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Although spatial polarization of attitudes is extremely common around the world, we understand little about the mechanisms through which polarization on divisive issues rises and falls over time. We develop a theory that explains how political shocks can have different effects in different regions of a country depending upon local dynamics generated by the preexisting spatial distribution of attitudes and discussion networks. Where opinions were previously divided, attitudinal diversity is likely to persist after the shock. Meanwhile, where a clear precrisis majority exists on key issues, opinions should change in the direction of the predominant view. These dynamics result in greater local homogeneity in attitudes but at the same time exacerbate geographic polarization across regions and sometimes even within regions. We illustrate our theory by developing a modified version of the adaptive voter model, an adaptive network model of opinion dynamics, to study changes in attitudes toward the European Union (EU) in Ukraine in the context of the Euromaidan Revolution of 2013 to 2014. Using individual-level panel data from surveys fielded before and after the Euromaidan Revolution, we show that EU support increased in areas with high prior public support for EU integration but declined further where initial public attitudes were opposed to the EU, thereby increasing the spatial polarization of EU attitudes in Ukraine. Our tests suggest that the predictive power of both network and regression models increases significantly when we incorporate information about the geographic location of network participants, which highlights the importance of spatially rooted social networks. [ABSTRACT FROM AUTHOR]