Republican leaders’ response to the armed insurrection at the U.S. Capitol and other recent events suggested that some are unwilling to accept the legitimacy of free and fair elections. Trump’s incitement of the Jan. 6 insurrectionists, Sen. Josh Hawley’s (R-Mo.) salute to the armed mob and the unwillingness of over 100 GOP House members to certify the election results are a problem not just for the Republican Party but for U.S. democracy more broadly.

What happens when a major democratic party has a significant anti-democracy faction?

Here’s what we can learn from elsewhere in the world. Our research in Africa and Latin America suggests that democratic regimes often have authoritarian parties, or party factions that are anti-democratic, like the one in today’s GOP. Authoritarian parties or factions might try to undermine democratic institutions and procedures, or just violate democratic norms in order to concentrate power and evade checks and balances in pursuit of their goals.

There’s no single way in which authoritarian parties become less dangerous to democracy. Here are three of the most common ways that democracies reject authoritarian factions — although these efforts sometimes fail.

Sometimes authoritarian parties reform themselves

Sometimes, a party with a significant authoritarian wing can slowly reform itself. Voters and other parties might press the party to behave more democratically, while judges, donors and bureaucracies limit its authoritarian impulses.

That happened in Ghana during the 1990s and 2000s. The ruling National Democratic Congress (NDC) transformed itself from an authoritarian ruling party into a democratic party with authoritarian factions while participating in competitive multiparty elections. Inside the party, leaders who wanted to win power through elections gradually prevailed over those who preferred violence.

Ghana’s NDC pro-democracy leaders weren’t necessarily deeply committed to democracy. Instead, they calculated that it was in the party’s self-interest to accept the authority of the judiciary and Electoral Commission over elections, given the pressure they faced from social groups, donors, the lawyers’ association, and coalitions of working class, farmers and other unions. When democracy prevailed, leaders persuaded their followers to accept it, because it offered the leaders economic, social and personal security, and a chance to win again if they lost any given election.

Sometimes, instead, the anti-democratic party breaks apart

Sometimes the anti-democratic party or faction breaks up. That might enable the pro-democracy individuals and factions to form new coalitions, strengthening democracy. Equally, it might destabilize party politics, weakening party elders and party structures, and making parties less accountable to voters and more vulnerable to demagogues.

Both happened in Benin in 1990, after the authoritarian ruling party broke up. Benin adopted a volatile multiparty system, where new parties formed and others dissolved with almost every election. This democracy was inclusive and participatory — for nearly three decades, the country had high voter turnout, citizen engagement with their representatives, and many different types of candidates running for elected office. The lack of party structure recently allowed an authoritarian strongman to emerge, who threatened the other parties by limiting dissent, cracking down on the opposition and restricting human rights.

If an establishment party breaks up, it might help pro-democracy actors unite. But an existing party might also dissolve into many smaller parties, making it harder for pro-democracy actors to coordinate — that could open the door to a new, fully anti-democratic party winning a subsequent election with a slim plurality.

Sometimes, those who want democracy ally with each other to sustain it

A third — and potentially dangerous — scenario combines high polarization with a rift between two large parties over the value of democracy. In multiparty systems, small extremist or authoritarian parties can usually be contained and marginalized. However, in highly polarized systems like the United States, two-party competition can turn into a highly destabilizing contest between autocrats and democrats.

Citizens and political leaders who want to avoid this happening may have to compromise with democracy-respecting political opponents to protect democratic institutions. Countries such as Spain show how ideologically diverse coalitions can constrain and isolate authoritarian elements and uphold pro-democracy institutions. When far-right paramilitaries took over the Spanish parliament and attempted to overthrow the government in 1981, the Spanish monarch refused to support the coup, and conservative and Socialist parties came together to defend democracy.

But cross-party collaboration gets harder when extreme polarization leads to distrust. In the U.S. case, when moderate Republicans fear that working with Democrats means they’ll lose primary elections or won’t have opportunities to advance, they are less likely to try it. Polarization can hold moderates hostage to more radical or anti-democratic forces within their party, blocking bipartisan agreement.

Such polarization played a major role in the 1973 breakdown of Chile’s once-strong democracy. Socialist president Salvador Allende wanted to redistribute land and nationalize industry, leading to a backlash from conservative parties and business elites, who called for military intervention to remove Allende from office. Moderate leaders in Allende’s government tried to strike a compromise on economic reform with their centrist opponents, but hard-liners on both sides blocked it, leading centrists and conservatives to join in supporting a coup that derailed Chile’s democratic road to socialism.

What does all of this mean for the U.S.?

Lessons from other countries suggest that Republican leaders, together with Democratic party leaders and a supporting cast of courts, bureaucrats, electoral officials and private-sector leaders, could build a path to maintain and deepen democracy in the United States. Parties don’t have to agree on the policy issues that divide them, but they do have to agree to accept democratic rules and procedures. However, high polarization means that there is a serious risk that personal, partisan or factional goals could take precedence over the safeguarding of democracy itself.

Rachel Beatty Riedl (@BeattyRiedl) is a professor of government at Cornell University, director of the Einaudi Center for International Studies, and author of Authoritarian Origins of Democratic Party Systems in Africa (Cambridge University Press, 2014).

Kenneth Roberts is a professor of government at Cornell University, director of the Latin American Studies Program, and author of Changing Course in Latin America: Party Systems in the Neoliberal Era (Cambridge University Press, 2014).