Perhaps more this year than in recent election years, there is a robust debate about the fundamental integrity of the November election. President Trump and his allies routinely, and contrary to the best evidence, say that an increase in mail balloting will result in voter fraud. Trump has even claimed that mail ballots will produce “the most rigged election” in U.S. history.

A more realistic concern, which the intelligence community warns is already happening, is foreign interference — something that Joe Biden and Democrats worry about quite a bit.

In past elections, research has shown, the outcome influences views of the legitimacy of the winners. The presidential elections of 2016 and 2020 suggest a different possibility: Both parties may fear that the election’s integrity was compromised, regardless of whether they win or lose. Indeed, Trump has routinely questioned his 2016 popular-vote loss despite his victory in the electoral college.

Whether voters are concerned about voter fraud or foreign interference matters a great deal for how the rest of the election year plays out. New survey evidence helps illuminate how many Americans have these concerns and, in particular how the parties are divided not only from each other but even internally. But perhaps more troubling is that majorities in both parties actually share a concern: that election officials will cheat when the votes are counted.

The new evidence comes from The American Social Survey, which is sponsored by the Weidenbaum Center of Washington University. The survey was fielded from Aug. 6-24 to a probability sample of 1,567 American adults in NORC’s AmeriSpeak panel. The survey had a margin of error of plus or minus 3.3 percent. Respondents were asked how concerned they were about “fraud in mail-in voting,” “intervention by foreign countries in the campaign,” and “cheating in vote counting by election officials.”

Trump and Biden supporters’ concerns about mail-in ballot fraud and foreign intervention are mirror images of each other. Nearly 87 percent of Trump supporters are very or somewhat concerned about fraud in mail-in balloting, but only 42 percent of Biden supporters are. Over 88 percent of Biden supporters are very or somewhat concerned about foreign intervention, compared with 47 percent of Trump supporters.

But concerns about cheating in vote counting were prevalent in both parties. A sizable majority of both Trump (75 percent) and Biden supporters (60 percent) are concerned about the threat of cheating by election officials. This concern runs counter to the evidence: Election administration experts find few serious problems associated with the integrity of state and local election officials.

Despite these partisan differences, there are variations in opinion within parties as well. One important source of variation is how attentive people are to politics, which we can approximate in this survey with people’s level of formal education. Americans with more formal education tend to be more attentive to politics. They may therefore be more likely to hear and accept both the views of election experts — such as that fraud in mail-in ballots and cheating by election officials is not a serious problem — and the views of the intelligence community that foreign interference is an ongoing problem. Meanwhile, less-well-educated individuals may tend to accept more partisan claims, such as that voter fraud is rampant.

The graph below focuses on concern about mail ballots and shows an educational divide among Biden supporters but not among Trump supporters or undecided respondents. Whatever their education level, 80 to 90 percent of Trump supporters are concerned about mail-in ballot fraud.

Biden supporters show the expected effects of education. Less-well-educated Biden supporters are more like Trump supporters in their concern about mail-ballot fraud. But better-educated Biden supporters tend to reflect the expert consensus that fraud is rare.

For concern about foreign interference, the pattern is different. Now it is Biden supporters who are universally concerned, regardless of their level of formal education. Among Trump supporters, there is less concern overall, especially among those at the lowest and highest levels of education recorded in the survey. Indeed, the best educated Republicans are the least concerned overall. They may be more attentive to messages from Trump and his allies playing down the threat of foreign interference than to the warnings from the intelligence community.

Concern about cheating by election officials is fairly widespread among Trump supporters, but especially among those with at least a four-year college degree. Among Biden supporters, this concern generally decreases among those with more formal education — although half or more of Biden supporters with at least a college degree are still concerned about cheating. The figure below illustrates how prevalent this concern is.

Among the respondents who were undecided, there is only modest variation across education levels. Overall, the undecideds’ concerns about election integrity are more like Republicans on foreign interference and split the difference between Democrats and Republicans on mail-ballot fraud.

Plainly, the legitimacy of U.S. elections is at stake. If the election night results are close, partisan differences over the threats to election integrity lead many Americans to question the outcome. Who leads on election night, which may change as mail-in and challenged ballots are counted after Election Day, is surely to influence who considers the vote count to be accurate.

This could get ugly. Just how ugly will be determined by the quality of election administration and the rhetoric of political leaders.

Steven S. Smith (@ProfStevenSmith) is professor of political science at Washington University.