<p>Referendum practices and other forms of antagonistic political participation have become more commonplace in the last two decades. These practices have significant social and economic consequences and, as such, economic theory must study their development. In this work, we study the cases of binary political choices, encompassed in what we call the evolutionary political economy of dichotomized societies. We see the origins of these phenomena in certain streams of socio-political thought and analyze the conditions of their evolution. We also link our study with contributions to polarization research in socio-physics and mathematical sociology. Drawing on these fields, we present a new model that allows us to analyze these processes and obtain scenarios with different implications. Drawing on the model, we ask questions such as: can we determine specific conditions under which a referendum may end up truly reflecting the structural trend of public opinion? Are there situations in which dichotomized political processes may lead to surprising results? Can we characterize polarization as an emergent property of evolving political economies? Depending on specific parametric regimes, very different answers to these questions emerge.</p>