is considered here – an institution is information about actions and consequences obtained by
an individual through reading regulatory documents or observing the behavior of agents. Consequences are
the sum of resources gained (incentives) and resources lost (constraints) because of an action. Institutions
influence the behavior of an agent (the probability of the agent performing actions) but do not "control"
them.
Nevertheless, it is worth noting the existence of works attempting to define approaches to the calculation
of MI. In (Verzilin & Shahygin, 2011), the authors note: "When studying the processes of managing a social
system, modeling tools must fully implement the system approach principle and represent a set of
formalized models ... of various scales and purposes, taking into account all the most important factors ...,
providing the development of well-founded and timely recommendations when making decisions ..."
(Verzilin & Shanygin, 2011, p. 83). Here, a hierarchical system is considered, requiring decisions on
management tasks through "coordination selection." This refers to management where the upper-level
element controls the lower-level elements through actions that influence the development of decisions in
the governing bodies of these elements (Verzilin & Shahygin, 2011, p. 81).
Note that specifically, the digital twin (DT) of an organization can serve as a tool for calculating MI in the
decision-making process.
Works related to modeling MI often do not consider the calculation of impact but rather describe certain
actions in a specific situation. For instance, in (Alidodov A., & Averchenkov , 2022), the BPMN
specification is used to describe the management process in the system 'Tajik students admitted to Russian
universities' (Alidodov A., & Averchenkov, 2022, p. 87). While useful as an experiential description, it
does not reveal the full set of factors influencing the decision, nor does it provide calculation algorithms,
etc.
In some works, the focus is on informational impact and human perception of information. For example, in
(Liberman, 2023), the calculation of the strength of informational impact is oriented towards computer
application for measurement and recording. Psychology and sociology also pay attention to how humans
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perceive different types of information, including hidden MI. However, it's important to note that there is
often an unjustified division of essentially the same influence based on the goals of the management subject:
if it's explicit and 'well-intentioned,' it's considered management; if implicit and/or 'pursuing one's own
goal,' it's considered manipulation. For instance, in (Sheynov, 2006), a technology of hidden control is
defined, consisting of stages: '1) collecting information about the addressee; 2) detecting targets of influence
and bait; 3) attraction; 4) compelling the addressee to act; 5) gain for the initiator of the impact ' (Sheynov,
2006, p. 56). There is a somewhat negative connotation with terms like 'bait,' 'compelling'... However,
viewed impartially, any influence involves informational impact, and the distinctions between these
influences are based on the goals of the management subject.
From the perspective of information perception, psychology and sociology focus on the alphabet people
use. In (Kara-Murza, 2017), it's demonstrated how different symbolic systems affect perception, noting that
words can suggest something to a person, influencing their behavior (Kara-Murza, 2017, p. 141). A.V.
Savchenko's work (Savchenko, 2008) explores latent control – covert purposeful impact where the subject
of activity (management object) consciously accepts and implements decisions predetermined by the
subject of latent control. Acting rationally and reasonably, individuals or groups subjected to latent impact,
due to distorted information, lack of knowledge, or biased event assessment, act in the interests of the
subject of latent control (Savchenko, 2008, p. 10-11). The rationale for modeling MI is emphasized. For
this purpose, a DT can be used, including an imitation model of the organization.
In some works (see, for example, (Rogachev et al., 2019)), MI is presented as streams of financial resources.
However, it should be noted that such representation can only be used for certain large-scale management
tasks, as the calculation error becomes significant due to unjustified abstraction from all other factors
influencing the behavior of the social system.
Methodology
We utilize a mathematical agent-based simulation model of a social system, which defines the data structure
required for calculating the system's dynamics and enables the computation of the social system's dynamics
in the SES (Samosudov, 2021; Samosudov, 2019; Samosudov, 2019a; Samosudov, 2021a; Samosudov,
2022; Samosudov & Bagrin, 2022; Bagrin & Matyash, 2022).
The model is based on a resource-functional approach to the analysis of social systems. This approach
assumes an understanding of social systems of various purposes and scales as functional systems that
require a specific resource base, including material, informational, intellectual, social, spatial, and human
time resources. A key condition is the ability to formulate functions correctly and consider resources in the
utmost specificity (Samosudov, 2019), avoiding unnecessary generalizations. The developed
methodological materials allow for precise calculation of the necessary resource base for implementing
specific functions.
The creation of the model was preceded by the following fundamental scientific achievements relevant to
this task (Samosudov, 2012; Samosudov, 2019; Samosudov, 2019a; Samosudov, 2021; Samosudov, 2021a;
Samosudov, 2022; Samosudov & Bagrin, 2022):
• Development of a rigorous theoretical framework describing the dynamics of the social system in the
SES and defining the conditions for functional stability.
• Development of a method for quantitative assessment and consideration of all types of resources,
including intellectual, informational, social, organizational, etc.
• Development of a method for formalizing processes (activities) through the documentation of resource
transformations using multidimensional matrices.
• Development of a method for formalizing the content of documents and informal rules (social
institutions) and their influence on the likelihood of individuals performing certain actions.
• Development of a method for accounting for the systemic activeness of agents.
• Development of a method for reflecting the influence of the environment on agent behavior through
the calculation of gradients at the point of SES.
• Identification of invariants and variable quantities characterizing the process of agent interaction.
This allowed defining a data structure for capturing the state of the social system in the digital twin (DT)
database for dynamic system calculations. The model implements a Markov process, so modeling a specific
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organization does not require a significant amount of data on past activities. It is sufficient to describe the
current state of the organization and the environment to calculate its dynamics.
The work on the project "Digital Twin of a Social System: Substantiation of Content and Application
Possibilities for Management" (Russian Science Foundation (n.d.)) demonstrated the possibility of
describing the state of any social system with a structurally identical set of phase variables. While the values
of variables may change, the structure remains the same. It also confirmed the feasibility of implementing
a digital twin of a social system and identified approaches to using the digital twin in the management
system.
Results and discussions
The activity of a social system is inherently tied to its constant change and occurs in a continually changing
environment. Social systems are inherently dynamic and active systems, operating in a dynamic and active
environment8. Due to the system's activeness, the environment reacts to its presence by redistributing
resource flows. If the system's impact is adequate, such redistribution will lead to the formation of resource
flows entering the system. However, the system's activeness arises from the activeness of agents shaping
the system (not only founders and organizers but also other participants in corporate relationships).
Due to the absence of stationary states for both the system and the environment, for the system to function
and maintain this capability in the future, management of the system's movement in the environment is
necessary – a change in its state over time. While the state will naturally change, relying on random
processes and the natural course of events is not advisable in an active and, arguably, aggressive
environment where economic agents seek to redirect resource flows in their favor. It is necessary to manage
the change in the system over time to ensure the necessary incoming resource flow from the environment
for the social system's existence.
MI should lead to a change in the system's trajectory towards a target state. Its consequence is the alteration
of the values of phase variables (system parameters), leading to a change in the state and properties of the
system.
In the context of social systems, we might be interested in the functional stability of the system (the ability
to maintain functionality in changing conditions); the attractiveness of the system to certain agents and, if
necessary, unattractiveness to others (e.g., raiders, dishonest employees, clients, etc.); the ability to adapt
to operating conditions (directly related to manageability); as well as other similar properties.
The change in the system is determined by the actions of interacting agents – if their actions lead to a change
in the system's resource base, functional concentration of resources, then the properties of the system
change.
Let's introduce the theorem: to correct the movement of a social system in a SES, it is necessary to
appropriately change the behavior of agents by transmitting flows of messages and resources to them.
Let Ω be a system moving in the SES Θ. A functional social system can be considered as a subset of the
SES, with a sufficient concentration of resources and structured activeness by agents to maintain the
functionality of the system (ΩΘ). It is precisely the combination of resources in an active form that
provides the possibility of implementing a function. However, for the activities of social systems, resources
inseparable from humans (intellectual resources, some social resources, etc.) are also necessary, requiring
structured activeness of agents.
The combination of the states of the system and the environment determines the system's situation,
characterized by incoming resource flows from agents interacting with it (resources should be considered
broadly – not only financial but also other resources that are significant).
8 That is, at any given moment in time, there is at least one parameter of the system and the environment, the rate of change of which
is not equal to zero.
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If the incoming resource flows (IRF) are sufficient, in the SES corresponding to the considered social
system, a certain spatiotemporal concentration of resources in an active form will emerge, enabling the
realization of necessary functions, and the system will be capable of functioning9.
The movement of the social system Ω in the SES is characterized by the rate of change of the system, dΩ/dt,
and its trajectory is described by the following equation10
󰇛󰇜󰇛󰇜


(1)
The management subject's task is to minimize the deviation of the actual trajectory from the calculated
trajectory of the system's movement towards a specific target state.
The target state is the condition of the system that ensures functioning results aligned with the expectations
(desires) of key participants in corporate relationships. This could involve the system's ability to generate
sufficient IRF or other properties such as functional sustainability, the capability to produce the required
products in the desired quantity, attractiveness to specific agents, etc.
The rate of change of the system depends on the flows of resources󰇛󰇜 and messages
󰇛󰇜, emanating
from the points of the SES. If the k-th point of the SEP (receiver) is within the region corresponding to the
system Ω, the system changes – the resource base changes, the information received by agents changes,
and their activeness changes. As a result, the properties of the system change.
In other words, the system undergoes movement, more or less aligned with the management task. If the
Inflowing Resource Streams correspond to what is necessary for the adaptation of system Ω to changing
conditions, the trajectory of movement will change accordingly. If not, the mismatch between the system
and the environment will increase.
The resource flow
entering the system Ω from the SES Θ is determined by the actions of SES agents –
by performing actions , the j-th agent transforms the resource base under its control11 󰇛󰇜 into 󰆒󰇛󰇜
and creates outgoing flows of resources 󰇛󰇜 and messages
󰇛󰇜 from the j-th point of the SES to the k-
th point of the SES:
󰇛󰇜
󰆒󰇛󰇜󰇛󰇜
󰇛󰇜
(2)
Note: In general, the possibility of zero flows of messages and resources emanating from point j of the SES
should be taken into account, but the transformation of the resource base always occurs.
However, as shown earlier in (Samosudov, 2021a; Samosudov, 2022), the set of actions of the j-th
agent󰇛󰇜, performed by him at time t, is determined by the value of his behavior vector (BV) 󰇛󰇜 – its
components equal to 1 are elements of this set:
󰇛󰇜󰇛󰇜󰇛󰇜
(3)
As a result of the agent's interpretation in accordance with the alphabet of the received streams of
messages
󰇛󰇜 and resources 󰇛󰇜 the BV of the agent changes under the influence of the received
information 󰆺󰇛󰇜 – a set of stimuli, constraints, and the probability of the consequences of certain actions
occurring, which in the model is taken into account by means of a matrix of size k(2[n+m]+1):
9 That is, at any given moment in time, there is at least one parameter of the system and the environment, the rate of change of which
is not equal to zero.
10 The system's state is described by a state vector, each element of which is the value of a phase variable (system parameter). However,
for the sake of simplicity, we do not detail the change in state by individual parameters here.
11 For simplicity, we do not consider here that the transformation of the resource base takes some time, and we write 󰇛󰇜
󰆒󰇛󰇜󰇛󰇜
󰇛󰇜, as if assuming instant transformation.
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󰇫󰇛󰇜
󰇛󰇜󰇬
󰇒
󰇏
󰆺󰇛󰇜
󰆺󰇭

󰇛
󰇜 󰇛
󰇜
󰇛
󰇜 󰇛
󰇜
󰇛
󰇜 󰇛
󰇜
󰇛
󰇜 󰇛
󰇜󰇮
(4)
–
x-e conditional action;
–
stimuli for action (resources of type n obtained when performing the action);
–
constraints for action (resources lost when performing the action of type m);
󰇛
󰇜,
󰇛
󰇜
–
probability of obtaining resources of type n and losing resources of type m when
performing action .
Under the influence of the received information, there arises a divergence of the component of the potential
that corresponds to the action :
󰇡󰆺󰇛󰇜󰇢󰇧 
󰇛󰇜
󰇛󰇜
󰇛󰇜 
󰇛󰇜
󰇛󰇜
󰇛󰇜
󰇛󰇜
󰇛󰇜󰇨
(5)
The BV of an agent at time t is determined as follows:
󰇛󰇜󰇛󰇜󰇭󰆺󰇛󰇜
󰆺󰇛󰇜
󰆺󰇛󰇜
󰇮
(6)
Thus, considering (2), the change in the behavior of agents in the social system Θ alters the outgoing flows
of resources 󰇛󰇜 and messages
󰇛󰇜, from them, thereby changing the state of the system evolving in
the SES.
The theorem is proven.
Considering the foregoing, MI is an influence on agents that alters their resource flows, leading to changes
in system parameters to adapt the system to a changing environment12.
In a social system, the following entities exist, determining information that influences the behavior of
agents:
• Message flows from one agent to another (or from the organization to agents) – they are interpreted by
agents, and in their subjective subspace, subjective assessments of stimuli and constraints related to
actions arise.
• Resource flows are also interpreted by agents as information influencing behavior – signals that define
subjective assessments of the probability of gaining or losing benefits from interaction in SES, and the
existing (accumulated) resource base of the agent affects the subjective assessment of the value of the
proposed benefits.
• Institutional environment – formal and informal rules transmitting information about stimuli and
constraints associated with actions.
It is important to note that for changing the probability of an agent performing actions, the subjective
assessments that arise due to the interpretation of received messages and resources are crucial. Information
(a variable entity) between agents is not transmitted; messages and resources (invariant entities,
12 This should not be regarded as a strict definition of MI, rather as additional information specifying the peculiarities of MI for the
tasks of managing social systems.
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independent of the SES point in which they are considered) are transmitted. These are interpreted on the
receiving end based on the agent's alphabet, considering the resources available and needed by the agent.
In general, in the management process, the subject needs to ensure that, considering the influence of the
environment and the subject of management, the BV of the target agent provides the transmission of the
necessary resources and messages to the system. Since the influence of the environment and individual
subjects on the agent is formalized by calculating the gradient at the SES point corresponding to the agent,
this condition can be expressed as follows:
󰇛󰇜
󰇛󰇜󰇛󰇜󰇛󰇜
(7)
In light of the above, let's consider some "typical" actions of the leader to manage the organization (Table
1).
Table 1.
Comparing the actions of the leader with the content in accordance with the discussed concept.
Manager’s actions
Contents
Approval by the governing
body of a document regulating
activities (regulation,
provision, etc.)
The change in the institutional environment of the company, as a result, affects
the utility functions of agents and their future activeness:
• Prescribed actions are determined – actions that need to be performed in
specific situations.
• Stimuli and constraints associated with the performance of such actions
are identified. 󰇛󰇜󰇛󰇜
Having read the document, the agent obtains information about the stimuli and
constraints specified in the document:
󰇛󰇜
󰇒
󰇏
󰆺
󰇭󰆺󰇛󰇜
󰆺󰇛󰇜
󰇮
Another way to obtain this information is by observing the actions of agents
whose behavior has changed as a result of reading the document. Changes in the institutional environment can also alter resource flows, which
may affect agents' subjective assessments and their behavior.
Order (oral or written)
Information about incentives and constraints associated with specific actions,
and a flow of resources towards particular participants. This also leads to a change in the institutional environment – the formation of
formal social institutions in the case of a written order.
Official conversation between
a leader and a subordinate
Targeted direct or indirect (depending on the form and signals) communication
about the possibility of taking certain actions and gaining certain benefits. Properly calculated signals will appropriately modify the agents' activeness.
Informal conversation
between the leader and
subordinate(s)
Informing specific agents, transmitting signals that influence behavior, as a
result of interpreting which agents will receive information about necessary
actions, incentives, and constraints associated with them. Subjective assessments of expected and desired benefits are formed, and as a
result, their activeness changes, leading to the emergence of the necessary
outgoing flows of messages and resources if the leader has calculated
everything correctly.
A meeting or assembly with
subordinates organized by a
leader
Informing a group of participants (information flow towards the group of
participants). During a meeting or assembly, subordinates receive information about
necessary actions, stimuli, and constraints associated with them. Informational
resources that facilitate work and consequently reduce the significance of
constraints (resources lost by a person in the process of activity) related to task
execution can also be conveyed.
Besides the impacts listed in the table, tasks, advice, recommendations, instructions, etc., can be considered.
However, essentially, they do not differ from the ones discussed.
To reflect (record) the MI in the DT of the organization, it is necessary to record the following information
in the database:
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• Identifier of the Impact – a unique code for the impact. It is advisable for the code to reflect the type
of impact and possibly the functional direction, but the main requirement is uniqueness.
• Subject of management creating the impact (active agent).
• Agent or agents for whose behavior the impact is intended.
• Content of the message implementing the impact:
• Transmitted signals;
• Translated meaning – a combination of actions, stimuli, constraints, and probabilities of consequences
that the agent will "see" when interpreting the impact in accordance with (4).
• Parameters related to the selected channel and method of message transmission:
• Probability of the agent receiving a message transmitted through the channel, or better yet, the
distribution of this probability over time if possible. For example, the approved document may be read13
by the agent with a low probability within the first day of its validity, with a slightly higher probability
within a week, and with a high probability within a month. However, the distribution of probability
can be reversed – for example, in messengers, the likelihood that the agent will see the message may
decrease over time. An option is to fix the time of guaranteed acquaintance with the transmitted
message and calculate the effect for the worst-case scenario, but this may reduce the number of possible
actions for the manager.
• Information background of receiving the message by the agent – against the background of which
messages the agent will interpret the message.
From the perspective of organizing the activities of a social system, it is advisable to record additional
accompanying information – the purpose of this impact (i.e., the expected change in agent behavior); the
result of the agents' functioning with changed BV (system effect). However, this is more needed for
organizing activities, subsequent analysis, etc. For the operation of the DT, this is additional information.
The DT's computational block will process this information and calculate the effect of the MI:
• Using the agent's alphabet14 the information that the agent will receive as a result of the impact is
calculated.
• In accordance with (5), the divergence of the agent's BV is calculated, taking into account information
about the agent's existing resources and needs, as well as considering the gradient of the environmental
impact at this point in the SES.
• Based on the calculation of the divergence of the agent's utility function, its resulting utility function
is determined in accordance with (6).
Based on the value of MI, it is determined whether the agent will perform the actions necessary to generate
the required message and resource flows in accordance with (3).
For this, accordingly, the parameters of the agents receiving the message implementing MI must be
recorded in the DT:
• Agent identifier15.
• The agent's BV in the context of actions related to obtaining information. This includes determining
the probability of the agent receiving information16 through the communication channels used for the
impact.
• Alphabet of the agent.
• The resources available to the agent and its needs.
In addition to information about the agent, to calculate MI in the DT, information about the environment in
which interaction occurs, more precisely, about the impact that the environment has on the agent (the
gradient of the environmental impact at the point of SES corresponding to the agent) must be recorded.
13 The receipt of a document should be taken into account based on the actual reading, not just its delivery through the transmission
channel.
14 In a simple implementation, the alphabet is a table that corresponds signals to a set of stimuli and constraints related to the action
that the agent will "see" when interpreting the message.
15 In general, the model used allows calculating dynamics at any level of detail, down to individual agents. However, it is often
appropriate to detail it to the level of subsets of agents with similar characteristics.
The ability to use the same approach for calculations at any level of detail is a fundamental feature of the employed model.
16 Notice: obtaining information, not messages. Obtaining information implies the agent's familiarity with the content of the message.
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This can be calculated through modeling the behavior of agents or, if appropriate to the task conditions,
obtained through expert assessments.
Conclusion
The ability to mathematically model the dynamics of social systems in SES, creating a DT for an
organization, enables solving a wide range of applied and scientific tasks.
For practical applications, it opens the possibility to calculate the MI of leaders, significantly increasing the
efficiency of organizational work. Traditional decision-making often proves inadequate to the situation,
leading to resource losses and reduced efficiency. This approach also transforms the organization of
marketing research, allowing for precise calculations of agent impact and capturing results, providing much
more information about the market using significantly smaller data volumes. For many small and medium-
sized companies, traditional methods based on processing extensive customer data are not feasible.
The DT of a social system can be a powerful tool for fundamental research in social sciences.
The model underlying the DT allows representing research results from various fields in a unified format.
The work conducted demonstrates that most observed phenomena in social systems (if not all) can be
described using the variables used in the model. Essentially, a model of a social system (similar to a
"standard model" in physics) can be created, enabling the formulation of hypotheses and the calculation of
experiments. This addresses the methodological problem of social sciences, as traditional methods relying
on statistical processing of observational results provide sufficient data only with the repeatability of
experimental conditions, which is practically impossible in social systems.
The presence of a "standard model of a social system" creates the possibility of coordinating research efforts
among different groups and contributes to the development of a theory and model anticipated in the
Program of Fundamental Scientific Research until 2030, approved by the Government of the Russian
Federation, as one of the expected promising results of scientific activity.
In this work, we demonstrate the feasibility of recording a leader's decisions in the DT of an organization
and calculating the effect of implementing such a decision, which is one step towards creating a fully-
fledged digital twin of an organization.
Acknowledgments
The research was conducted with the support of the Russian Science Foundation grant No 22-28-20458,
available at https://rscf.ru/project/22-28-20458/.
The authors express their gratitude to the "Delicate Moving" group of companies, with whom they have
established long and fruitful relationships. This group essentially served as a laboratory, providing the
opportunity to refine solutions, approaches, and tools. It also allowed for the testing of organizational
decisions during the research on the organization and management of social systems.
Bibliographic references
Alidodov A., & Averchenkov, A. (2022) Managing Impact on the Social System of Tajik Students Studying
in the Russian Federation: Formalization of the Management Process. Automation and Modeling in
Design and Management, 2, 82-91. https://doi.org/10.30987/2658-6436-2022-2-82-91
Bagrin, P.P., & Matyash, A.V. (2022) Description of the Institutional Environment in the Digital Twin of
the Socio-Economic System. Economics and Entrepreneurship, 7, 306-311. DOI: doi:
10.34925/EIP.2022.144.7.056
Danilova, I.A. (2009) Sociology and Psychology of Management: Scientific Book. Moscow: LitRes.
https://www.litres.ru/book/i-danilova/sociologiya-i-psihologiya-upravleniya-177676/
Fundamentals of management (n.d.) Mechanism and methods of management. The system of management
methods, their content, interrelation and interaction. https://acortar.link/Tx4VSs
Kara-Murza, S.G. (2017) Manipulation of Consciousness. XXI Century: Publicistic Book. Moscow: TD
Algorithm LLC. ISBN 5926500036
148
www.amazoniainvestiga.info ISSN 2322- 6307
Liberman, Y.L. (2023) On the Definition of the Strength of Information Impact on a Person When Studying
the Level of His Mental Reaction. Symbol of Science: International Scientific Journal, 2-1, 53-58.
https://os-russia.com/SBORNIKI/SN-2023-02-1.pdf
Russian Science Foundation. (n.d.). The digital twin of the social system: substantiation of the content and
the possibility of use in the process of enterprise management. Retrieved from
https://www.rscf.ru/project/22-28-20458/
Rogachev, A.F., Briskin, E.S., & Kozlova, L.E. (2019) Mathematical Modeling of the Dynamics of
Development of Socio-Economic Systems in the Conditions of State Regulation. In: Briskin E.S.,
Kozlova L.E. (eds.) Proceedings of the XIII All-Russian Conference on Management Issues VSPU-
2019, 1804-1812. https://doi.org/10.25728/vspu.2019.1804
Samosudov, M.V. (2012) Theory of Corporate Interaction as a Tool for Analysis in the Process of Corporate
Governance. Management Sciences, 2(3), 24-30. (In Russian)
Samosudov, M.V. (2019) Resource Footprint of Activity as an Element of the Digital Twin of an Enterprise.
E-Management, 2(3), 38-47. (In Russian) https://doi.org/10.26425/2658-3445-2019-3-38-47
Samosudov, M.V. (2019a). The Model of The Incoming Resource Flow of The Social System for
Digitalization of Management. Journal of Advanced Research in Dynamical & Control Systems, 11(08),
2892-2900. http://jardcs.org/abstract.php?id=3053
Samosudov, M.V. (2021) Reflection of Documents in the Digital Twin of an Enterprise and Calculation of
Their Impact on Human Behavior in an Simulation Model. E-Management, 4(3), 50-60.
https://doi.org/10.26425/2658-3445-2021-4-3-50-60
Samosudov, M.V. (2021a) Formalization of the impact of information on human behavior for the
automatization of the calculation of marketing influence. International Journal of Engineering
Research and Technology, 13(12), 4849-4854. http://www.irphouse.com/ijert20/ijertv13n12_113.pdf
Samosudov, M.V. (2022) Comprehensive mathematical agent-based model of the social system for
management automation purposes. In: Ashmarina S.I., Mantulenko V.V., Vochozka M. (eds)
Proceedings of the International Scientific Conference “Smart Nations: Global Trends In The Digital
Economy”. Lecture Notes in Networks and Systems, vol 397. Cham: Springer, pp. 346-353.
https://doi.org/10.1007/978-3-030-94873-3_43
Samosudov, M.V., & Bagrin, P.P. (2022) Matrix method of reflecting activity in the digital twin of the
social system. Amazonia Investiga, 11(57), 181-188. https://doi.org/10.34069/AI/2022.57.09.19
Savchenko, A.V. (2008). Latent Management: Essence and Mechanism of Use: spec. 08.00.05 "Economics
and Management of the National Economy" (author's abstract of the thesis for the degree of candidate
of economic sciences). Department of Management of State University, Moscow.
Sheynov, V.P. (2006). Hidden Control of a Person (Psychology of Manipulation). Moscow: AST Harvest
(In Russian)
Tyunkov, V.V., & Bocherova, O.A. (2012). On the model of adaptation of control actions to ensure the
reliability of a complex structure under probable extreme influences. Proceedings of the Irkutsk State
Economic Academy (Baikal State University of Economics and Law), 2, 1-9. https://acortar.link/trCZCJ
Verzilin, D.N., & Shanygin, S.I. (2011) Management of Target Processes in Organizational Modeling of
Social Systems. Economics and Management, 9, 79-83. https://acortar.link/GDO1XB