Proof of the inevitability of mistakes in legislation

The theory of mistakes is the branch of mathematic statistics upon the basis of which the methodology of the exposure and evaluation of errors (mistakes) developed. As a completely developed, strong mathematic apparatus, it has inter-disciplinary significance and may be applied to any conceptual apparatus and in any field: in physics, chemistry, biology, sociology, history and also in law.

In the theory of complex systems it is proved that any complex system (a system consisting of a large number of complex, interlinking elements with complex and diverse links) will definitely contain one or more mistakes. In addition, knowing the approximate complexity of the system and probability of mistakes, it is possible to calculate their number with sufficient precision.

This rule is used particularly often in information technology and its branch, i.e. programming, where it is well-known that any complex program will necessarily contain a mistake(s). An example of this could be the Windows 95 program, which, despite being issued by the huge corporation Microsoft, still contains a large number of errors, which can be discovered by almost any competent user. The presence of mistakes in this program is normal, as the capacity of the hard disk is 80 MB, which is equal to 640,000,000,000 elementary bytes.

Some of the indicators of a complex system are the complexity of the conceptual apparatus and the complexity of relationships between concepts.

For example, in the binary code there are two concepts in total: zero and one. There are also two relationships: addition and negation.

At the same time, in mathematical analysis, the concept of the variable is even harder to define, and so is the complex relations of the integral and factorial.

In legislation the notions themselves are rather complex (for example, gangsterism or contraband), and the same can be said of the logical relations of inclusion, exclusion, complex equality etc. It is therefore necessary to note the immensely large number of concepts, used in law and the very large number of different types of interlinks between the most varied norms, both within laws as well as between them. Consequently it is possible to state with confidence that from the point of view of mathematical statistics law is a complex system.

Thus, knowing that:
legislation is a complex system,
a complex system necessarily contains mistakes,

we can conclude that legislation necessarily contains mistakes and the more complex and ramified the law, the more mistakes will be contained within it.

It thus follows that in many laws high in content and complexity, the presence of mistakes is highly probable.

Following on from the theory of complex systems, it is possible to reveal the following norm:
N ~ C,
Where N is the number of mistakes;
C is the cybernetic (information)complexity of the norm.

Accordingly, complexity is directly proportional to:
1) the volume of the norm (V);
2) the number of legal links between concepts (LC):
C ~ V × LC.

It is also well-known that the more «worn in» the law, the more thought through, the more times it has been examined and debated, then the less mistakes it will contain, i.e.
N ~ 1/NE,
where NE is the number of examinations.

Equally the application of the law affects its «worn-in-ness». It is obvious that the law on theft, applied by courts quite often, is better thought through than, for example, the law on changes of citizenship, which is applied extremely rarely.
N ~ 1/NA,
Where NA is the number of applications.
Then we get the formula:N ~ V × LC/NA × NE.

From this formula it is possible to conclude that there are more mistakes in laws which:
1) are complex in their wording;
2) are strongly interlinked;
3) are passed in haste;
4) are formulated without considering the positive experience of foreign legislators;
5) are borrowed from legislation of another country, but with an inaccurate translation;
6) have not been applied before i.e. are being applied for the first time.

The chapters of the Civil Code of the Russian Federation which deal with money, securities, banking operations and entrusted administration can be described using all of the above-listed properties.

And although we are obliged to observe laws (even if they contain mistakes), it should not follow that they are regarded as a dogma. It is necessary to facilitate the removal of contradictions in the legislation when they are revealed.