The concept of a bounded confidence level is incorporated in a nonconservative kinetic exchange model of opinion dynamics model where opinions have continuous values $\in [-1,1]$. The characteristics of the unrestricted model, which has one parameter $\lambda$ representing conviction, undergo drastic changes with the introduction of bounded confidence parametrized by $\delta$. Three distinct regions are identified in the phase diagram in the $\delta -\lambda$ plane and the evidences of a first order phase transition for $\delta ⩾0.3$ are presented. A neutral state with all opinions equal to zero occurs for $\lambda ⩽{\lambda }_{c_1}\simeq 2/3$, independent of $\delta$, while for ${\lambda }_{c_1}⩽\lambda ⩽{\lambda }_{c_2}\left(\delta \right)$, an ordered region is seen to exist where opinions of only one sign prevail. At ${\lambda }_{c_2}\left(\delta \right)$, a transition to a disordered state is observed, where individual opinions of both signs coexist and move closer to the extreme values ($\pm 1$) as $\lambda$ is increased. For confidence level $\delta <0.3$, the ordered phase exists for a narrow range of $\lambda$ only. The line $\delta =0$ is apparently a line of discontinuity, and this limit is discussed in some detail.

• Received 3 May 2012

DOI:https://doi.org/10.1103/PhysRevE.86.016115