Влияние малых отклонений в начальных условиях на мнение коллектива при голосовании

Рассмотрены некоторые аспекты проблемы формирования мнения коллектива как множество интеллектуальных агентов, каждый из элементов которого обладает целенаправленным действием и находится во взаимодействии с другими элементами. Получено приближенное уравнение, которое может быть использовано для прогнозирования результатов голосования. Показано существенное влияние изменения начальных условий на показатель процесса голосования и дана их оценка.

Influence of Small Deviations in Initial Conditions on Voting Result in Opinion of Collective

In this article, we would discuss about process of public opinion and its transformations, where the community is considered a group of intelligent agents, that each of which has a certain point of view on a certain subject studied, where there is interaction between these agents, by entering into a collective (vote) debate, where each agent shows his opinion about a subject and as a result of this discussion, some agents change their opinions. Each element is influenced by other surrounding elements based on the majority and as a final result of this vote; we acquire a society in which most of intelligent agents have same opinion, by reaching close to a certain stable point. The process of forming collective opinion has been studied, as a result of this study we can obtain an approximate equation describing the process how public opinion changes during a vote; this equation helps us conduct three different points of stability. And the result of this voting would lead to one of these stable points, which mean the collective opinion, would relatively follow the same opinion that would be expressed by the point of stability. Through study and experiments, we found that the resulting equation is very sensitive to the initial conditions in some cases, as they show variation in results when a small change is made in the initial conditions and therefore very large change maybe happen in the collective opinion, this effect appears clearly when there is number of elements with opposite opinions that are numerically close. Thus, the result of the vote would be unclear, in such case the initial conditions play a major role in guiding collective opinion showing changes in the final results of the vote, whose grades vary according to the variable initial condition, as they change the accuracy of the vote and the degree to reach the result to point of stability. This small change in initial conditions would later lead to a chaotic change in the final result of the voting, this chaotic change is called the “Butterfly Effect”, this effect can be used in many mathematical, phylogenetic, technical and possibly medical subjects to control some equations and machines, and perhaps the movement of a driverless or unmanned vehicle by influencing initial conditions in a certain way or developing contingency plans to a sudden change in the conditions surrounding it. The results of the study were simulated by the computer to ascertain the voting process and how the initial conditions affect the steering of collective opinion.