House Speaker John Boehner announces his resignation with tears in his eyes on Sept. 25, 2015.  (Astrid Riecken/Getty Images)

In rebelling against House Speaker John Boehner, some Republicans believe that he has been insufficiently aggressive in pushing a conservative agenda. Boehner has, for instance, repeatedly violated the Hastert Rule that “The job of the Speaker is not to expedite legislation that runs counter to the wishes of the majority of his majority.”

Perhaps channeling Kenny Rogers’s “The Gambler,” Boehner has argued  “Where’s the ground that we fight on? Where’s the ground that we retreat on? Where are the smart fights? Where are the dumb fights that we have to stay away from?” However, some of the more conservative members of his party have decided that Boehner retreats too much. In their view, Boehner only knows how to “fold ’em.”

My new research, however, suggests that House conservatives are playing a dangerous game. Parties who rigidly follow the Hastert Rule do so at their electoral peril.

The key problem posed by the Hastert Rule is that it prevents the passage of policies supported by majorities in Congress and in the public. This can create potent issues for the minority party to campaign on. Then, moderate voters otherwise inclined to support the majority party may come to recognize that the only way to get the policies they want is to defeat the majority party and hand control over the agenda to the party that had been the minority.

In other words, the majority party sometimes faces a stark choice: accept the passage of legislation opposed by a majority of the party — thereby violating of Hastert’s Rule — or face the loss of majority status. Several of my findings suggest that when the majority party blocks legislation, it suffers at the ballot box.

First, the majority party is at a greater risk of losing seats and majority status when the median majority party member — who is the pivotal vote if the party follows the Hastert Rule — is ideologically further from the median member in the House as a whole. This creates exactly the condition where a majority party could be seen as catering to an ideological extreme rather than more centrist members and voters.

Second, the majority party is at greater risk the more current policies — the status quo — favor the majority party. In such a case, the majority has an incentive to block any policy that would change the status quo — including, perhaps, policies that the majority of voters would favor.

Third, the majority party party is at greater risk when fewer issues make it to the House floor and when more issues are blocked at the committee stage. That is, voters appear to punish the party for controlling the legislative agenda too strictly.

I show that only modest shifts in these factors can have serious consequences for the majority party. For example, if the number of issues raised declined by 16 percent, I estimate that the majority party would lose about 10 seats. Similarly, for every 1 percent increase in the number of issues not blocked in committee, the majority party typically wins almost two additional seats.

Whose seats might be most put at risk by the Hastert Rule? The model I develop suggests that moderates in the majority party are most likely to suffer. After all, these members often represent districts where winning moderate voters is key, and stringent obedience to the Hastert Rule may block the very policies that would appeal to moderate voters.

But more ideologically extreme members are less affected at the ballot box — although they do hate losing policy battles when the Hastert Rule is violated. This sets up precisely the kind of conflict between moderates and conservatives that we’ve seen in the House GOP.

To be clear, my results do not speak directly to Boehner’s plight. My analysis did not include the 113th or 114th Congresses, and it cannot demonstrate that Boehner’s decisions to fold on key issues, such as the Violence Against Women Act or renewal of the Bush tax cuts, helped his party’s electoral chances. But in general, the majority party faces a trade-off between winning elections and winning policy battles by controlling the agenda.

My findings also show exactly how much is at stake in the House leadership battle. A Speaker from the House Freedom Caucus might rack up some additional policy victories through brinksmanship and blocking. But if taken too far, obeying the Hastert Rule could help ensure that that this speaker soon has a different title: “Minority Leader.”

Jesse Richman is Associate Professor of Political Science at Old Dominion University.