Our studies show that Republicans have good reason to keep their criticism to themselves: A legislator who rebukes Trump risks losing voter support in the next primary.

Here’s how we did our research

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To study how Republican voters might respond to Republican politicians who rebuke Trump, we fielded two experiments in May shortly after news broke about the relevant events. One experiment, fielded in early May, related to the Comey firing, and a second, fielded in mid-May, related to the news that, in a meeting with Russian officials, Trump revealed classified intelligence on the Islamic State’s strategy in Syria. Respondents were recruited on Amazon’s MTurk platform and included 144 (in early May) and 197 (in mid-May) self-identified Republicans. While not representative of the national population of Republicans, these samples include similarly sized proportions of people who identify with the party strongly and weakly.

In each study, respondents who identified as Republicans were split into two groups. All were told about the relevant action and Trump’s justification for it.

In the first group, respondents were then told that the Republican leadership echoed Trump’s justification. In the second group, however, respondents were told that the Republican leadership condemned the president’s action. We then asked follow-up questions, which we will look at below.

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Republican voters were more willing to disapprove of the president’s actions if their party’s leaders criticized him.

First, we asked respondents whether Trump did the right thing or the wrong thing.

In both experiments, respondents in the second group — who had been told that GOP leaders had criticized the president — were more likely to say that Trump had done the wrong thing.

You can see this in the graph below, which shows our results from the Comey experiment. When told that GOP leaders backed Trump, 59 percent of respondents said Trump did the right thing, and only eight percent said he had done the wrong thing. When told that Trump was rebuked by congressional leaders, 49 percent said he did the right thing, while the number who said he did the wrong thing jumped to 25 percent.

Results were similar when we asked about Trump giving classified information to a visiting Russian delegation. The share of Republicans who said Trump did the wrong thing increased from 21 percent, when told GOP leaders supported the president, to 42 percent, when told GOP leaders rebuked the president. This suggests that partisans are more likely to be critical of their leader when the party is critical.

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But voters were also critical of their party’s leadership.

Second, we asked respondents how much they agreed with the Republican leadership’s response. What we found might worry GOP officials who criticize Trump.

When told that the Republican Party leadership supported Trump, voters were significantly more likely to support their leaders than when told that they’d been critical of the president. In the Comey experiment, on a scale from 0 to 1, Republican voters’ average agreement with their leadership fell from 0.66 to 0.51. In the intelligence experiment, Republican voters’ average agreement with the party leadership fell from 0.62 to 0.55.

In another question, we also found that those in the second group were less likely — by about 0.12 and 0.07 on the 0 to 1 scale, for the Comey and intelligence studies, respectively — to say they thought the Republican Party response was appropriate than those in the first.

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Trump’s approval rating stayed the same, whether supported or rebuked by other Republicans.

Third, we checked on whether this theoretical Republican rebuke affected Trump’s approval rating. It didn’t. Even when voters were told that GOP leaders had criticized Trump, it didn’t affect their overall approval of the president.

But rebuking the president looked politically risky for members of Congress.

Fourth, but only in the intelligence-sharing experiment, we asked respondents how they would vote in the general election and whether they would support their senator in the next primary if their senator signed on to the leadership’s response, positive or negative.

As you can see in the graph, few Republicans would abandon their party’s nominee in the general election. But Republican voters who said they’d support their Republican senator in the primary dropped — from 88 percent to 77 percent — for senators who supposedly signed on to this theoretical rebuke. These numbers do not include respondents who said “not sure” for how they would vote in the general election; the “not sure” group was about the same for both groups.

Not surprisingly, Trump supporters were more likely to say they wouldn’t support a primary candidate who had criticized the president. For instance, among respondents who had tepid feelings about Trump — rating him at 40 on a 100-point “feeling thermometer” — being told that their senator had rebuked Trump did not significantly affect whether the voter said they’d support him or her in the primary.

But among more fervent Trump supporters — those who gave him an 80 on the feeling thermometer — their likelihood of supporting the senator in a primary election fell from 97 percent to 75 based on whether they were told he/she supported or criticized the president. That’s a statistically significant difference of 22 percentage points.

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Although not a typical Republican in any way, Trump has cultivated a strong personal following among the Republican base. Loyalty to Trump may lead strong partisans to penalize Republican critics as disloyal. Recent reports suggest that some Republicans who dislike Trump are leaving the party. That means the hold that Trump has on the remaining base may be even more of a problem for critics within the party.

Alexandra Filindra is associate professor of political science and psychology at the University of Illinois at Chicago, where her research focuses on the effects of race and ethnicity on public policy. Find her on Twitter @aleka1972.