Unanimity, Coexistence, and Rigidity: Three Sides of Polarization.

Political polarization is perceived as a threat to democracies. Using the Galam model of opinion dynamics deployed in a five-dimensional parameter space, I show that polarization is the byproduct of an essential hallmark of a vibrant democratic society, namely the open and informal discussions among agents. Indeed, within a homogeneous social community with floaters, the dynamics leads gradually toward unanimity (zero entropy). Polarization can eventually appear as the juxtaposition of non-mixing social groups sharing different prejudices about the issue at stake. On the other hand, the inclusion of contrarian agents produces a polarization within a community that mixes when their proportion $x$ is beyond a critical value $x_c=\frac{1}{6}\approx 0.167$ for discussing groups of size 3 and 4. Similarly, the presence of stubborn agents produces also a polarization of a community that mixes when the proportion of stubborns is greater than some critical value. For equal proportions of stubborns $a$ along each opinion, $a_c=\frac{2}{9}\approx 0.22$ for group size 4 against $a_c=\frac{1}{4}= 0.25$ for group size 3. However, the evaluation of the proportion of individual opinion shifts at the attractor $\frac{1}{2}$ indicates that the polarization produced by contrarians is fluid with a good deal of agents who keep shifting between the two opposed blocks (high entropy). That favors a coexistence of opposite opinions in a divided community. In contrast, the polarization created by stubborn agents is found to be frozen with very few individuals shifting opinion between the two opinions (low entropy). That yields a basis for the emergence of hate between the frozen opposed blocks.