The 2016 presidential campaign has become a referendum on the process of American electoral democracy itself.

Republican candidate Donald Trump’s baseless claims of a “rigged” election and his refusal to promise to accept the outcome of November’s vote have focused renewed attention on allegations of voter fraud.

Meanwhile, Trump has been criticized for calling on his supporters to “go out and watch” polling places, statements that have been interpreted as attempts to intimidate minority voters. Along with the implementation of stricter voter identification laws in several states, activists and politicians on the left have called out these efforts as voter suppression.

But to what extent do Americans believe voter fraud and voter suppression occur? And are there differences that fall along party lines, as we might expect?

In a poll conducted immediately after the third presidential debate (for more on our methodology, see here, data collected using Pollfish), we asked respondents a series of questions to assess their views of the electoral process.

Although there is no evidence of major fraud in U.S. elections, Trump has a receptive audience for his claims, as other polls have found.

Eighty-four percent of Republicans believe that a “meaningful amount” of voter fraud occurs in U.S. elections, along with 75 percent of independents. Even a majority of Democrats — 52 percent — believe voter fraud is occurring.

But what do people mean when they say they believe voter fraud is happening? Are they talking about people voting multiple times, “dead people” voting, voting by illegal immigrants or something else?

In the figure below, we find that nearly 60 percent of Republicans believe that illegal immigrants are voting, a claim that has been circulated by Trump in recent days and debunked by political scientists. The share of independents and Democrats who believe non-citizens are voting is considerably lower, but not insignificant.

One odd thing about this belief — the most widely believed method of voter fraud — is that it seems like an especially unlikely type of fraud. By going through the voter registration process, illegal immigrants would risk generating records that would presumably increase their chances of getting deported.

We also found that 43 percent of Republicans believe people vote under the names of registered voters who have died, and that 36 percent believe that election officials are manipulating vote totals. We did not find very many people who believe double-voting — or someone voting twice — is common.

On the other hand, rhetoric about voter suppression is not resonating with Democrats the way voter fraud does with Republicans.

More Republicans (30 percent) than Democrats (27 percent) say that voter suppression occurs through the purging of eligible voters from the registration rolls. And 34 percent of Republicans believe that intimidation is used to suppress the vote, something that just 24 percent of Democrats believe.

We do find a small partisan difference in the direction we would assume regarding voter ID laws. Thirty-two percent of Democrats believe voter ID laws contribute to voter suppression, while that number is 26 percent among Republicans (see the graph below).

But two things are clear — a majority of Democrats do not consider voter ID laws as voter suppression, even though this is a prominent part of Democratic elite rhetoric, and the responses are not nearly as polarized along party lines as on questions about voter fraud.

Sam Corbett-Davies is a PhD candidate at Stanford University in computer science. Find him on Twitter @scorbettdavies. Tobias Konitzer is a PhD candidate in communication at Stanford University. Find him on Twitter @KonitzerTobias. David Rothschild is an economist at Microsoft Research. Find him on Twitter @DavMicRot.