| Summary: | 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 open and informal discussions among agents. Indeed, within a homogeneous social community with floaters, the dynamics lead 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 <i>x</i> is beyond a critical value <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>x</mi><mi>c</mi></msub><mo>=</mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>≈</mo><mn>0.167</mn></mrow></semantics></math></inline-formula> for discussing groups of size three and four. Similarly, the presence of stubborn agents also produces a polarization of a community that mixes when the proportion of stubborn agents is greater than some critical value. For equal proportions of stubborn agents <i>a</i> along each opinion, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mi>c</mi></msub><mo>=</mo><mfrac><mn>2</mn><mn>9</mn></mfrac><mo>≈</mo><mn>0.22</mn></mrow></semantics></math></inline-formula> for group size four against <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mi>c</mi></msub><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>=</mo><mn>0.25</mn></mrow></semantics></math></inline-formula> for group size three. However, the evaluation of the proportion of individual opinion shifts at the attractor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfrac><mn>1</mn><mn>2</mn></mfrac></semantics></math></inline-formula> and 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.
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