www.seipub.org/ijc International Journal on Communications (IJC) Volume 3, 2014 16 Voting Procedure and Neural Networks Ibragim Suleimenov *1 , Oleg Gabrielyan 2 , Grigoriy Mun 3 , Sergey Panchenko 1,3 , Tungysh Amirzhan 1 , Kamilya Suleimenov 4 1 Almaty University of Power Engineering and Telecommunications, Almaty, Kazakhstan 2 Crimean University of Culture, Arts and Tourism, Simferopol, Ukraine 3 Al-Faraby Kazakh National University, Almaty, Kazakhstan 4 Birmingham University, Birmingham, United Kingdom * esenych@yandex.ru; gabroleg@mail.ru; mungrig@yandex.ru; sergey@panchen.co; greentuns@gmail.com; mlldefer@yandex.ru Received Jan 21, 2014; Accepted Mar 17, 2014; Published Jun 18, 2014 © 2014 Science and Engineering Publishing Company Abstract It is shown that even elementary systems, in which behaviour determined by the voting procedures often cannot come to the stabilized conditions. The fact is determined by different oscillations that can occur in such systems compliant with polar change of opinions with the certain frequency. This conclusion has the fundamental importance; in particular, for theoretic sociology because it shows that there are no functional, which may be used for mathematical description of the systems of the considered type by their maximization of minimization. Keywords Voting Procedure; Neural Network; Theoretic Sociology Introduction As mentioned in (McKenzie, 1986), nowadays a number of economical models are created on the basis of the analogy with classic mechanics. A number of functional are proposed (for example, a utility function), whose extremum is compliant with an equilibrium condition of the system where it spontaneously comes after some time. Nowadays, a wide range of such functions is in use (Arrow, 1954 and Balasko, 1989). As highlighted in (Polterovich, 1997), all the efforts to create the similar description (i.e. to determine an evident kind of the functional whose extremum could be compliant with the system equilibrium condition) have not been successful yet within sociologic sciences. Besides, it is supposed in (Polterovich, 1997) that such functional cannot exist at all. Reasons for such point of view are based on the Arrow’s impossibility theorem (Arrow, 1951) and similar results obtained for the last decades. Based on the analogy with neuronal networks, it is proved in this paper that there are sets of examples of systems of social nature where any stabilized condition is impossible at all. We consider a certain example – a Council where voting takes place;obtains conclusions can be generalized for any voting procedures. It is shown in (Suleimenov, 2010) that a feedback diagram in the voting Council topologically is completely equivalent to the feedback diagram in the Hopfield neural processor. However, as determined in this work, matrix of weight coefficients describing a feedback system in the voting Council, as usual, is not symmetrical against a classic diagram of the Hopfield neuroprocessor. This factor causes instabilities (oscillation). It is also shown in this work that the principal impossibility of the stabile state results in hypersensitivity of the social system of the considered type to the external impacts. In particular, there is a mode of oscillation synchronization when an external impact with insignificant amplitude can cause inconvertible changes of the system in whole. This result provides an opportunity of quantitative description of such phenomena as influence of telecommunications on initiation of the revolutionary situations (such as ‘Arabic Spring’) and the certain recommendations to manage the processes occurring in the society. Basic Model Background Fig. 1 provides an example of the classic Hopfield neuroprocessor diagram. This diagram contains three formal neurons whose outputs are mutually connected