  This paper proposes a conditional Curie-Weiss model as a model for opinion
formation in a society polarized along two opinions, say opinions 1 and 2. The
model comes with interaction strength $\beta>0$ and bais $h$. Here the
population in question is divided into three main groups, namely: Group one
consisting of individuals who have decided on opinion 1. Let the proportion of
this group be given by $s$. Group two consisting of individauls who have chosen
opinion 2. Let $r$ be their proportion.
  Group three consisting of individuals who are yet to decide and they will
decide based on their environmental conditions. Let $1-s-r$ be the proportion
of this group. We show that the specific magnetization of the associated
conditional Curie-Weiss model has a first order phase transition (discontinuous
jump in specific magnetization) at $\beta^*=\left(1-s-r\right)^{-1}$. It is
also shown that not all the discontinuous jumps in magnetization will result in
phase change. We point out how an extention of this model could serve as a
random field Curie-Weiss model where the random field distribution has
nonvanishing mean.
