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We study an opinion dynamics model that explores the competition betweenpersuasion and compromise in a population of agents with nearest-neighborinteractions on a two-dimensional square lattice. Each agent can hold either apositive or a negative opinion orientation, and can have two levels ofintensity --moderate and extremist. When two interacting agents have the sameorientation become extremists with persuasion probability $p$, while if theyhave opposite orientations become moderate with compromise probability $q$.These updating rules lead to the formation of same-opinion domains with acoarsening dynamics that depends on the ratio $r=p/q$. The population initiallyevolves to a centralized state for small $r$, where domains are composed bymoderate agents and coarsening is without surface tension, and to abi-polarized state for large $r$, where domains are formed by extremist agentsand coarsening is driven by curvature. Consensus in an extreme opinion isfinally reached in a time that scales with the population size $N$ and $r$ as$\tau \simeq r^{-1} \ln N$ for small $r$ and as $\tau \sim r^2 N^{1.64}$ forlarge $r$. Bi-polarization could be quite stable when the system falls into astriped state where agents organize into single-opinion horizontal, vertical ordiagonal bands. An analysis of the stripes dynamics towards consensus allows toobtain an approximate expression for $\tau$ which shows that the exponent$1.64$ is a result of the diffusion of the stripe interfaces combined withtheir roughness properties.

Opinion dynamics in two dimensions: domain coarsening leads to stable bi-polarization and anomalous scaling exponents