  Recently, a model of opinion formation with kinetic exchanges has been
proposed in which a spontaneous symmetry breaking transition was reported [M.
Lallouache et al, Phys. Rev. E, {\bf 82} 056112 (2010)]. We generalise the
model to incorporate two parameters, $\lambda$, to represent conviction and
$\mu$, to represent the influencing ability of individuals. A phase boundary
given by $\lambda=1-\mu/2$ is obtained separating the symmetric and symmetry
broken phases: the effect of the influencing term enhances the possibility of
reaching a consensus in the society. The time scale diverges near the phase
boundary in a power law manner. The order parameter and the condensate also
show power law growth close to the phase boundary albeit with different
exponents. Theexponents in general change along the phase boundary indicating a
non-universality. The relaxation times, however, become constant with
increasing system size near the phase boundary indicating the absence of any
diverging length scale. Consistently, the fluctuations remain finite but show
strong dependence on the trajectory along which it is estimated.
