  Opinion dynamics concerns social processes through which populations or
groups of individuals agree or disagree on specific issues. As such, modelling
opinion dynamics represents an important research area that has been
progressively acquiring relevance in many different domains. Existing
approaches have mostly represented opinions through discrete binary or
continuous variables by exploring a whole panoply of cases: e.g. independence,
noise, external effects, multiple issues. In most of these cases the crucial
ingredient is an attractive dynamics through which similar or similar enough
agents get closer. Only rarely the possibility of explicit disagreement has
been taken into account (i.e., the possibility for a repulsive interaction
among individuals' opinions), and mostly for discrete or 1-dimensional
opinions, through the introduction of additional model parameters. Here we
introduce a new model of opinion formation, which focuses on the interplay
between the possibility of explicit disagreement, modulated in a
self-consistent way by the existing opinions' overlaps between the interacting
individuals, and the effect of external information on the system. Opinions are
modelled as a vector of continuous variables related to multiple possible
choices for an issue. Information can be modulated to account for promoting
multiple possible choices. Numerical results show that extreme information
results in segregation and has a limited effect on the population, while milder
messages have better success and a cohesion effect. Additionally, the initial
condition plays an important role, with the population forming one or multiple
clusters based on the initial average similarity between individuals, with a
transition point depending on the number of opinion choices.
