In a country with many elections, it may prove economically expedient to hold multiple elections simultaneously on a common polling date. We show that in a polarized society, in which each voter has a preferred party, an increase in the simultaneity of polling will increase the likelihood of a single-party sweep, namely, it will become more likely that a single party wins all the elections. In fact we show that the sweep probability goes up for \emph{every} party. Thus the phenomenon we describe is independent of the ``coattail'' or ``down-ballot'' effect of a popular leader. It is a \emph{systemic} and \emph{persistent} macroscopic political change, effected by a combination of political polarization and simultaneity of polling. Our result holds under fairly general conditions and is applicable to many common real-world electoral systems, including \emph{first-past-the-post} (most voters) and \emph{party list proportional representation} (most countries). In the course of our proof, we obtain a generalization of the well-known Harris correlation inequality.