Nonconservative kinetic exchange model of opinion dynamics with randomness and bounded confidence.

The concept of a bounded confidence level is incorporated in a nonconservative kinetic exchange model of opinion dynamics model where opinions have continuous values ∈[-1,1]. The characteristics of the unrestricted model, which has one parameter λ representing conviction, undergo drastic changes with the introduction of bounded confidence parametrized by δ. Three distinct regions are identified in the phase diagram in the δ-λ plane and the evidences of a first order phase transition for δ ≥ 0.3 are presented. A neutral state with all opinions equal to zero occurs for λ ≤ λ(c1) ≃ 2/3, independent of δ, while for λ(c(1)) ≤ λ ≤ λ(c(2))(δ), an ordered region is seen to exist where opinions of only one sign prevail. At λ(c(2))(δ), a transition to a disordered state is observed, where individual opinions of both signs coexist and move closer to the extreme values (±1) as λ is increased. For confidence level δ < 0.3, the ordered phase exists for a narrow range of λ only. The line δ = 0 is apparently a line of discontinuity, and this limit is discussed in some detail.