Analytical approach to the Axelrod model based on similarity vectors

Complex problems of social interaction are usually studied within the framework of agent-based models. Some of these problems, such as issue alignment and opinion polarization, are better suited in the framework of n-dimensional opinion space. Although this kind of complex problem may be explored by numerical simulations, these simulations can hinder our ability to obtain general results. In this work, we show how, under certain conditions, a classical multidimensional opinion model such as the Axelrod model can give rise to a closed set of master equations in terms of vector similarities between agents. The analytical results fully agree with the simulations on complete networks, accurately predict the similarity distribution of the whole system in sparse topologies, and provide a good approximation of the similarity of physical links that improves when the mean degree of the system increases.

Automated summary

This study explores complex problems of social interaction within the framework of agent-based models, specifically focusing on n-dimensional opinion space. The findings reveal how a classical multidimensional opinion model can lead to a set of master equations based on vector similarities between agents, providing accurate predictions for similarity distributions in sparse topologies and physical links. The analytical results align well with simulations and offer improved approximations with higher mean degrees in the system.