We introduce and discuss kinetic models describing the influence of the competence in the evolution of decisions in a multi-agent system. The original exchange mechanism, which is based on the human tendency to compromise and change opinion through self-thinking, is here modified to include the role of the agents' competence. In particular, we take into account the agents' tendency to behave in the same way as if they were as good, or as bad, as their partner: the so-called equality bias. This occurred in a situation where a wide gap separated the competence of group members. We discuss the main properties of the kinetic models and numerically investigate some examples of collective decision under the influence of the equality bias. The results confirm that the equality bias leads the group to suboptimal decisions.

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Agent-based models are now largely adopted to describe how opinions emerge in a group of people. This survey provides an analysis of the literature on the subject, highlighting the major characteristics of such models. Over the last decade, the number of papers has grown at an overall annual rate of 16%, though not continually. Two communities contribute to the research effort: physics and control systems. However, their mutual awareness and collaboration are rather low. The prevailing mechanism adopted to describe the interaction among the agents is bilateral, but not symmetric. In most cases, the opinion is described by a continuous variable. Just a few papers consider a utility function for the agents.INDEX TERMS Agent-based modeling, decentralized control, multi-agent systems, opinion dynamics.

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