Protester Bryan Sander is punched by a Donald Trump supporter as he is escorted out of the Republican presidential candidate’s rally at the Tucson Arena in Tucson on March 19. (Mike Christy/Arizona Daily Star via Associated Press)

As we enter the final stretch of a uniquely contentious U.S. presidential race, many wonder whether violence will erupt after the results are in. After a similarly bitter contest earlier this year in the United Kingdom over European Union membership, some observers found a rise in racial hate crimes. Will the same happen in the United States?

Most who’ve worried about this have been focused on supporters of Republican nominee Donald Trump. But this year’s minor-party candidates have (as in previous years) also complained that the system is rigged, railing against their lack of news media coverage, their exclusion from debates and the two-party system in general.

So is there a risk of violence next week? Our research begins to answer that question. We looked at the U.S. environmental movement to see whether ideological extremists perpetrate more violence if their political representatives don’t win office. The answer: yes. When the Green Party consistently fails to win elections, environmental sabotage becomes more frequent.

Let’s look at what happens when the Green Party loses

The Green Party, a minor U.S. party, has run high-profile presidential campaigns, such as those of Ralph Nader in 2000 and Jill Stein this year. Its candidates also enter dozens of local and state races every election cycle, winning many. For example, in California from 1985 to 2005, the Green Party ran 377 candidates for various local offices through the state and won 174 times.

We find that losing in these down-ballot races prompts more illegal sabotage from environmental extremists than do losses in higher-profile campaigns.

Most environmental activists oppose violence. But some advocate violence as a way to make change — leading to such incidents as those at the Twin Elks Lodge in Vail, Colo, the Animal Diagnostics Laboratory at the University of California at Davis, the Center for Urban Horticulture at the University of Washington and the tree spiking in the Nez Percé National Forest.

Our research (and that of others, for example, as you can see here, here, here and here) finds that the Green Party and environmental sabotage are two sides of a seesaw. If the Green Party does well over a long period (the past five years, in our research), then environmental radicals appear to think that violent actions are less necessary, and are less able to find accomplices (usually from the ranks of more moderate environmentalists). But if the Green Party does poorly, the same environmental radicals become frustrated with democracy and seem to find violence more legitimate.

Radical environmentalists get more violent

Radical environmentalists attest to this frustration-to-mobilization process. For example, in 1990, Howie Wilkie, co-founder of Earth First!, explained: “We played the game, we played the rules. We were moderate, reasonable, and professional. … And we got f—–. That’s when I started thinking, ‘Something’s missing here. Something isn’t working.’ ”

For some, that missing ingredient is sabotage.

Here’s how we examined this

We collected information on Green Party electoral history in Connecticut, and combined it with the Global Terrorism Database records on environmental sabotage in that state. We found that, on average, the rate of environmental sabotage increases approximately threefold (from 0.06 incidents per year to 0.21 incidents per year) when the Green Party is failing compared to when it’s winning.

That is, imagine that the Green Party runs an average number of campaigns at the local and state levels. If its candidates win all those races, we would predict 0.06 sabotage incidents within that state. But if they lose all those races, we would predict 0.21 sabotage incidents. This is clear when you move from left to right on the graph.

Please note that in our article, we discuss the process of radicalization in detail, and conduct empirical analyses that account for a variety of other attempts to influence environmental policy.

So what will happen after Nov. 8?

What, if anything, does this imply for violence after the election next week?

Let’s start with the Green Party. Its share of the vote — both in the presidential election and in state and local elections — could have violent repercussions. Poor results could portend more environmental sabotage incidents.

Can we generalize from the Greens to other third parties, or to followers of Trump or Democratic nominee Hillary Clinton? The analogy is imperfect. Environmental sabotage groups are cell-based and have no direct connection to the Green Party, which explicitly disavows them. Environmental sabotage damages property, not people. Dynamics may be different for hate crimes and other violence against individuals.

But whatever the candidate’s ideology, activists are probably motivated in the same way. If they’re frustrated with democracy, some people on the fringes of the movement may get more involved in direct action.

But Donald Trump’s campaign may have accomplished the opposite of this. Activists who’ve felt marginalized may now feel encouraged by his capture of the Republican nomination. They may get involved in legal democratic politics rather than staying outside that system.

Even if Clinton wins, violence won’t necessarily result. For the Greens’ more radical supporters, what leads to violence isn’t a single loss; it’s sustained frustration, measured as repeated electoral losses at a variety of levels. As long as there are other elections ahead, Trump’s more extreme activists and supporters may turn their attention to those races rather than to violence.

In that way, the Brexit referendum might actually have resulted in more violence had the “remain” vote won. Yes, the campaign may have prompted some Britons to perpetrate anti-immigrant hate crimes. But its success may have salved the frustration that many others would have felt about democracy.

Ben Farrer is an assistant professor of environmental studies at Knox College. 

Graig R. Klein is an assistant professor and graduate program coordinator in the department of professional security studies at New Jersey City University. Find him on Twitter @graigklein.