Collective contributions to polarization in political voting

Politics around the world exhibits increasing polarization, demonstrated in part by rigid voting configurations in institutions like legislatures or courts. A crux of polarization is separation along a unidimensional ideological axis, but voting behavior is in reality more complex, with other signatures of collective order. We extend a foundational, statistical physics framework, restricted Boltzmann machines, to explain the full complexity of voting. The models we propose are minimal, fit strongly correlated voting data, and have parameters that transparently give vote probabilities. The model accounts for multi-dimensional voter preferences and the context in which such preferences are expressed to disentangle individual from collective contributions; for example, legislative bills can negotiate multiple issues, whose appeals add up or compete for individual votes. With the example of the U.S. Senate, we find that senators have multi-dimensional preferences, and, as one consequence, non-polarized coalitions coexist with polarized ones. Increasing polarization is predominantly explained by fewer votes that elicit bipartisan coalitions. We show that these accounts can be consistent, if far more parsimonious, than interaction-driven order. The findings highlight the collective choice of the content of and the rules of voting in the ebb and flow of polarization.