Does Ideological Polarization Lead to Policy Polarization?

I study an election between two ideologically polarized parties that are both office- and policy-motivated. The parties compete by proposing policies on a single issue. The analysis uncovers a non-monotonic relationship between ideological and policy polarization. When ideological polarization is low, an increase leads to policy moderation; when it is high, the opposite occurs, and policies become more extreme. Moreover, incorporating ideological polarization refines our understanding of the role of valence: both high- and low-valence candidates may adopt more extreme positions, depending on the electorate's degree of ideological polarization.