Open vs. closed primary and single choice voting varies pretty widely based on the state in question- for example, several states don't have party registration, so any registered voter can cast a primary ballot. You hear lots of stories about strategic voting in another party's primary in these cases, and sometimes it actually can happen.
In caucus states(Iowa, for example), you can have multiple rounds of balloting with viability thresholds, meaning people walk in with first and second choices and end up shifting significantly over the course of the evening.
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