The paper aims to propose an analytical framework for social influence and mathematical formulation for its main components: conformity and peer-pressure. The framework is conceived to explain why certain behaviours and beliefs propagate in a society and some others disappear. It can also be used to study the emergence and the evolution of the status of the norms in terms of their adoption by the population.
The paper is theoretical, making use of economic quantitative methods. The author proposes a new formulation for the evolutionary dynamics, increasingly borrowed by social scientists. Then, mathematically treating the equation, the author draws general conclusions in form of lemmas, which are proved.
The author's main contribution is to show that even behavioural rules and beliefs that emerge in a minority subset of the population, do not procure any benefit for the agents adopting them can under certain conditions, evolve into the consensus of a society, become a norm.
More general conclusion (theorems and lemmas) could be stated and proved. But given that the main contribution of the paper is to the fields of social and behavioural economics, along a number of disciplines less mathematical than economics, the author kept the analysis that required fairy advance mathematics for later.
The paper contributes to the evolutionary game theory, evolution of preferences, and evolution of beliefs and social norms. More precisely, the equation proposed in the paper can be used in the contexts the patterns of heterogeneity in a population are affected or caused by social influence. Or in the contexts, the social institutions are susceptible to affect an agent's sense of identity (e.g. voting, fashion industry, marketing).
In this paper, for the first time, a mathematical formulation is proposed for the social influence and its main psychological components (conformity and status seeking). Using the above, the author proposed a new parametric fitness function for the evolutionary dynamics. The author believes the paper matters to a multidisciplinary public. It answers a question that challenged and puzzled the economists (as well other social scientists): the reasons behind the emergence and the prevalence of social norms do not positively contribute to the utility or payoff of the agents adopting them (and at times they are costly).
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