Candidate strategies in primaries and general elections with candidates of heterogeneous quality

I consider a model in which candidates of differing quality must win a primary election to compete in the general election. I show that there is an equilibrium in which Democrats choose liberal policies and Republicans choose conservative policies, but higher quality candidates choose more moderate policies than lower quality candidates. In this equilibrium, higher quality candidates choose more moderate policies if they have a larger quality advantage or there is less uncertainty about the median voterʼs ideal point in the general election, and the candidates in a given primary choose closer policies to one another when there is a smaller quality difference between the candidates in a primary. I further show that if the candidates have policy motivations, then a low quality candidate may strategically choose to enter a primary even if running for office is costly and the candidate will lose the primary election with certainty in equilibrium.