  It is known that individual opinions on different policy issues often align
to a dominant ideological dimension (e.g. "left" vs. "right") and become
increasingly polarized. We provide an agent-based model that reproduces these
two stylized facts as emergent properties of an opinion dynamics in a
multi-dimensional space of continuous opinions. The mechanisms for the change
of agents' opinions in this multi-dimensional space are derived from cognitive
dissonance theory and structural balance theory. We test assumptions from
proximity voting and from directional voting regarding their ability to
reproduce the expected emerging properties. We further study how the emotional
involvement of agents, i.e. their individual resistance to change opinions,
impacts the dynamics. We identify two regimes for the global and the individual
alignment of opinions. If the affective involvement is high and shows a large
variance across agents, this fosters the emergence of a dominant ideological
dimension. Agents align their opinions along this dimension in opposite
directions, i.e. create a state of polarization.
