  We have studied a walk in a one-dimensional virtual space corresponding to an
extended version of the three-state BChS model of opinion formation, originally
proposed in Physica A {\bf 391}, 3257 (2012), in which the agents are located
on a two dimensional lattice. The opinions are designated by the values $\pm1$
and zero. Here we also consider switches between the extreme states $\pm 1$.
The model involves two noise parameters representing the fraction of negative
interactions $p$ and the probability of extreme switch denoted by $q$. The
study shows that the nature of the walks changes drastically as the noise
parameters exceed certain threshold values. The order-disorder phase
transitions are independently obtained using the finite size scaling method
showing that these threshold values are indeed consistent with those values of
the parameters where a phase transition exists. The criticality is found to be
Ising-like even when extreme switches are allowed. A new critical exponent
associated with the probability distribution of the displacement is also
obtained independent of the values of the critical parameters. The nature of
the walks is compared to similar virtual walks studied earlier.
