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Invalidity in Socio-Economic Systems

For complex machines, systems and processes, reliability is evaluated in order to make a decision to increase this and thereby reduce possible losses by eliminating or reducing the number of failures, accidents and catastrophes.

Economics has great complexity, there are losses, ruin and crises with large losses, but there are no methods for economic reliability assessment and management of reliability. The development and research of reliability theory in economics is an actual problem.

To achieve this goal we created a scientific discipline "Top-Economics", one of the central concepts is the invalidity of events. The problem of the invalidity of socio-economic systems (SES) appeared recently due to new tasks: an assessment of the quality of systems and products under requirements by the World Trade Organization (WTO); management of the state and evolution of socio-economic systems; assessment of the failure risk in decision of difficult social and economic problems; forecasting evolution and assessment of danger of the system's state.

"Invalidity" is a deviation of system's parameters from given ones but for quantitative estimation we need scientific definition of invalidity. Invalidity is an event after which the system can perform a specified assignment, but with loss of quality.

The concept of Boolean "event-statement" is expanded with the purpose of constructing logical-probabilistic (LP) risk models for validity (quality) loss for socio-economic system (SES) and processes. An invalid event-statement is the deviation of an indicator from a zero or a given value. The indicators are normalized and have values in the interval [0, 1]. The indicator of invalidity (system quality) is formally used as a indicator of reliability or risk (probability) in engineering.

Example 1. The invalidity of the system is a complex indicator of system's quality, which takes into account invalidity of elements. We introduce: A1, A2, ..., An are system's elements; R1, R2, ..., Rn are indicators (probabilities) of invalidity of system's elements, defined within the interval [0, 1]; Y1, Y2, ..., Yn are event-statements about invalidity of elements and corresponding logical variables.

The logical model of the risk of validity (quality) loss for the system Y is determined by the formula of disjunction of events:

Y = Y1 ∨ Y2 ∨ ... ∨ Yn. (1)

Logical model of the risk of validity (quality) loss for the system in the orthogonal form:

Y = Y1 ∨ Y21 ∨ Y312 ∨ ... ; (2)

The probability model (or arithmetic model) of the risk of validity (quality) loss for the system is written from expression (2):

R(Y) = R1 + R2(1 - R1) + R3(1 - R1)(1 - R2) + ... . (3)

For example, if R1 = R2 = R3 = 0.5, then К(У) = 0,875.

Example 2. Calculation the invalidity coefficient (probability, risk).

The State legislatively established for a certain group of scientists a salary indicator of 1000.0 USD per month. If (by result at the end of the year) actual average value of the salary indicator is equal to 800.0 USD (due to inflation), then the invalidity indicator or the risk of validity (quality) loss for the salary indicator is equal to:

Rok = (1000 - 800) / 1000 = 200 /1000 = 0.2

If the system has several invalid indicators, then the system's invalidity is determined by the formula (3) and will always be less than 1.

Examples of logical-probabilistic models of the risk of validity (quality) loss: a risk model for control system's quality loss; risk model for loss of the safe space for humanity, etc. [3].

For invalidity, the following definitions are formulated [1, 2]:

  1. The invalidity in the economics is introduced by analogy with the failure in reliability theory in engineering. In comparison with reliability in engineering, invalidity takes a set of values within the interval [0, 1] rather than two values (failure state and working state, 0 and 1).
  2. The International Standard ISO 9000-2015 uses terms "validity" and "invalidity" for estimation the quality of performed work, provided services, products, and management of systems.
  3. The invalidity of a system is the deviation of its state from the value given by project and conditions. The invalidity of a system's parameter or indicator is the deviation of its value from a given or normative one.
  4. The invalidity of a state is considered as an event-statement, which has corresponding logical variable. The indicator of invalidity takes values within the interval [0, 1] and is considered as an indicator of system's quality.
  5. The invalidity of a system (as event) is calculated under invalidities of its event-parameters.
  6. If the parameter is const, then it is not considered as event in the system's state. For example, the "number of women" is a constant parameter in the current state of SES "Birth rate in the country". This parameter is not entered in the risk LP-model.
  7. LP-models of invalidity for different SES can be combined into one model by logical operations AND, OR, NOT.

Following factors determine scientific and practical importance of the Top-Economics with invalid events for the management of social and economic safety [1, 2]:

  1. Management of social and economic safety is performed by the invalidity (quality) criterion.
  2. The LP-model of risk of system's quality loss can be constructed under one state of the system.
  3. LP-models of risk of quality loss can be used for comprehensive analysis of the socio-economic safety for each SES.
  4. In comparison with reliability theory in engineering, where the states of system's elements take only two values (failure and work), the state of the system's invalidity takes many values. Quantitative assessment of invalidity (quality) of the system's state is determined by values of invalidity of its elements with use of the probabilistic (arithmetic) model of the risk of quality loss.
  5. The connection of LP models of the risk of validity (quality) loss is appeared by means initiating events being included in the LP-models of the risk of quality loss in different SES.

Objective and subjective in invalidity. The central concept of the Top-Economics is the invalidity of the socio-economic system. Let make philosophical explanations of this concept by analogy with the concept of safety in engineering [1, 2].

Invalidity is an event when the system can function, but with loss of quality. In practice, there are difficulties in estimation of the invalidity. Some specialists suppose, there is deviation from given requirements, but other specialists say there is no deviation. Why we have various minds for the same fact concerning to invalidity and validity of the system? What is objective here, and what is subjective?

To answer this question, let consider the "technology", which is usually used before the evaluation of the event (i.e. invalidity). Any system (object) can be described in various ways. One way is to compile a finite set of requirements that an object have to satisfy. If the object meets the requirements, then object is consider as valid.

A set of requirements for the system is connected with the activities of some persons and, therefore, this is a subjective act, depending on the knowledge about the system, experience and other facts. At the same time, mistakes may be made in the assignment of certain requirements and omissions of some of them. Moreover, these requirements can be varied according to the wills and desires of developers, i.e. they are dynamic.

In despite of the relativity of requirements for the system and the subjective nature of their establishment, at any moment, a certain set of these requirements have to be identified and fixed in order to we could objectively estimate the invalidity or validity of a system. This is the dialectic of the subjective and objective in estimation the system's invalidity: we subjectively give requirements for the system and objectively - system's state in relation to these requirements. The dangerous condition of the invalid system is a synonym for the state with low unacceptable quality. The danger of the system is the ability to pass into invalid state with unacceptable quality. The safety means the ability of a system to function without passing into a dangerous unacceptable state.

It is necessary to emphasize the fundamental feature in the construction of a system of concepts in the invalidity theory. Here, fundamental concepts are "invalidity" and "dangerous state", other derived concepts and definitions are formed on basis of these main concepts. The invalidity of the system's state can be measured. The system's validity is a particular single variant of invalidity, which equal to zero.


  1. Соложенцев Е. Д. Топ-экономика. Управление экономической безопасностью. 2-е изд. СПб. Троицкий мост. 2016. 272 с.
  2. Solozhentsev E. D. The Management of Socioeconomic Safety. - Cambridge Scholars Publishing, 2017, 255 p.
  3. URL:

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