  The effects of interpersonal interactions on individual's agreements result
in a social aggregation process which is reflected in the formation of
collective states, as for instance, groups of individuals with a similar
opinion about a given issue. This field, which has been a longstanding concern
of sociologists and psychologists, has been extended into an area of
experimental social psychology, and even has attracted the attention of
physicists and mathematicians. In this article, we present a novel model of
opinion formation in which agents may either have a strict preference for a
choice, or be undecided. The opinion shift emerges during interpersonal
communications, as a consequence of a cumulative process of conviction for one
of the two extremes opinions through repeated interactions. There are two main
ingredients which play key roles in determining the steady state: the initial
fraction of undecided agents and the conviction's sensitivity in each
interaction. As a function of these two parameters, the model presents a wide
range of possible solutions, as for instance, consensus of each opinion,
bi-polarisation or convergence of undecided individuals. We found that a
minimum fraction of undecided agents is crucial not only for reaching consensus
of a given opinion, but also to determine a dominant opinion in a polarised
situation. In order to gain a deeper comprehension of the dynamics, we also
present the theoretical master equations of the model.
