Closed primaries versus top-two primaries

The top-two primaries recently approved in several US states eliminate closed party primaries and create instead a single ballot in which the first and second place winners pass to the general election. We conduct a theoretical analysis to compare the electoral consequences of top-two primaries with those of closed primaries. Each primary procedure induces a sequential game with three stages: candidate-entry stage, primary elections, and general election. We analyze the equilibria of these games and show that top-two primaries contribute to political moderation. In particular, when the median voter is extreme, closed primaries always generate extreme winners and, yet, top-two primaries can generate moderate winners. Furthermore, when the median voter is moderate but the partisan median voter of her party is extreme (and some additional mild conditions hold), closed primaries always generate extreme winners while top-two primaries always generate moderate winners. We also show that top-two primaries increase the number of swing states since, in certain cases, the party affiliation of the winner under top-two primaries may not coincide with the party affiliation of the median voter.