One of the most interesting papers presented at APSA (of the panels that I attended) addressed the role that political primary types have on inducing legislative polarization. Eric McGhee, Seth Masket (who writes on Enik Rising), Boris Shor and Nolan McCarty considered the argument that closed primaries are more likely to result in more ideologically extreme legislators than open primaries. In brief, they compile a really impressive dataset to find that primary type actually has no discernible effect on legislative polarization. The argument they consider (and find against) is a popular one. States that only allow declared members of a particular party to participate in a primary election should have more ideologically extreme members in the legislature than states that allow anyone to vote in a primary. According to the story, if you allow all registered voters to select a political party's candidate, the more ideologically moderate candidate is likely to win. By contrast, if you only allow dyed-in-the-wool partisans to select candidates in a closed primary, the winning candidate is far more likely to be less moderate.
While this seems like a reasonable contention, this stylized story makes a number of dubious assumptions. First, the role of party activists is largely unspecified, or even summarily ignored. Regardless of the primary type, activists have the chance to recruit and lend support to ideologically extreme candidates. Second, given the ideological sorting into political parties; and the geographic sorting of like minded individuals into cohesive communities, there's no guarantee that the general electorate in any given district is actually as moderate as the story suggests. Third, even if the median voter in a district is moderate and can vote in a political primary doesn't mean many people will. While voting turnout in general elections still hangs below 60%, turnout in primary elections can be as low as 17%.
What's the take-away? Without over-stating their results, we can consider the option that primary type is actually way less important than the characteristics of the voters who participate in them. Perhaps it makes more sense to stop trying to blame particular institutional arrangements (see also: redistricting) for legislative polarization, and start to pay more heed to the notion that ideologically extreme voters are the reason that legislatures are polarized.