Danielle Thomsen is a doctoral candidate at Cornell University and a member of the Scholars Strategy Network. She will begin a post-doctoral fellowship at Duke University in January. This piece was published in partnership with the Scholars Strategy Network.

According to a new Gallup poll, Americans are more frustrated with Congress than ever before. In the aftermath of the government shutdown in October, who can blame them? Here is one solution for all those who are fed up with the dysfunction of Congress: Elect more Republicans.

Well, not just any Republicans. Elect more Republican women.

This may sound surprising to those who blame the GOP for the government shutdown. Yet as you may recall, a group of female senators led by Republican Sen. Susan Collins of Maine has been credited for moving beyond obstructionist politics and compromising to reach a deal to reopen the government.

Soon after the shutdown ended, the Scholars Strategy Network released a brief by political scientists Craig Volden of the University of Virginia and Alan Wiseman of Vanderbilt University showing that women are more effective legislators than their male counterparts.

But it isn’t that simple. To maximize the effectiveness of women in office, we must focus on recruiting, training, supporting and electing more Republican women to Congress. While there is a dearth of females in Congress, Democratic congresswomen now outnumber Republican congresswomen more than three to one in the House and four to one in the Senate.

Just 30 years ago, women were evenly distributed between the two parties, but the number of Democratic women in Congress has increased dramatically. The 1992 “Year of the Woman” elections brought the first significant jump; it was followed by steady gains in the number of Democratic congresswomen in almost every election cycle. Women now make up 30 percent of both House and Senate Democratic delegations. By contrast, the ranks of GOP women in Congress have barely budged. Of the 231 Republicans now serving in the lower chamber, a mere 19, or 8 percent of the party delegation, are women. The pattern is similar in the Senate, where Republican women hold only four of their party’s 45 seats.

Unfortunately, unless there is a serious change in strategy and outreach, the GOP’s recent shift to the right will cause this trend to get worse.

As the growing ranks of females in the House and Senate have tilted sharply Democrat, partisan polarization in Congress has reached record highs and ideological moderates have all but disappeared from today’s Congress. This chasm in the middle has disproportionately cut the ground out from under Republican women.

There has been a near complete makeover of women in the GOP caucus, as virtually all of the moderate Republican women from the 1980s and 1990s have either been defeated or chosen to leave. Of the 19 Republican women serving in the U.S. House of Representatives, only two — Florida’s Ileana Ros-Lehtinen and Texas’s Kay Granger — have served in Congress since before 2000.

And, an analysis of the state legislative pipeline to congressional office suggests that moderate state legislators are less likely to launch a congressional bid than those at the ideological poles. Using data from political scientist Adam Bonica of Stanford University , my research shows that very conservative GOP female state legislators are much more likely to run for Congress than those with moderate preferences. Probabilities of running for Congress are low overall, of course, but the likelihood that a conservative state legislator (someone like Michele Bachmann) runs for Congress is nearly 20 times greater than that of a moderate state legislator (someone like Olympia Snowe) — 3.8 percent and 0.2 percent, respectively.

Research shows that Republican women tend to hold views to the left of their male co-partisans and that voters perceive them to be more liberal than they actually are. On top of this, the state legislative pipeline contains shockingly few conservative women. In the state legislator data used above, between 2000 and 2010 nearly 6,600 Republican state legislators were in the conservative half of the GOP pool, but only about 1,050 were women.

Simply stated, conservative men are much better situated to run for and win GOP congressional seats. For the sake of the Republican Party and Congress as a whole, Republicans — and good governance allies — ought to take a page out of the Democrats’ playbook and recruit, train and support more women candidates to run for seats in state legislatures and Congress.

Since compromise is the linchpin of an effective government in our two-party system, the real answer to improving our democracy is electing more Republican women to Congress. And you don’t have to be a Republican to believe that.