The push is, first and foremost, an attack on the party system, which the advocates say has abused its gatekeeper role in politics and led to the gridlock and hyper-partisanship so often on display in Congress. “The problem isn’t the money. The problem is the parties themselves,” John Opdycke, the president of Open Primaries, told me in a recent interview. A veteran election-reform activist, Opdycke has been pushing for nonpartisan primaries as part of a succession of different advocacy groups for more than a decade. He worked on former Mayor Michael Bloomberg’s campaign to implement nonpartisan elections in New York at the beginning of his tenure, which by Opdycke’s own telling was a spectacular failure. “We got crushed,” he conceded.

Yet with California and Nebraska serving as successful state-level models, and with independent voters steadily increasing as a share of the electorate, Opdycke says he sees at least the early signs of momentum. The effort won a key endorsement last year from Senator Charles Schumer, the likely next Democratic leader in the Senate, who along with just about every party leader in New York opposed the change when Bloomberg pushed for it in 2003. And Open Primaries is now working with state activists to enact nonpartisan elections through 2016 ballot initiatives in Arizona and South Dakota.

The idea behind the top-two system is that in thousands of congressional and state legislative races across the country, partisan gerrymandering has made the traditional general election between a Republican and a Democrat non-competitive. In many races, incumbents run unopposed, and if they aren’t, the only competitive elections are the party primaries, which in most states are closed to independent voters. Some states have primaries in which independents can vote (in one party or the other), but the Supreme Court has ruled that the government can’t force a political party to open up its primary, so advocates instead are pushing for the creation of nonpartisan elections outside of party control. This would allow millions more people who aren’t registered as Republicans or Democrats to participate at the earliest stages of the election, which Opdycke argues is often the most important part of the process. Primaries, he said, “don’t just determine party nominees. They determine the shape and the tenor and tone of the campaign, the issues that are on the table, the coalitions that are on the table.”

In California, the shift to a top-two system in 2012 has meant that Republicans often face Republicans, and Democrats face Democrats, in general elections, which forces candidates to appeal beyond their party base. The result, according to a white paper by Open Primaries, is more competitive races, higher voter participation, and a more “functional legislature” that works more on coalition-building than party loyalty. The system has also produced some anomalies, such as in 2012, when Democrats failed to get a candidate into a general election for a competitive House district, missing a key opportunity to pick up a seat from Republicans. And the change hasn’t helped independent candidates as much, since they now must compete in the primary instead of skipping to the general election.