10.14489/vkit.2019.08.pp.032-037

DOI: 10.14489/vkit.2019.08.pp.032-037

Пупков К. А., Ибрагим Ф.
ВЛИЯНИЕ МАЛЫХ ОТКЛОНЕНИЙ В НАЧАЛЬНЫХ УСЛОВИЯХ НА МНЕНИЕ КОЛЛЕКТИВА ПРИ ГОЛОСОВАНИИ
(с. 32-37)

Аннотация. 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.

Ключевые слова: голосование; мнение коллектива; множество агентов; биномиальное распределение; хаос; эффект бабочки.

Pupkov K. A., Ibrahim F.
INFLUENCE OF SMALL DEVIATIONS IN INITIAL CONDITIONS ON VOTING RESULT IN OPINION OF COLLECTIVE
(pp. 32-37)

Abstract. 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.

Keywords: Vote; Team opinion; Set of machines; Binomial distribution; Chaos; Butterfly effect.

+ - Информация об авторах (About the Authors) Click to collapse

Рус

К. А. Пупков (Московский государственный технический университет им. Н. Э. Баумана (национальный исследовательский университет), Москва, Россия) E-mail: Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript
Ф. Ибрагим (Российский университет дружбы народов, Москва, Россия)

Eng

K. A. Pupkov (Bauman Moscow State Technical University, Moscow, Russia) E-mail: Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript
F. Ibrahim (Peoples’ Friendship University of Russia, Moscow, Russia)

+ - Библиографический список (References) Click to collapse

Рус

1. Ott E. Chaos in Dynamical Systems. University of Maryland, College Park, Maryland, USA, 1993. 22 р. URL: http://catdir.loc.gov/catdir/samples/cam033/ 2001052863.pdf (дата обращения: 02.07.2019).
2. Девятков В. В. Системы искусственного интеллекта. М.: Изд-во МГТУ им. Н. Э. Баумана, 2001. 352 с. (Сер. Информатика в техническом университете).
3. Kelman H. C. Process of Opinion Change // Public Opinion Quarterly. 1961. V. 25. P. 57 – 78. URL: https://scholar.harvard.edu/files/hckelman/files/ProcessesofOpinion.pdf (дата обращения: 02.07.2019).
4. Стефанюк В. Л. Локальная организация интеллектуальных систем. М.: ФИЗМАТЛИТ, 2004. 328 с.
5. Боровков А. А. Теория вероятностей. М.: Наука, 1986. 432 с.
6. Pupkov К. А., Ibrahim F. Collective Opinion Formation as a Set of Intelligent Agents to Achieve the Goal // XIIIth Inter. Symposium “Intelligent Systems” (INTELS’18). 22 – 24 October 2018, St. Petersburg, Russia. St. Petersburg, 2018. P. 25.
7. Садовничая И. В., Фоменко Т. Н., Хорошилова Е. В. Математический анализ. Дифференцирование функций одной переменной [Электронный ресурс]. 2-е изд., перераб. и доп. М.: Юрайт, 2019. 156 с. URL: https://urait.ru/uploads/pdf_review/A0E0F4AE-66A0-4383-908A-231BE7A79832.pdf (дата обращения: 02.07.2019).

Eng

1. Ott E. (1993). Chaos in Dynamical Systems. University of Maryland, College Park, Maryland, USA,. Available at: http://catdir.loc.gov/catdir/samples/cam033/2001052863.pdf (Accessed: 02.07.2019).
2. Devyatkov V. V. (2001). Artificial intelligence systems. Moscow: Izdatel'stvo MGTU im. N. E. Baumana. (Seriya Informatika v tekhnicheskom universitete). [in Russian language]
3. Kelman H. C. (1961). Process of Opinion Change. Public Opinion Quarterly, Vol. 25, pp. 57 – 78. Available at: https://scholar.harvard.edu/files/hckelman/ files/ProcessesofOpinion.pdf (Accessed: 02.07.2019).
4. Stefanyuk V. L. (2004). Local organization of intellectual systems. Moscow: FIZMATLIT. [in Russian language]
5. Borovkov A. A. (1986). Probability theory. Moscow: Nauka. [in Russian language]
6. Pupkov К. А., Ibrahim F. (2018). Collective Opinion Formation as a Set of Intelligent Agents to Achieve the Goal. XIIIth International Symposium “Intelligent Systems” (INTELS’18). Saint Petersburg.
7. Sadovnichaya I. V., Fomenko T. N., Horoshilova E. V. (2019). Mathematical analysis. Differentiation of functions of one variable. 2nd ed. Moscow: Yurayt. Available at: https://urait.ru/uploads/pdf_review/ A0E0F4AE-66A0-4383-908A-231BE7A79832.pdf (Accessed: 02.07.2019). [in Russian language]

+ - Заказать электронную версию статьи (Purchase digital version of a single article) Click to collapse

Рус

Статью можно приобрести в электронном виде (PDF формат).

Стоимость статьи 350 руб. (в том числе НДС 18%). После оформления заказа, в течение нескольких дней, на указанный вами e-mail придут счет и квитанция для оплаты в банке.

После поступления денег на счет издательства, вам будет выслан электронный вариант статьи.

Для заказа скопируйте doi статьи:

10.14489/vkit.2019.08.pp.032-037

и заполните форму

Отправляя форму вы даете согласие на обработку персональных данных.

Eng

This article is available in electronic format (PDF).

The cost of a single article is 350 rubles. (including VAT 18%). After you place an order within a few days, you will receive following documents to your specified e-mail: account on payment and receipt to pay in the bank.

After depositing your payment on our bank account we send you file of the article by e-mail.

To order articles please copy the article doi:

10.14489/vkit.2019.08.pp.032-037

and fill out the form