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This is an Open Access article, distributed under the terms
of the Creative Commons Attribution CC BY 4.0

1 Central Research Institute of the Armed Forces of Ukraine, Ukraine (corresponding author)
E-mail: military.technology@icloud.com
ORCID: https://orcid.org/0000-0003-3542-5407
2 Central Research Institute of the Armed Forces of Ukraine, Ukraine
E-mail: solosa1@gmail.com
ORCID: https://orcid.org/0000-0001-8061-8895

DOI: https://doi.org/10.30525/2256-0742/2023-9-2-157-163

ASSESSMENT AND FORECASTING METHOD
OF STATE STABILITY

Volodymyr Mozharovskyi1, Oleksiy Solomytskyi2

Abstract. In the article, the authors propose a method for assessing and forecasting the stability of the state.
The relevance of the work is due to the complex military and political processes taking place in and around
Ukraine, attempts at large-scale interference in internal affairs (including by military means), attempts to destroy
Ukrainian statehood and make the country under total control, and the lack of a methodological apparatus
that can be used to assess the state's ability to withstand external and internal threats and preserve its own
identity and structural integrity. The authors analyze the content of the concept of "stability", offer their own
interpretation of this term and identify the factors that significantly affect it. In accordance with these factors,
the article presents a hierarchical system of indicators consisting of two main groups characterizing the ability of
the state to withstand internal and external influences, and contains indicators that allow to assess the military
capabilities of the country, the level of conflict potential, taking into account ethnic and religious problems,
the state of its economy, social and political spheres, the ability of law enforcement agencies to counter
internal threats, energy security and the level of corruption. Subject of research. Assessment and forecasting of
state stability. Methodology. In order to obtain functions that explicitly describe the dependence of the state's
stability on lower-level indicators, the proposed approach involves the use of the theory of experimental design
to form a training sample for each of the groups of indicators, followed by its processing using the method of
group consideration of arguments. This approach is demanding on the level of competence of experts, but it
allows obtaining dependencies that can be used to directly calculate the value of the state's stability indicators,
which is of great importance in the preparation and decision-making on ensuring Ukraine's national security.
The authors propose an integrated approach to forecasting the level of stability, which will make it possible to
obtain both exploratory and normative forecasts, and this will increase the validity of decisions on ensuring the
national and military security of the State. The purpose. The article outlines the main provisions of the method
of assessing and forecasting the stability of the state, which allows obtaining a numerical assessment of
stability and forecasting its development over time, taking into account a wide range of indicators covering
both civilian and military spheres of the state, and also allows taking into account possible external influences
(destructive or positive). Results. The article presents the system of indicators by which it is proposed to assess
the stability of the state, the general procedure for calculations using the proposed method, and some results
of a numerical experiment which confirmed the efficiency of the proposed approach, its sufficiently high
accuracy and clarity of the results obtained. The calculations show that Ukraine's overall level of stability has
declined significantly since 2014, but there is reason to believe that the state has managed to maintain it and
even gradually improve it amid large-scale aggression.

Key words: stability of the state, external and internal threats, military-political situation, method of group
consideration of arguments, forecasting.

JEL Classification: С25, С53

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1. Introduction
The military-political situation in the world, in the

region, or between individual countries escalates
when economic, diplomatic, and other instruments
for regulating and solving internal and external
problems exhaust their possibilities and one of the
parties resorts to aggression to solve them.

In such circumstances, the ability of the state to
counter internal and external threats and preserve its
independence and territorial integrity is extremely
important. After 2014, this became a vital issue for
Ukraine.

In order to determine a strategy for countering
threats, it is important to assess the potential of one's
own country, to identify its strengths and weaknesses,
as well as the conditions under which destructive
processes in society and the state can escalate and
lead to its destruction. This is especially important
when a country is located in an unfriendly
environment or is exposed to aggression. Therefore,
determining the degree of stability of a state is an
urgent scientific task.

The ability of a state to withstand internal and
external threats has been considered in many works
Sharp, 2010; Nayef R .F. Al-Rodhan, Kuepfer, 2007;
Carment, 2003; Milliken, Krause, 2002; Orel, 2018;
Reznikova, 2018; Goetze, Guzina, 2008). However,
these works are mostly of a general theoretical nature
and do not provide an answer to the question of
how exactly the stability or resilience of a state is
determined. The most interesting in this regard is the
work (Goetze, Guzina, 2008), which is devoted to the
assessment of the stability of the state to maintain the
status of a "center of power". The general approach
to such an assessment is noteworthy, but it is not
without significant drawbacks. The proposed system
of indicators does not fully reflect the set of factors
that affect the stability of the state, and some of
them are questionable (for example, the number
of citizens suffering from alcoholism and drug
addiction, which is considered a driving force behind
internal unrest). Most of the indicators reflect
purely economic issues, while military and social
aspects are hardly considered. The main drawback
is that the work does not provide a general form
of the function for assessing the stability of the
state. At the same time, the problem of forecasting
changes in the stability of the state is not
addressed at all.

The purpose of the article is to outline the
main provisions of the method for assessing and
forecasting the stability of the State, which would
be free from the above shortcomings and
would allow obtaining a numerical assessment
of stability and forecasting its development
over time.

2. The concept of state stability
The analysis has shown that there is currently no

unified view of such terms as "state resilience" and
"state stability ". Often, these terms are used to
mean the same thing. According to the authors,
they are closely related, but not identical.

Based on the basic definitions of resilience and
stability, it is more correct to speak of state stability
in the context of the ability to withstand internal
and external threats, especially in the event of an
aggravation of the military and political situation.

Indeed, if stability is the ability of a system to
function without changing its own structure and
to be in equilibrium (Paris, 2011), the authors
propose that the stability of the state is understood
as its ability to function and to be preserved for
a long time without drastic changes. In a broader
sense, this is a condition of the state characterized
by the existence of the necessary prerequisites and
factors that ensure the preservation of territorial
integrity and inviolability by the state, and the
preservation of its identity, civil peace and harmony
by society through the achievement of a balance
of interests of various social actors and political
forces, timely and legitimate resolution of emerging
problems and contradictions in the field of politics
through the mechanisms and means provided for by law.

The stability of the state, as well as the stability of
society, is conditioned by the laws of functioning and
development of society, the nature and methods of
interaction of its subsystems, changes and evolution of
which do not cause the destruction of the functional
unity of the structure and their balance.

The stability of the state is primarily ensured by
the political system of society and the effectiveness
of its functions, which, in turn, depends on the mass
support of citizens. At the same time, one should
not forget about military power as an integral part of
ensuring stability under the influence of external factors.

The main conditions that influence the level of mass
support for the existing political regime are: the level
of material security and social protection of citizens,
the existence of democratic institutions and
mechanisms that ensure public participation in the
political process, the principle of equality and justice,
security and legal guarantees for individuals. The
system of laws in force in a society must change in
accordance with new conditions and new challenges
of the time. An indicator of the stability of a state
is its ability to neutralize negative influences and
threats from outside (subversion, international
terrorism, economic blockade, political pressure,
blackmail, disinformation, threat of force, etc.) Such
negative influences can bring the state into a state of
extreme instability and even destroy it. The outbreak
of civil war or large-scale political violence by both

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supporters and opponents of the existing order is
particularly dangerous. That is why an adequate
and timely response by the state to threats to its
sovereignty, social interests and the security of its
citizens is so important.

In general, the stability of the state depends on
a combination of internal factors and external factors
that manifest themselves in the form of potential
claims by other countries or blocs (military threat).

That is, a state that seeks to preserve its indepen-
dence and avoid falling under external control
must be able to ensure its stability in the face of
possible external and internal negative factors.

3. Procedure for assessing
and forecasting stability

As the analysis of recent events shows, the
aggravation of the military-political situation between
two states does not always lead in an obvious way
to an armed conflict. Increasingly, pressure on the
state is exerted by non-military means (information,
economic, social, etc.), including from within the
country itself (Bohdanovych, Pavlovskyi, Solomytskyi,
2019). Thus, the importance of internal factors,
which can sometimes be decisive, is growing
significantly.

In general, the equation for assessing the level of
stability can be written as follows:

S f V Vins outs� � �, , (1)
where Vins, Vouts – the integral importance of the

state's ability to withstand internal and external
influence, respectively.

The choice of indicators that determine the
value of Vins, Vouts is important. For a comprehensive
assessment of the impact, it is proposed to use
a modified system of indicators, first proposed in
(Development of methodological foundations).
The novelty of this approach is that the list of
indicators is chosen situationally, based on the
adversary 's strategy of influence on Ukraine. That
is, the areas of state activity that will be primarily
targeted are identified, and stability is assessed
only for these areas. This approach will reduce the
amount of calculations and focus on developing
recommendations for stabilizing the situation in the
most critical areas.

The hierarchy of indicators for assessing a country 's
ability to protect itself from insider threats, shown
in Figure 1, will allow experts in the relevant field
to use an acceptable number of indicators
(Romanchenko, Butvin, Hvozd, Solomytskyi, 2018).

Thus, the ability to withstand internal threats is
proposed to be viewed as a function of appearance:

V f W I I I Iins VD ES GINI CP PRO� � �, , , , . (2)

For each country, the indicator of domestic tension
WVD is defined as follows:

W f I I IVD vc ec s� � �, , . (3)
The indicator of the internal conflict situation (Ivc) is

determined using such indicators as general conflict
potential (Izcd), ethnic (confessional) (Ievd) and
political relations (Ipvd), and characterizes the level
of danger of armed conflict within the state.

The overall conflict potential, in turn, is
determined by the following partial indicators: ivc is
an indicator of internal conflicts; itp is an indicator of
territorial manifestation; isr is an indicator of the
impact of internal conflicts on the stability of the
regime; iivp is an indicator of foreign military presence.

Ethnic relations are determined by the share of the
dominant ethnic group in the country 's population
structure (iet).

Political relations depend on the following
indicators: isar – an indicator of the presence of
illegal separatist or anti-government movements
in the country; iisr – an indicator of the presence of
legal secessionist movements in the country; izv – an
indicator of attempts at unconstitutional change
of power or coups d'état.

Similarly, other indicators depend on lower-level
indicators (Zghurovskyi, 2008; Zghurovskyi, 2009).

Given that the stability of the state under the
influence of external influence in the event of an
aggravation of the military-political situation will
depend mainly on the strength of the national armed
forces and their ability to withstand the enemy,
external stability is proposed to be considered as
a function of appearance:

V f W W W W W Wouts GFP GFP GFP N A GFP GFP GFP N B� �� � �� �� � � � � �1 2 1 2, , , , , , ,�� �
V f W W W W W Wouts GFP GFP GFP N A GFP GFP GFP N B� �� � �� �� � � � � �1 2 1 2, , , , , , ,�� � , (4)

where WGFP N is the Nth indicator according
to GlobalFirepower (GFP) (GlobalFirepower)
for countries A and B being compared. The GFP
includes values that characterize the armed forces
and are related to resources, finances, and geography
(55 indicators in total).

To determine the explicit form of the functions
S, Vins, Vouts, and other lower-level functions, it is
proposed to use the group method of data handling
(GMDH), which is intended for mathematical
modeling of multivariate data (Ivakhnenko,
Yurachkovsky, 1987).

This approach is described in detail in (Butvin,
Solomytskyi, Didichenko, 2016; Solomytskyi, 2020).

Based on the results of the obtained statistical data,
the level of stability is forecasted for a certain period
of time. Usually, given the non-stationarity of the
processes under study, the forecast horizon does not
exceed 3-5 years. In the course of forecasting, two

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types of forecasts are developed: exploratory (what
will happen if the existing trends continue) and
normative (what needs to be done to achieve the
desired state (optimization of indicators)). The
forecasting is based on the GMDH and will be
discussed in more detail in the following
publications. The results of the assessment and
forecasting are analyzed to determine critical
indicators (Development of methodological
foundations; Zghurovskyi, 2008), which will allow
developing appropriate recommendations to
ensure an appropriate level of stability and eliminate
problematic issues in the areas of state activity.

4. Practical calculation example
A numerical experiment was conducted to evaluate

the performance of the proposed approach.
Thus, the following expression was obtained for

the stability level indicator:

S V Vins outs� � �0 720703 1 96683 3, ,� � . (5)

The accuracy of the obtained function is quite
high, as the average error modulus (AEM) and root
mean square error (RMSE) are about 0.2, while the
coefficient of determination was 0.97. The diagram
of the function is shown in Figure 2.

Similarly, the dependencies for the remaining
indicators were obtained explicitly, but due to their
rather large size, they are not presented in this
article. Provided that the experts in the respective
fields were sufficiently trained, all functionalities
had a sufficiently high accuracy (the coefficient of
determination in the training sample was not lower
than 0.85, and in the test sample – not lower than
0.75). Based on the results, an appropriate model
was built in the AnyLogic program, which showed
high sensitivity to changes in the input data.

On the basis of the obtained data, the change
in the level of stability was predicted for the next
five years (Figure 3). The forecast was developed
according to the methodology outlined in
(Solomytskyi, 2020) for cases of stability as its
own time series and as a function of lower-level
indicators. The calculations show that the stability
of the state remains low, which is primarily due to
socio-economic factors and is complicated by
the aggression of the Russian Federation against
Ukraine, i.e. external influencein the military,
information and conflict spheres.

The developed regulatory forecast showed that to
ensure the required level of stability (S ≥ 3,5), it is
necessary to ensure Vouts_nec ≥ 3,6 and Vins_nec ≥ 3,93,
which are not expected to exceed 3.18 and 2.28,
respectively (see Figure 4).

5. Conclusions
The proposed method of forecasting the stability

of the state in the face of changing circumstances
allows quantifying the level of stability of the state

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025

YearS=f(V,W,E,I,PI,t) S=f(t)

Figure 3. Forecast of changes in the level of stability by 2025

Source: developed by the authors

Figure 2. Graph of dependence of the stability level indicator

Source: developed by the authors

𝑉𝑉𝑉𝑉𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
𝑉𝑉𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜

𝑆𝑆𝑆𝑆

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2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025

Vouts,
Vins

YearVouts Vins Vouts_nec Vins_necVouts Vins Vouts_nec Vins_nec

Figure 4. Results of regulatory forecasting of stability indicators

Source: developed by the authors

under the influence of internal and external factors.
It works with a large number of indicators that
sufficiently reflect the main factors influencing the
stability of the state both from the inside and from
the outside, while the indicators in the calculations
can be varied depending on the strategy of
influencing the state chosen by the enemy. For the
first time, it is proposed to take into account the
indicator of external governance in various spheres
of state activity. The method, based on the theory of
planning experiments and GMDH, allows to develop
two types of forecasts – exploratory and normative,
with different depth of detail. The method will allow
to substantiate measures to maintain and increase
the stability of the state under the influence of
external and internal factors, taking into account the
level of financing.

The calculations show that Ukraine's ability to
maintain its own stability is at such a low level that
a number of measures need to be taken to improve
the situation. At the same time, analyses and

calculations have shown that the most critical areas,
in addition to the military, due to Russia's large-
scale invasion of Ukraine are socio-economic, where
the situation is complicated by external influence
in the information and internal conflict spheres, as
well as a high level of external control in vital areas
of the state (politics, economy), and the situation in
the religious sphere has recently become more acute.

The construction of a normative forecast (the
solution of an optimization problem) made it
possible to determine the rational values of the
indicators on which the stability of the state
depends. At the same time, the calculations show
that it is impossible to achieve them in the near future
if the current level of financing is maintained.

Another area of research is to determine the
appropriate thresholds at which the state is at risk
of losing its stability and, as a result, its integrity, or
ceasing to exist altogether, and to develop an
approach for selecting the indicators necessary for
the calculations in each case.

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Received on: 07th of March, 2023
Accepted on: 29th of April, 2023
Published on: 23th of May, 2023