A voter wears an “I Voted” sticker after casting a ballot in the Indiana primary in Noblesville in May 2016.  (Darron Cummings/Associated Press)

A group called No Labels, which aims to support centrist, bipartisan federal action, is raising money to protect centrist lawmakers who fear that they’ll be “primaried” — challenged and defeated by a more extreme candidate in their party’s primary before they reach the general election, where, presumably, a centrist candidate has a better chance to win.

The voters most motivated to cast a ballot in primaries tend to be the most ideological. Many argue that that’s one reason more extreme candidates get elected to Congress. If true, one way to alter primary outcomes is to change the kind of people who turn out to vote. That would involve either higher turnout from party centrists or bringing independents or voters from another party to protect the centrist candidate from his or her party’s ideologues.

Would that work? How promising is the strategy of focusing on primary elections rather than the general election to push Congress in a particular direction?

Here’s how I did my research

Such a strategy has institutional hurdles. Rules for participating in primary elections vary across states. Some states have “closed” primaries, in which you must register as a Republican or Democrat to vote in congressional primaries. Others have more open rules, enabling voters to vote in whichever party’s primary or for whichever candidate they choose.For this analysis, I looked only at the 34 states that allow at least some crossover voting. These are the states that the National Conference of State Legislatures categorizes as “partially open,” “open to unaffiliated,” “open,” and “top-two” systems. In these states, I identified Republican members of the House who come from the 146 districts where the Federal Election Commission tabulated at least one vote from the 2014 primary elections (2016 results are not yet posted). The remaining districts in these states did not have a contested primary in 2014 or do not have votes recorded with the FEC.

Let me note that we could conduct the same analysis with Democratic members; I use Republicans here for the purpose of illustration.

How many Democrats would have to vote in a Republican primary to change that congressperson’s views?

I calculated how many 2016 Hillary Clinton voters from that district would have to vote in the Republican primary to match half the district’s 2014 primary electorate. The idea here is to provide a rough estimate of how feasible it would be for citizens who don’t normally vote in Republican primaries to participate in those primaries to create incentives for GOP candidates to take more centrist positions. Half of 2014 votes is an arbitrary choice, and readers may scale up or down to target different proportions of the 2014 primary turnout.

As an example, consider the 7th Congressional District of Wisconsin, represented by Republican Sean P. Duffy. In the 2014 GOP primary, voters cast 29,314 ballots. In the 2016 general election, 137,874 voters cast ballots for Clinton in this district. Thus, it would take about 11 percent of those Clinton voters to match half (14,657) of the 2014 Republican primary turnout in the district. That number of Clinton voters would very likely change the incentives for candidates trying to win the 2018 primary election.

The figure below shows this calculation for the 20 districts where the smallest percentage of Clinton voters would be required to alter the primary electorate. To match half of the 2014 primary electorate in these 20 districts, the share of Clinton voters required to participate ranges from about 5 percent in the most favorable district NJ-04 to 13 percent in GA-07.

Across these 146 districts, the percentage of 2016 Clinton voters required to match half of the primary electorate varies. In nine districts, it would take less than 10 percent of 2016 Clinton voters to match half of the 2014 Republican primary vote, while 66 districts would need 20 percent or less of the district’s general-election Clinton voters. In the most challenging district (NE-03), 80 percent of general-election Clinton voters would have to vote in the Republican primary. (For a graph of all 146 districts, please see here.)

Of course, using the count of Clinton voters is just one way to estimate how many eligible voters in a district who don’t currently vote in these primaries might be motivated to participate. Mobilizing more centrist GOP voters who would otherwise stay home for the primary or bringing out previous non-voters could also change the primary electorate enough to influence candidate calculations.

But how would this work?

But what are the prospects for such a mobilization strategy? In recent years, primary-election voters have been more partisan and more ideological than general-election voters. But Chris Tausanovitch and I have shown that primary electorates haven’t always been so ideological.

In the mid-20th century, the ideology of congressional primary electorates was much more like that of general electorates than it is today. Many liberals voted in Republican primaries; many conservatives voted in Democratic primaries. Of course, one reason is that the parties were more ideologically diverse then than they are now. Nonetheless, Thad Kousser and I have shown that in 2014 voters who had not previously voted in primary elections could be mobilized to vote when they were asked.

A concrete example is the 2014 primary for Thad Cochran’s Senate seat in Mississippi, which has an open primary. Cochran did not win the most votes in the first primary election. But in a runoff, his campaign was able to bring out new voters, including from Democratic portions of the state. The number of votes cast increased by nearly 20 percent, and Cochran won. This suggests that at least in some cases, entrepreneurial candidates can mobilize new voters in primary elections, altering the dynamics of the contest.

To be sure, such a strategy would require many individual voters to act strategically — for example, by voting in a primary of a party they may not generally agree with. And in many cases it would mean giving up the chance to vote in another party’s primary.

National groups trying to mobilize such an action on a large scale would have to contact voters and distribute information in many different places across states with different rules. That would require resources and coordination and would likely have to be facilitated by new entrepreneurial candidates across the country.

Crossover primary voting could revitalize politics

But additional benefits to this kind of participation might include breaking the ideological primary, reinvigorating civic engagement and helping change the polarization of our current politics. To date, institutional changes to primary rules have not had large effects on who turns out in primaries. Behavioral changes by the American citizenry could.

Members of Congress learning that thousands of new voters are mobilizing for their primary election could have important consequences for their actions in Washington.

Seth J. Hill is assistant professor of political science at the University of California, San Diego.