APPROACH TO MATHEMATICAL AND COMPUTER MODELLING OF LAW SUBJECT'S PERSONAL AUTONOMY - Наукові конференції
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APPROACH TO MATHEMATICAL AND COMPUTER MODELLING OF LAW SUBJECT'S PERSONAL AUTONOMY

16.03.2017 09:37

[Секція 1. Теорія та історія держави і права. Філософія права. Історія політичних і правових вчень]

Автор: Sheliazhenko Yurii Vadymovych, Post-graduate student, KROK University


Personal autonomy is the scope of rights of law subject, in particular human rights, and freedom to choose legal ways of realizing personal interests. The legal category of personal autonomy is linked to the rational choice theory in the economics, assuming that people make smart individual decisions for maximal realization of own interests.

In the book "Economic Analysis of Law" Richard Posner show that human desires to achieve the greatest possible success in life and satisfy all individual desires are equally evident in the fields of law and economics. That's why for the analysis of law can be used economics as the science of rational choice in a world where resources are limited, unlike human wants [1]. Illustrating that idea, Posner notes that from the offender's point of view punishment, for example, fine, is the price of unlawful actions needed to pay under the pressure of society. Thus, the economy of free choice between different (usually legal) behaviors includes interest, determined on the basis of personal autonomy, and efforts necessary for the implementation of this interest. Such interest and efforts can be valued in quantitative form, say, price and revenue of interest implementation.

The word "autonomy" in Greek (αυτος νομος) means "own law", for example, private legal doctrine that consists of personal beliefs and legal conscience, self-chosen strategy and tactics of lawful behavior. It should be noted that the establishment of an "own law" does not diminish the authority of mandatory public regulations. Establishing and keeping individual laws develops skills of self-discipline required for effective fulfillment of national legislation, that can't be violated by most of people due to high risks and costs of violation.

Author's study of personal autonomy in legal relations leaded to conclusion that artificial persons, abstract subjects of law can be constructed for scientific and educational purpose, like the business games and computer modeling in the studies of economics [2].

In this study author tried to construct mathematical and computer models of artificial personal autonomy, based on economical characteristics of interests of artificial persons like human interests in real life. Individual interests and resources for its implementation both are expressed in financial value. Artificial persons in this model are: the seller, interested to sell goods at maximum price on a competitive basis; and buyers who wish to participate in the competition and offer their prices for proposed goods. Interest of buyer X in merchandise is manifested by offering price F(X), and interest of seller is calculated as maximal price F(Y)=MAX(F(Z)), proposed by buyer Y from the set of all buyers Z, according to the formula of maximum:

MAX(F(Z)) = F(Y) : ∃Y∈Z ∀X∈Z F(Y)≥F(X)

For example, if there are three buyers, Z = {1, 2, 3}, offering prices 1720, 2450 and 936 dollars, i.e. F (1) = 1720, F (2) = 2450, F (3) = 936, in this case MAX (F(Z)) = F (2) = 2450 and the goods will be sold to the second buyer (Y=2), which offered the highest price of 2450 dollars. If the maximum price is offered by several buyers, the goods would be sold to first buyer who offered the highest price. That mathematical model can be represented as a graph, where the transaction (sale) occurs at the point of convergence of interests.

 

Figure 1. Mathematical model of the artificial personal autonomy of seller and buyers in the competition for the purchase of goods.

Computer simulation of the same legal relations of artificial persons author realized in Java programming language.




Figure 2. Computer model of the artificial personal autonomy of seller and buyers in the competition for the purchase of goods.

Like in the above models of artificial personal autonomy in private law relations without government interference, realizing of autonomous public interests and personal autonomy of public law subjects can be simulated using mathematics and programming. For example, digitization of legal values by using mathematical apparatus of classical mechanics was demonstrated by Italian scientists Massimiliano Ferrara and Roberto Gaglioti [3]. In Ukraine Iryna Onopchuk proposed mathematical model of legislative process by transforming legislation to the matrix and simulating its application to social relations as multiplication of matrix by a vector, also she determined objective of modeling as reaching the optimal social effect with minimal legislative regulation [4]. These considerations, in the author's view, can be amplified with concept of basic principle of saving the force and efforts, especially resources of law enforcement and legal coercion, during the implementation of the legal ideal. Economy of force principle explains why doctrine of natural law considers as the base of any legislation empirically found laws of nature, which remain in force always and everywhere because of causation and therefore does not require any law enforcement to implement them, despite laws of nature can't be taken as legal ideal without supplemental vision of better reality in the interests of human (liberty, security, prosperity etc.) and objective empirical knowledge of the practical effects of different methods of implementing chosen legal ideal. Mathematical and computer modeling of personal autonomy of private persons and organizations, as well as modeling of public legislation and law enforcement, allows soberly assess the cost and helping to choose lean approach to legal implementation of private and public interests.




References:

1. Richard A. Posner. Economic Analysis of Law. – Alphen aan den Rijn: Aspen Publishers, 2007. – 816 p.

2. Теоретико-правове значення особистої автономії суб'єкта права / Т.А. Француз-Яковець, Ю.В. Шеляженко // Прикарпатський юридичний вісник. – 2016. – № 3 (12). – С. 31-35.

3. A Mathematical Model for the Quantitative Analysis of Law. Putting Legal Values into Numbers / M. Ferrara, R. Gagliotti // Applied Mathematics in Electrical and Computer Engineering. – Cambridge, 2012. – P. 201-206.

4. Онопчук І. Ю. Математична модель управління законодавчим процесом // Конституція України – основа подальшого розвитку законодавства. Збірник наукових праць. – Вип. 2. – Київ, 1997. – С. 234-240.



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