How do geographically heterogeneous preferences affect political polarization in a multilevel electoral system? Using minimal assumptions, we develop a framework to describe the multilevel distribution of political opinions, using data from the United States between 1912 and 2020 as an example. We also introduce a general model of social ties and show how geography mediates their impact on both local and national electoral representation and (in)stability. Extending our analysis to multi-dimensional spaces of political opinion, we show that a decrease in the political salience of local issues can constrain the dimensions along which elections occur, limiting the effectiveness of a federal system as a safeguard against polarization. These analyses offer a precise formulation that ties together many observations raised in the study of federal institutions and enables future work—both formal and empirical—connecting geographical polarization to various properties of multilevel governance.