| Title:
|
Limit state analysis on the un-repeated multiple selection bounded confidence model (English) |
| Author:
|
Zhang, Jiangbo |
| Author:
|
Zhao, Yiyi |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
59 |
| Issue:
|
2 |
| Year:
|
2023 |
| Pages:
|
254-272 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we study the opinion evolution over social networks with a bounded confidence rule. Node initial opinions are independently and identically distributed. At each time step, each node reviews the average opinions of several different randomly selected agents and updates its opinion only when the difference between its opinion and the average is below a threshold. First of all, we provide probability bounds of the opinion convergence and the opinion consensus, are both nontrivial events by analyzing the probability distribution of order statistics. Next, similar analyzing methods are used to provide probability bounds when the selection cover all agents. Finally, we simulate all these bounds and find that opinion fluctuations may take place. These results increase to the understanding of the role of bounded confidence in social opinion dynamics, and the possibility of fluctuation reveals that our model has fundamentally changed the behavior of general DeGroot opinion dynamical processes. (English) |
| Keyword:
|
bounded confidence |
| Keyword:
|
probability bounds |
| Keyword:
|
order statistics |
| MSC:
|
62G30 |
| MSC:
|
91D30 |
| idMR:
|
MR4600377 |
| DOI:
|
10.14736/kyb-2023-2-0254 |
| . |
| Date available:
|
2023-06-19T09:07:05Z |
| Last updated:
|
2023-08-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151695 |
| . |
| Reference:
|
[1] Altafini, C.: Dynamics of opinion forming in structurally balanced social networks..Plos One 7 (2012), 6, e38135. |
| Reference:
|
[2] Blondel, V. D., Hendrickx, J. M., Tsitsiklis, J. N.: On Krause's multi-agent consensus model with state-dependent connectivity..In: IEEE Conference on Decision and Control 2009. MR 2571922 |
| Reference:
|
[3] Boyd, S., Ghosh, A., Prabhakar, B., Shah, D.: Randomized gossip algorithms..IEEE Trans. Inform. Theory 52 (2006), 6, 2508-2530. Zbl 1283.94005, MR 2238556, |
| Reference:
|
[4] David, E., Kleinberg, J.: Networks, Crowds, and Markets: Reasoning About a Highly Connected World..Cambridge University Press, New York 2010. |
| Reference:
|
[5] Deffuant, G., Neau, D., Amblard, F., Weisbuch, G.: Mixing beliefs among interacting agents..Adv. Compl. Syst. 3 (2000), 87-98. |
| Reference:
|
[6] Degroot, M. H.: Reaching a consensus..J. Amer. Statist. Assoc. 69 (1974), 345, 118-121. |
| Reference:
|
[7] Durrett, R.: Probability Theory: Theory and Examples (Fourth edition)..Cambridge University Press, New York 2010. MR 2722836 |
| Reference:
|
[8] Hatano, Y., Mesbahi, M.: Agreement over random networks..IEEE Trans. Automat. Control 50 (2005), 11, 1867-1872. MR 2182742, |
| Reference:
|
[9] Hegselmann, R., Krause, U.: Opinion dynamics and bounded confidence models, analysis and simulation..J. Artific. Soc. Social Simul. (JASSS) 5 (2002), 3. |
| Reference:
|
[10] Liu, J., Chen, X., Basar, T., Belabbas, M. A.: Exponential convergence of the discrete-time altafini model..Preprint, arXiv [math.OC]:1512.0715, 2015. |
| Reference:
|
[11] Marvel, S. A., Kleinberg, J., Kleinberg, R. D., Strogatz, S. H.: Continuous-time model of structural balance..Proc. National Academy of Sciences 108 (2011), 5, 1751-1752. |
| Reference:
|
[12] Peng, Y., Zhao, Y., Hu, J.: On the role of community structure in evolution of opinion formation: A new bounded confidence opinion dynamics..Inform. Sci. 621 (2023), 672-690. |
| Reference:
|
[13] Qualman, E.: Socialnomics: How Social Media Transforms the Way We Live and Do Business. |
| Reference:
|
[14] Zhang, J., Hong, Y., Hu, X.: Multi-agent opinion dynamics of bounded confidence with non-local aggregative interaction..SIAM J. Control Optim. 55 (2017), 4, 2543-2573. MR 3686786, |
| Reference:
|
[15] Zhao, Y., Xu, M., Dong, Y., Peng, Y.: Fuzzy inference based Hegselmann-Krause opinion dynamics for group decision-making under ambiguity..Inform. Process. Management 58 (2021), 5, 102671. |
| . |
