  We investigate the opinion formation with upper and lower bounds. We
formulate the binary exchange of opinions between two individuals, and effects
of the self-thinking and political party using the relativistic
Boltzmann-Vlasov type equation with the randomly perturbed motion. The
convergent form of the distribution function is determined by the balance
between the cooling rate via the binary exchange of opinions between two
individuals and the concentration of opinions by the political party, and
heating rate via the self-thinking.
