Wisconsin has an "open primary" system, but it could be opened up a lot more with benefits to our political culture.
Wisconsin's system is "open" only to the extent that you don't have to declare yourself as a Republican or Democrat to vote in that party's primary. But you still have to choose which party's primary to vote in.
California is experimenting with a different form of truly open primary that holds the promise of breaking away from the two-party system. In that state, the two highest vote-getters move on to the general election, regardless of party. So you could have two Democrats competing in the general, or two Republicans, or two independents, or a Democrat and a Green Party member, or any of an endless variety of combinations.
In theory, this should drive our politics toward the center and strengthen independent candidates and new parties. That's because under our current system, candidates need to appeal to the partisans in their own parties. That's why a moderate Republican like Mary Panzer, for example, lost to an extremist like Glenn Grothman. She got knocked off in a primary because she was too reasonable. Had California's new process been in place, Panzer would have survived the primary in second place and probably easily won the general as she appealed to a broader base of moderate voters.
California tried out its new system for the first time last week with mixed results. But it seems to me that if this system were in place for a long enough period of time, it would have the effect of weakening the hard ideologues on both sides, and making our political culture more moderate, reasonable, and productive.