  Opinion formation in the population has attracted extensive research
interest. Various models have been introduced and studied, including the ones
with individuals' free will allowing them to change their opinions. Such
models, however, have not taken into account the fact that individuals with
different opinions may have different levels of loyalty, and consequently,
different probabilities of changing their opinions. In this work, we study on
how the non-uniform distribution of the opinion changing probability may affect
the final state of opinion distribution. By simulating a few different cases
with different symmetric and asymmetric non-uniform patterns of opinion
changing probabilities, we demonstrate the significant effects that the
different loyalty levels of different opinions have on the final state of the
opinion distribution.
