  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.
