Stochastic evolution of competing social groups

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Abstract
A model is considered for a situation in which two social groups compete with each other, ultimately resulting in the possible suppression of one of the groups. Using the method of system‐size expansion, an asymptotic analysis of the model, including the time evolution of both deterministic and stochastic aspects of the process, is carried out. The probability distribution of the maximum size attained by the weaker group, just before the commencement of its decline, is examined and the results are compared with the previous work of Osei and Thompson on the “supersession of one rumour by another.” The present model, which generalizes the Osei‐Thompson model in a number of ways, is also relevant to the problems of opinion formation and attempted conversion of people from one viewpoint to another.

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