Models based on "estimation bias" as a tool for predicting potential threats

Tikhanychev Oleg Vasilyevich ORCID: 0000-0003-4759-2931 PhD in Technical Science Deputy Head of Department in the Office of Advanced Development, Technoserv Group  111395, Russia, Moscow, Yunosti str., 13 tow65@yandex.ru Other publications by this author

Introduction

In practice, when processing statistical results, the concept of "estimation bias" is sometimes used. Most often, the need for this arises when processing data from sociological surveys or other events conducted with the participation of a person. The "bias" factor is determined by the subjectivity of an individual's assessments of any event, especially it is enhanced by the self-formation of the sample under study, when involvement in the survey occurs on a voluntary basis. In statistics, the "bias" factor is quite simply taken into account, its influence is either compensated by correction coefficients, or it is simply neglected as insignificant, especially when forming estimates for the same type of events for which the "bias" is approximately the same and does not affect the final comparative estimates. The phenomenon of "displacement" is much more complicated and problematic, as the world practice of using destructive social technologies in the last few decades has shown, in the field of social engineering. This danger is especially evident for States and societies based on democratic principles of governance ^{[1, 2]}.

Historically, the basis of any democracy is the free expression of the will of every capable member of society, based on voting in the process of choosing power and making the most significant decisions. For many centuries, this approach ensured the electability of power through the reflection of the will of the majority, as, in fact, the word "democracy" is translated from Greek. It is the possibility of a public, public statement of the population on the problems of public life and the influence of the expressed position on the development of socio-political relations that reflects the essence of public opinion as a special social institution, which is a combination of many individual opinions on a specific issue affecting a group of people.

Quite simple but reliable methods are used to determine the results of the expression of will. In the Greek polis, the number of people who voted was counted, at the Novgorod veche, the winning opinion was determined by the volume of its expression, and sometimes by the results of a fist fight and the like. With the increase in the scale of States and, accordingly, the coverage of the target audience, statistical methods of processing results based, in general, on the modification of the same approaches began to be used.

For the time being, these methods worked quite successfully and allowed us to obtain adequate results. But, with the growth of the scale of society, these methods, for various reasons, began to fail. There was even a theory about the impossibility of applying democratic principles in a society of more than five thousand people ^[3]. Then came the era of the information revolution, characterized, from the point of view of public relations, by increased communication and activity of the population. Social networks, informal public organizations, do not just influence the government, they begin to compete with it, including by acquiring some signs of the state. An example is multinational information corporations such as Meta (Facebook) or Twitter Inc. And suddenly it turned out that the state, which uses the old methods of taking into account public opinion to interact with its citizens, is not ready for the challenges of the present time. This conclusion is confirmed by the practice of recent decades, numerous "color" revolutions based on the right of squares and Maidans. But why did this happen? The need to answer this question determines the relevance of the topic of the article.

2       Analysis of the problem of "bias" of estimates

To carry out the analysis, it is proposed to analyze the main approaches to determining public opinion and the principles of its consideration in the activities of the state and society. Within the framework of the methods currently used, it is considered that public opinion is a set of individual opinions, attitudes, and, possibly, beliefs of a certain group of people in relation to the population of a certain state or its territorial unit. In modern society, the usual channels (and forms) of expressing public opinion are: elections of authorities, participation of different groups of the population in legislative and executive activities, the activities of the press and other mass media, holding meetings, demonstrations, etc. Along with this, statements caused by political, research interest and taking the form of elections, referendums, mass discussions of any problems, meetings of specialists, sample surveys of the population on the given "focus groups", etc. are also widespread. It has always been believed that a well-chosen and sufficiently presentative sample of respondents, correctly formulated questions and adequate methods of processing them provide accurate estimates of the results of such events. However, the practice of the last few decades has shown that statistical methods are increasingly beginning to fail. Why? The analysis shows that the problems are generated by the peculiarities of communications of modern society existing in the conditions of total informatization.

There are quite a lot of reasons for these problems, both objective and subjective. Most of the reasons are generated not by the mathematical apparatus of statistical calculations used, verified and tested for a long time, but by the methods of its use. One of these reasons, as the analysis of the data processing practice of conducting sociological surveys shows, is complex, lying on the border of sampling and calculating the final score. It is proposed to consider it in more detail.

Differences in the work of existing methods in the conditions of the information society can be explained by the example of evaluating the activities of any arbitrarily selected organization formed on the basis of an analysis of reviews about it on the Internet. Practice has shown that a user who is satisfied with the activities of an organization very rarely spends his time to leave a positive review. According to statistics, the share of such users ranges from one third to half of respondents. At the same time, a user dissatisfied with the service leaves a negative review in 80-90% of cases. The processing of such an estimate by classical statistical methods gives a significant shift in the negative direction. The estimate is "biased" and does not correspond to the real situation (Figure 1). Another possible option is a deliberate "shift" of the mathematical expectation of the E*[X] assessment, as it happens when forming understated or overstated plans (Figure 2). A similar situation is developing in the field of obtaining social assessments using modern communication networks, sociological surveys, etc. ^[4,5,6].

In this regard, we can recall the concept of unbiased evaluation used in mathematics. In mathematical statistics, it is a point estimate, the mathematical expectation of which is equal to the estimated parameter.

For example, let X 1,...Xn,... be a sample from a distribution depending on the parameter ? ? ?. Then the estimate is called unbiased if:

   ?? ? ?,

where E[X] is the mathematical expectation of the value X;

          - quantifier of universality.

Otherwise, the estimate is called biased, and the random variable is called its offset ^[2,4].

Figure 1. Graphical interpretation of the estimation bias in case of incorrect sampling

Figure 2. Graphical interpretation of the estimation bias when setting an incorrect expectation

In mathematical statistics, bias occurs due to gross errors in the formation of a sample or an incorrect choice of the distribution law describing it. In the social sphere, the mechanism is similar, although it is more influenced by subjective factors. Especially considering that in the latter case, the estimated sample, most often, is not selected randomly, but is formed arbitrarily, based on subjective factors. A clear practical example of the implementation of the principle of "shifting" social assessments is modern elections. As in the case of evaluating the activities of organizations, citizens who are satisfied with the authorities are not rushing to the polls, they are already doing well and have no desire to change anything. But the discontented, even if they are a minority, go to vote. Another influencing factor is the presence of the turnout threshold, which additionally helps to ensure the bias of the resulting estimates. And the mechanism usually used to distribute unrealized votes in proportion to the share result given for certain candidates further aggravates the situation, increasing the "bias". And the lower the turnout threshold, the easier it is for the active part of the population to make a decision that does not take into account common interests. Or to implement the "bias" of the assessment through the implementation of PR technologies. At the same time, the "step–by-step" system of elections adopted in some countries does not correct the situation - it only changes the nature of the shift from the general assessment to the private, for individual groups and territories.

In terms of the influence of "bias" on the electoral process, the so-called "smart voting" methodology is of research interest. When it is implemented, the possibilities of achieving success at each site (district) are calculated, unpromising areas are cut off, and efforts are redistributed to potentially ensuring the achievement of local success at specific points.  From the point of view of mathematics, this is not exactly a "shift" of the estimate, but a decrease in variance, increasing the probability of obtaining the required value at a given point (Figure 3). Although the principle here is the same as with the "displacement" of the estimate – an artificial modification of the random distribution law to obtain the desired result, just the "displacement" does not occur on a horizontal scale, but vertically.

Figure 3. Graphical interpretation of the principle of "smart voting" from the point of view of artificial "bias" of estimates

And the problem is not only and not so much in the mathematical methods used, as in the principles of forming the processed statistical sample. If a sample is formed randomly during sociological research, then, for example, in elections, the aggregate of voters is formed under the influence of certain factors, sometimes even determined by external influence. Accordingly, the result of processing this sample is biased relative to the real state of affairs. The result is that the election results do not quite meet the expectations of society. Subsequently, this results in protests, distrust of the authorities and discrediting of the basic principles of democracy.

The analysis of the essence of the problem of forming an estimated sample makes it possible to understand the content of the selection process itself, during which each participant balances between the expected usefulness of the result and the costs of achieving it ^[7,8]. The cost of achieving the goal in the framework of the example under consideration is the need to spend time visiting a polling station. Utility – the expected results of the implementation of the will. Each individual can be forced to go to the polls either by a strong desire to change something, or by an equally strong fear of change. But people with conscious assessments in any society, as a rule, are a minority, and they are unevenly distributed among social groups and regions. In most cases, it is the imbalance of this mechanism that generates a "shift" of the results of the expression of will.

One of the recent examples of shifting estimates may be the holding of the BREXIT vote on the UK's exit from the European Union. With an approximate equality of supporters and opponents, mostly elderly people spoke out for the exit. Since their electoral activity is usually higher, the result turned out to be noticeably "shifted" ^[9]. The young part of the population began to be active only after receiving the election results, certain actions were taken, but this did not solve the problem.

The given example is a variant of a random, unintentional "bias" of the estimate. Much more interesting are the cases of intentional "bias" of estimates aimed at achieving a particular goal.

A typical example of intentional "bias" is the assessment of the correctness of the organization of planning in any areas of production. In any economic system, certain elements of activity planning are used, the difference, as a rule, is only in the proportion of planned processes from their total number. And when planning, the question arises: how well the plans are drawn up, are they overstated or understated. To answer this question, a mechanism similar to the mechanism of searching for "bias" estimates can be used. It is simple: assuming that, as it happens most often, the probability of plans being fulfilled, as it most often happens, is distributed according to a normal law, it is possible to assess how correctly planning is evaluated. Namely: if the share of those who exceeded and did not fulfill the plan is distributed approximately equally, the plan is drawn up correctly. But, in practice, it happens that the implementation is declared as 100 percent. This is a typical forced "shift", when the plan is deliberately underestimated to ensure that it can be fulfilled by almost all participants in the process, and the facts of over-fulfillment are hidden for postponement to the next period.

The methodology of the so–called "smart voting" mentioned earlier is no less obvious and, perhaps, more dangerous manifestation of the deliberate "bias" of the assessment in the social sphere. The formation of discrete estimates and the influence on those that can be changed, theoretically, provides a solution to the particular problems of conducting the maximum possible number of candidates for the necessary authorities. From the point of view of mathematics: the problem is solvable and quite trivial, from the point of view of social engineering – effective and dangerous. And, accordingly, it requires the development of methods for detecting and countering such "displacements". Moreover, the facts of the use of such methods in the framework of destructive social technologies are already being recorded ^[10].

3       Suggestions for finding and parrying the "bias" of estimates

As for most similar problems, methods of countering the "bias" of assessments can be divided into organizational and technical.

Organizational measures of counteraction, as shown by the recent elections to the State Duma of the Russian Federation, show sufficient effectiveness. At the same time, they are inherently characterized by insufficient flexibility and a certain inertia. In today's dynamic world, such shortcomings can be critical. In addition, they do not prevent outside interference, and, as experience shows, this has recently become a frequent practice in geopolitics.

Therefore, organizational methods must necessarily be supplemented with a set of technical measures. Which are more difficult to implement, but seem quite promising.

In our case, we are talking about methods to counteract the bias of the assessment, and not about any other technologies that ensure the reliability of the results, such as, for example, the use of blockchain technology. Returning to the last elections to the State Duma, at which blockchain technologies were announced, which, however, were not used in full, with restrictions:

· only one server was used to host the data;

· hash-sum control (hash) was performed not arbitrarily at the request of users, but according to the regulations.

But, anyway, the experience of using this technology to ensure the reliability of the results can be considered successful, but only in terms of processing the results. Because, as the analysis of the blockchain matapparat shows, it provides control over the collection and processing of data, but not the conditions of their formation that affect the "bias". And to control the "bias", we need methods that provide an analysis of the process of forming the sample being surveyed.

To implement the latter, a mathematical apparatus is needed to determine the magnitude and direction of the "bias" of the assessment and to develop recommendations for parrying the results of this phenomenon.

The search and compensation of "displacement" can be carried out using various approaches:

1) heuristic, based on the use of subjective expert data:

• expert assessment of the structure and correctness of the sample under study;

• evaluation of final results based on formal logic;

• formation of comparative estimates using similarity theory.

2) methods of mathematical statistics:

• evaluation of the form and characteristics of the distribution law of statistical processing results, identification of differences between its parameters and normal;

• search for correlations for the parameters of the distribution laws and expectations obtained in different areas (plots, under different conditions), search for their anomalous "bursts".

The expediency of using certain methods is determined by the purpose of the study, the accepted limitations and accuracy requirements, the structure of the source data, and the possibilities for conducting calculations.

The mathematical model of the estimation bias analysis constructed using the proposed mathematical apparatus may have two obvious aspects of application:

1) in the field of economics – assessment of the correctness of the set plans and their subsequent adjustment;

2) in the field of sociological research:

• evaluation of voting results and clarification of estimates taking into account their bias;

• assessing the legitimacy and forecasting the parameters of protest movements.

In terms of the security of society and the state ^[11], the second appendix seems to be the most significant. Within the framework of such use of the proposed mathematical apparatus, for example, it is possible to provide an assessment of the election results. Mathematical methods of assessment include the use of a model of the state of society, which provides the calculation of the "bias" of the assessment and the development of proposals for its parry. In mathematics, such measures are presented quite widely and have been well tested ^{[12, 13]}.

The second aspect of the application of the biased assessment matrix in the field of sociology, namely, the assessment of the state of protest movements, will potentially increase the objectivity of the analysis of their main parameters, primarily representativeness and legitimacy.

Conclusion

It is known that in recent years, as part of the use of technologies of social impact on society, implemented through the so-called "color" revolutions, tens of thousands of people come out to squares and avenues, positioning themselves as carriers of the will of the whole society. To assess whether this is true or not, the apparatus of unbiased estimates can: by calculating the ratio of the number of protesters to the total number of active population (taking into account the spatial localization of the protest), it is possible to estimate what proportion of the population the protesters represent and how much their views are shifted relative to the needs of society as a whole. And then it is time to draw a conclusion about the legitimacy of their demands, to develop measures to implement them or to stop the process.

And in general, the formulation of the problem formulated in the article of the applied use of mechanisms for searching for "bias" of estimates and parrying this phenomenon may be important in different areas of management activity. The solution of this problem will provide a certain optimization of the management cycle by increasing the accuracy of assessing the situation and predicting the consequences of decisions taken.