The Closed Primaries versus the Top-two Primary

The top-two primary is the new primary system passed in several states of the US that creates a single ballot in which the top two vote getters pass to the general election. Primary elections induce a sequential game with three stages: the candidate-entry stage, the primary election stage, and the general election. We analyze the electoral winner in equilibrium of the top-two primaries versus the traditional closed party primaries in terms of the Condorcet Consistency criterion, when voters and candidates are strategic. We show that up to four potential candidates (with no more than two democrats and no more than two republicans), the top-two system generally elects the median voter?s most preferred candidate. On the contrary, with the closed party primaries, extreme candidates can be elected even when the median voter prefers the moderated counterpart. When there are more potential candidates, the closed primaries system does not show, in general, any other di¤erent deviation. The top-two system then shows every type of deviation from the Condorcet Consistency criterion: it can elect an extreme candidate when the median voter prefers the moderated counterpart, or it can elect a democratic candidate when the median voter?s most preferred candidate is republican (or the other way around).