Trump protester Bryan Sanders, center left, is punched by a Trump supporter as he is escorted out of Republican presidential candidate Donald Trump’s rally at the Tucson Arena in downtown Tucson on March 19. (Mike Christy/Arizona Daily Star via AP)

Many Americans have been startled by brawls at Donald Trump’s rallies and the candidate’s sometimes violent rhetoric. Trump’s own campaign manager was recently charged with battery of a journalist in Florida.

Election-related violence has been rare in recent U.S. history. But it’s common around the world. What does political science research tell us about whether violence and violent rhetoric help or hurt the politicians associated with it?

1. What does election violence look like around the world?

Globally, election violence is widespread. By one estimate, violence instigated by incumbent politicians alone — i.e. excluding violence launched by opposition groups — took place in more than 30 percent of elections worldwide between 1981 and 2004.

Violence can erupt before and after elections. It takes many forms: riots between supporters of rival parties or factions, polling stations seized to stuff ballot boxes, individual candidates killed and voters dragged to the polls.

Some disturbances seem spontaneous and uncoordinated. But political leaders are often behind attacks, whether orchestrating them, financing them, egging them on with hostile rhetoric, or refraining from sending in the police or army to stop them. Many politicians think violence will yield electoral gains — so much so that it’s been described as a “particularly brutal form of campaign expenditure.”

2. But how could violence help a candidate get elected?

One way is by making politicians look tough to the electorate. A voter might believe that aggressive politicians are more able get things done. Particularly in places where police don’t go or can’t help, vulnerable voters might see supporting these types of candidates — and the gangs they control — as their only source of protection.

Another way is by polarizing voters along group lines. Pre-arranged clashes between different ethnic, religious or racial groups are an especially common form of election violence. We know from psychology that when individuals sense that “their group” is under attack, they are more likely to identify with that group. So violence can induce voters of the same ethnic, racial or religious background to forget about their other differences (like class or economic interests) and come together to support candidates who claim to defend their group against others (see here, here, here and here).

Consistently, research shows that parties and candidates that mobilize through ethnic or religious appeals — as opposed to multiethnic or secular ones — are most likely to engage in this kind of electoral violence.

In India, for example, Hindu nationalist parties have been implicated in fomenting riots against minority Muslims. Our own research shows that when the local politician is from the secular-leaning Congress Party, there are fewer such riots. And evidence increasingly shows that the riots increase support for such Hindu nationalist parties as the Bharatiya Janata Party (BJP) at the expense of secular parties.

These findings suggest that the recent incidents at Trump rallies — violence that has often taken place between white attendees and protesters of color, and rhetoric that is aimed at mostly non-white groups such as Muslims and Latinos — could help unite white voters with diverse ideological views behind Trump’s candidacy, especially voters with authoritarian psychological profiles. Evidence that this may be true: Trump’s rise has been associated with more traffic at white nationalist websites, which get a surge in postings whenever he makes one of his charged anti-immigrant statements.

3. Can the mere threat of violence affect voting?

Research suggests that it can. Studies of Nigerian elections show that the threat of violence can stop opposition supporters from going to vote, because they worry about being intimidated when they cast their ballots.

Meanwhile, when parties and candidates threaten post-election violence if they lose, that can scare citizens into voting for those threatening politicians to prevent the violence from occurring. Trump’s suggestion that we should expect riots if he’s not selected as the Republican nominee may target party delegates rather than voters, but it could be understood in this light.

4. Can violence bring voter backlash?

But violence doesn’t always pay dividends. Recent studies suggest that being associated with violence might damage candidates’ reputations and hurt their electoral prospects more than it helps.

That’s what one of us found in our own research on Kenya. There, over the past 25 years, a tremendous amount of blood has been shed in electorally motivated ethnic clashes. But we are finding that when offered a choice between otherwise identical candidates, voters strongly prefer the nonviolent to the violent option. Kenyan politicians themselves seem to dramatically underestimate this potential for backlash — and so perhaps elections could become more peaceful if politicians are informed that violence doesn’t work as well as a campaign strategy as they might think.

What’s more, although many assume that violence helps politicians seem like tough guys who can get things done, we found no such advantage in our Kenya study (nor did another study from India).

Take Peter Mwathi, a former Kenyan Member of Parliament from Limuru. He allegedly asked members of the Mungiki criminal gang to arm themselves to defend his Kikuyu tribe in the heated aftermath of the 2007 election. When he stood for reelection in 2013, he failed to even win his party’s primary. Running on a different party’s ticket, he lost the general election by nearly 50 percentage points.

Could Trump’s loss to Ted Cruz in Wisconsin and his weak poll numbers in general election matchups result from popular backlash against the violence associated with his campaign?

Steven Rosenzweig is a PhD candidate in political science at Yale University, where he studies political violence and electoral accountability in developing countries.

Gareth Nellis is a PhD candidate in political science at Yale University, where he studies political parties, focusing especially on South Asia.