  In many social situations, a discrepancy arises between an individual's
private and expressed opinions on a given topic. Motivated by Solomon Asch's
seminal experiments on social conformity and other related socio-psychological
works, we propose a novel opinion dynamics model to study how such a
discrepancy can arise in general social networks of interpersonal influence.
Each individual in the network has both a private and an expressed opinion: an
individual's private opinion evolves under social influence from the expressed
opinions of the individual's neighbours, while the individual determines his or
her expressed opinion under a pressure to conform to the average expressed
opinion of his or her neighbours, termed the local public opinion. General
conditions on the network that guarantee exponentially fast convergence of the
opinions to a limit are obtained. Further analysis of the limit yields several
semi-quantitative conclusions, which have insightful social interpretations,
including the establishing of conditions that ensure every individual in the
network has such a discrepancy. Last, we show the generality and validity of
the model by using it to explain and predict the results of Solomon Asch's
seminal experiments.
