[QUOTE=Walloon]
States and territories with open primaries (any voter may vote in the primary of either major party, but not both): Alabama, Arkansas, Idaho, Illinois, Indiana, Michigan, Mississippi, Missouri, Montana, Puerto Rico, South Carolina, Texas, Tennessee, Vermont, Virginia, Wisconsin.
States and territories with open caucuses (any voter may vote in the primary of either major party, but not both): American Somoa, Minnesota, North Dakota, Virgin Islands.
States with modified primaries (independents may vote in the primary of either major party): Georgia, Maryland, Massachusetts, Nebraska, New Hampshire, New Jersey, North Carolina, Ohio, Rhode Island, West Virginia.
State with modified caucus (independents may vote in the caucus of either major party): Utah
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In addition to the open caucus, Minnesota also has an open primary (for any races where a candidate does not abide by the endorsement). In 2006, it affected the DFL (Democratic-Farmer-Labor) race to be the Attorney General candidate. The DFL-endorsed candidate lost to another candidate, who eventually won the office. That specific race was kind of a clusterf**k, though, and isn’t a great example of how the system usually works.
ETA: I forgot to write the think I meant to write in the first place. In MN’s open primary, every voter gets the same ballot (at least we do, out here in the sticks). It has all the contested primary races for all the parties. You can only vote for one party (so, you can’t vote on who is going to be the GOP candidate for State Auditor, and then turn around and vote for who is going to be the DFL candidate for Attorney General). If you make a mistake, the scantron machine you put your paper ballot into tells you, and you get to fix it.