  Recent empirical findings suggest that societies have become more polarized
in various countries. That is, the median voter of today represents a smaller
fraction of society compared to two decades ago and yet, the mechanisms
underlying this phenomenon are not fully understood. Since interactions between
influential actors ("activists") and voters play a major role in opinion
formation, e.g. through social media, we develop a macroscopic opinion model in
which competing activists spread their political ideas in specific groups of
society. These ideas spread further to other groups in declining strength.
While unilateral spreading shifts the opinion distribution, competition of
activists leads to additional phenomena: Small heterogeneities among competing
activists cause them to target different groups in society, which amplifies
polarization. For moderate heterogeneities, we obtain target cycles and further
amplification of polarization. In such cycles, the stronger activist
differentiates himself from the weaker one, while the latter aims to imitate
the stronger activist.
