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    Mathematical Models of Self-Appraisal in Social Networks

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    Authors
    Anderson, B.D.O.
    Ye, Mengbin
    Date
    2021
    Type
    Journal Article
    
    Metadata
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    Citation
    Anderson, B.D.O. and Ye, M. 2021. Mathematical Models of Self-Appraisal in Social Networks. Journal of Systems Science and Complexity. 34 (5): pp. 1604-1633.
    Source Title
    Journal of Systems Science and Complexity
    DOI
    10.1007/s11424-021-1193-y
    ISSN
    1009-6124
    Faculty
    Faculty of Science and Engineering
    School
    School of Elec Eng, Comp and Math Sci (EECMS)
    URI
    http://hdl.handle.net/20.500.11937/89030
    Collection
    • Curtin Research Publications
    Abstract

    In social networks where individuals discuss opinions on a sequence of topics, the self-confidence an individual exercises in relation to one topic, as measured by the weighting given to their own opinion as against the opinion of all others, can vary in the light of the self-appraisal by the individual of their contribution to the previous topic. This observation gives rise to a type of model termed a DeGroot-Friedkin model. This paper reviews a number of results concerning this model. These include the asymptotic behavior of the self-confidence (as the number of topics goes to infinity), the possible emergence of an autocrat or small cohort of leaders, the effect of changes in the weighting given to opinions of others (in the light for example of their perceived expertise in relation to a particular topic under discussion), and the inclusion in the model of individual behavioral characteristics such as humility, arrogance, etc. Such behavioral characteristics create new opportunities for autocrats to emerge.

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