Editor’s Note:John Avlon is a CNN senior political analyst and anchor. He is the author of “Lincoln and the Fight for Peace.” The views expressed in this commentary are his own. View more opinion at CNN.

CNN  — 

New Hampshire might be the last, best chance to stop former President Donald Trump from seizing the Republican presidential nomination. That’s because New Hampshire’s election laws allow independent voters to participate in its first-in-the-nation primary on Tuesday. This opens up the process and tends to have a broadening effect on what would otherwise be a solely play-to-the-base exercise that elevates the most polarizing, hyperpartisan candidates.

America is a divided nation, even on the subject of open primaries. About half the states have some form of open primary in place, as opposed to a closed process in which only  partisans can participate. But that number is a constantly shifting battleground, and this year there are active efforts to roll back open primaries in key states while opening them in others.

New Hampshire is a good example of why more states should move toward more open primaries, not fewer.

In New Hampshire, there are more registered independent – or “undeclared” – voters than Republicans or Democrats. New Hampshire also has a high percentage of voters who identify as moderate rather than liberal or conservative. This makes the Granite swing state look like the nation. Here’s another measure: In recent years, New Hampshire’s primaries have seen more than twice the turnout of the Iowa caucuses. In Iowa, just 110,000 people – or 3.5% of the total state population – voted in the caucuses.

The battle over closing versus opening America’s primary elections reflects a fundamentally different vision of whether to put party or country first in our politics. Even when hard-won reforms prove their worth, partisans try to roll back those gains to serve their own special interests.

For instance, Louisiana has long enjoyed an open primary, but its new GOP governor is swearing to make a closed partisan primary reality. Sometimes these efforts can seem cartoonish caricatures of partisanship, as in Tennessee, where the Republican state legislature is trying to require signs saying that only genuine party members can vote in the primary despite the fact that the state does not have party registration. That’s a solution in search of a problem.

Democrats are not above trying to keep primaries closed when they have decisive partisan control, either. That’s why an effort to create open primaries in Washington, DC, is meeting stiff resistance from local Democrats.

But there’s a countervailing force at work in American politics as well, with several states engaged in various efforts to open their primaries. In Nevada, voters will need to re-approve an initiative to have its 900,000 independent voters participate in the primaries for statewide elected officials. In Arizona, the state legislature is looking at nonpartisan primaries with a run-off between the top candidates. In Pennsylvania, there’s an effort underway to open the state’s currently closed partisan primaries as well. And those are just examples in pivotal presidential swing states.

There’s a reason open primaries appeal to open-minded political leaders who are trying to solve problems rather than simply hold onto power in perpetuity. Listen to G.T. Bynum, mayor of Tulsa, Oklahoma, and a self-described “convert” who initially opposed nonpartisan primaries because he thought they would lead to decreased turnout.

“I was totally wrong. We have seen no decline in voter turnout in elections in Tulsa. The big change that we have seen is that the debates on the city council and at city hall are not partisan anymore. They have shifted to issues. You still have disagreements about policy,” he said, but they’re “not tied up in this partisan superstructure based on federal issues at best that have no relevance to whether or not you’re fixing a street or hiring more police officers.”

Bynum went on to praise the change as incentivizing an “approach of moving beyond partisanship and focusing on the issues that really impact people and how you can bring people together around those and find common ground.” That sounds like the opposite of Congress these days, but it just goes to show that if you change the rules, you change the game.

An open or semi-open primary does not solve all the problems facing our democracy. New Hampshire’s open primary didn’t stop Trump from winning there in 2016 and, of course, 2020. But it shifts the incentive structure decidedly toward reaching out beyond the partisan base, which is where the constructive compromise of democracy actually occurs.

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If America had more open primaries on a local, congressional and presidential level, it could have a powerful impact in adjusting the incentive structure to reflect the priorities of the country and not simply the priorities of the most partisan wing of that party, which furthers the vicious cycle of hyperpartisan polarization. It would increase the courage of elected representatives to do what they know is right rather than cave to threats by the most extreme members because of a combination of cowardice and careerism.

Here’s evidence that members of Congress will appreciate: The only two Republican House members to win reelection after voting for Trump’s post-January 6 impeachment were elected in states that don’t restrict primary participation by party.

History is clear that democracies deteriorate when hyperpartisanship and polarization hijack every level of the political process. Election reform efforts like open primaries are a practical, citizen-led step towards healing our divisions and fitfully forming a more perfect union.

Correction: An earlier version of this article gave an incorrect first name for Tulsa Mayor G.T. Bynum.