Kinetic modeling of opinion formation of peoples via multiple political parties

We investigate the opinion formation among the peoples and multiple political parties using the one dimensional relativistic Boltzmann-Vlasov equation for multi-components. A political party is constituted of politicians. The opinion formation depends on self-thinkings of peoples and politicians, and the constraint of the political party over opinions of politicians, when we restrict ourselves to the conciliatory exchange of opinions between two individuals. In particular, shock like profiles are obtained in the distribution of opinions of peoples, when the self-thinking of politicians are absent at the binary exchange of opinions between two politicians in the same political party.