We expand the substantive terrain of QI's reach by illuminating a body of political theory that to date has been elaborated in strictly classical language and formalisms but has complex features that seem to merit generalizations of the problem outside the confines of classicality. The line of research, initiated by Fiorina in the 1980s, seeks to understand the origins and nature of party governance in two-party political systems wherein voters cast partisan ballots in two contests, one that determines partisan control of the executive branch and another that determines party control of a legislature. We describe how research in this area evolved in the last two decades in directions that bring it now to the point where further elaboration and study seem natural in the more general formalistic and philosophical environments embraced in QI research. In the process, we find evidence that a restriction of a classical model that has animated work in the field appears violated in a form that leads one naturally to embrace the superposition principle. We then connect classical distinctions between separable and nonseparable preferences that are common in political science to their quantum and quantum-like counterparts in the QI literature, finding special affinity for a recently-introduced understanding of the distinction that provides a passageway into the boundary between fully quantum and fully classical views of the distinction and thereby provides new leverage on existing work germane to the theory.