What system for selecting party nominees does the passage descrribe?

Open primary

Explanation:

A primary election (primary of nomination), or simply primary, is a choice in which the voters under a jurisdiction select the candidate that a party will present to a later public election. In other words, it is a democratic way of pre-selecting the candidate that a party will present to a certain electoral process. The "Primaries" are more common in the United States, not only for the presidential elections but also to choose the candidates for representatives, senators, mayors and governors, among others, and their origins go back to the progressive movement.

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