  Motivated by empirical research on bias and opinion formation, we formulate a
multidimensional nonlinear opinion-dynamical model where agents have individual
biases, which are fixed, as well as opinions, which evolve. The dimensions
represent competing options, of which each agent has a relative opinion, and
are coupled through normalization of the opinion vector. This can capture, for
example, an individual's relative trust in different media. In special cases
including where biases are uniform across agents our model achieves consensus,
but in general, behaviors are richer and capture multipolar opinion
distributions. We examine general fixed points of the system, as well as
special cases such as zero biases toward certain options or partitioned
decision sets. Lastly, we demonstrate that our model exhibits polarization when
biases are spatially correlated across the network, while, as empirical
research suggests, a mixed community can mediate biases.
