By sheer strength of numbers, ideologically moderate Americans should be the most potent force in politics. Since at least 1980, self-identified moderates have outnumbered both liberals and conservatives in presidential exit polls, comprising 41 percent of voters in 2012. Moderates are also a plurality in 25 states, according to 2014 data from Gallup.

Yet this moderate strength seems nowhere evident in Congress. Among House Democrats, the moderate Blue Dog and New Democratic coalitions have shrunk by nearly half since 2010. And among Republicans, the Tea Party’s ascendance has purged most of the GOP’s few remaining moderates. Congressional polarization today, say political scientists Christopher Hare, Keith Poole, and Howard Rosenthal, is at its worst since Reconstruction.

One key step toward reversing this polarization is to replenish the stable of moderates in Congress. Moderates can bridge divides, encourage bipartisanship, and check ideological excesses. And given the vast pools of moderate voters, Congress should have more moderates than it does now to reflect the share of moderates in the electorate. The current political system, however, effectively disenfranchises moderate voters.

There’s one solution that can help reverse that dismal trend: creating more at-large seats in the House of Representatives. If every state with more than two representatives allocated just one seat to an at-large member (while also redrawing its remaining seats), moderates in those states could better exercise their plurality strength as they do in other statewide elections, such as those for the Senate and the White House. And while the remaining geographically determined districts would become somewhat larger as a result, this system would also grant each voter two representatives in the House: one from the voter’s district, and one from the voter’s state.

The creation of new “plurality-moderate” at-large seats in many states would increase the number of competitive seats while bolstering the odds for moderate candidates. Moderates trapped in otherwise deeply red or blue districts would have an outlet for their influence and not feel that their votes are being wasted.

This approach would also guarantee that at least one House member from virtually every state hails from a “district” that can’t be gerrymandered, which would help delegations better reflect a state’s overall ideological and party makeup (43 states have at least two representatives; seven states have only one congressional district). In some states, an at-large seat could help bring better partisan balance to delegations now badly skewed by gerrymandering. The potential for hyper-extremist candidates to win would also diminish, even in the deepest red, most polarized states. In Mississippi, the most conservative state in the country, conservatives still make up fewer than half of residents statewide. An ultraconservative Freedom Caucus candidate who might coast to victory in a majority-conservative district would find the going tougher in an at-large race where he or she also needs moderates to win.

Creating at-large congressional districts would require changes in both state and federal law, which is why some scholars who have considered at-large and “multi-member” districts in the past now believe them to be infeasible. But such a change is hardly less realistic than other critically needed reforms, such as redistricting or campaign finance reform. Many Americans are also already familiar with the concept of at-large seats, such as on city councils, which makes them potentially more achievable than other, more alien-sounding proposals, like switching to a parliamentary system. And for frustrated moderates and political independents, the possibility of a “plurality-moderate district” where they could have genuine influence could be an attractive alternative to supporting a doomed-to-fail third party.

Perhaps the most serious concern is the potential impact of at-large districts on minority representation, which scholars such as Thomas Schaller argue is the greatest obstacle to their adoption. Indeed, at-large and “multi-member” districts were fairly common in the nineteenth and early twentieth centuries, according to Stephen Calabrese of Carnegie Mellon University. But their use as a tactic to dilute minority representation—particularly in the South—led Congress to ban at-large districts in 1967.

Amending federal law to allow just one at-large district per state could help mitigate these concerns by preventing states from creating multiple at-large districts as a tactic to eliminate majority-minority districts. Another mitigating factor is demography. With the nation poised to become majority-minority in 2044, at-large districts could even benefit some populations approaching plurality status in the same way that they would benefit moderates.

Of course, the biggest political obstacle to this reform would be the political parties, which have a vested interest in maintaining safely partisan seats. But challenging the status quo might be an excellent and concrete opportunity to test moderate muscle. If moderate voters want to realize their power, their first step is to re-enfranchise themselves. American politics would only benefit.