An optimization model of the acceptable consensus and its economic significance
Abstract
Purpose
The purpose of this paper is to construct an optimal resource reallocation model of the limited resource by a moderator for reaching the greatest consensus, and show how to reallocate the limited resources by using optimization methodology once the consensus opinion is reached. Moreover, this paper also devotes to theoretically exploring when or what is the condition that the group decision-making (GDM) system is stable; and when new opinions enter into the GDM, how the level of consensus changes.
Design/methodology/approach
By minimizing the differences between the individuals’ opinions and the collective consensus opinion, this paper constructs a consensus optimization model and shows that the objective weights of the individuals are actually the optimal solution to this model.
Findings
If all individual deviations of the decision makers (DMs) from the consensus balance each other out, the information entropy theorem shows this GDM is most stable, and economically each individual DM gets the same optimal unit of compensation. Once the consensus opinion is determined and each individual opinion of the DMs is under an acceptable consensus level, the consensus is still acceptable even if additional DMs are added, and the moderator’s cost is still no more than a fixed upper limitation.
Originality/value
The optimization model based on acceptable consensus is constructed in this paper, and its economic significance, including the theoretical and practical significance, is emphatically analyzed: it is shown that the weight information of the optimization model carries important economic significance. Besides, some properties of the proposed model are discussed by analyzing its particular solutions: the stability of the consensus system is explored by introducing information entropy theory and variance distribution; in addition, the effect of adding new DMs on the stability of the acceptable consensus system is discussed by analyzing the convergence of consensus level: it is also built up the condition that once the consensus opinion is determined, the consensus degree will not decrease even when additional DMs are added to the GDM.
Keywords
Acknowledgements
The authors would like to thank the anonymous referees for their valuable comments and suggestions. This research was supported by the National Natural Science Foundation of China (71171115, 71173116, 71571104), the reform Foundation of Postgraduate Education and Teaching in Jiangsu Province (JGKT10034), Qing Lan Project, the Project of Philosophy and Social Science Research in Colleges and Universities in Jiangsu (2012SJD630037), the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions, the Natural Science Foundation of Jiangsu, China (BK20141481), and the Six Talent Peaks Project in Jiangsu Province (2014-JY-014).
Citation
Gong, Z., Xu, X., Forrest, J. and Yang, Y. (2016), "An optimization model of the acceptable consensus and its economic significance", Kybernetes, Vol. 45 No. 1, pp. 181-206. https://doi.org/10.1108/K-04-2014-0070
Publisher
:Emerald Group Publishing Limited
Copyright © 2016, Emerald Group Publishing Limited