This past year, in high-profile confrontations across the country, student activists have been making demands about campus climate and diversity. Those have included removing symbols or institutional names linked to slaveholders or to institutional racism, and removing administrators accused of racial insensitivity.

But mobilized students share at least one demand: supporting demographic diversity on campus. The informal collective compiles appeals by student groups at, by now, 79 universities. The single most common demand is for schools to increase diversity among faculty. But media coverage of the protests, demands and resistance to such initiatives (here, here, here and here) suggest that campuses are deeply divided.

So what do students really think about whether universities should make diversity a priority when recruiting students and faculty? Are campuses polarized into pro- and anti-diversity camps? These are important questions, but uncovering what students really think about hot-button issues is not simple.

Here’s how we asked the question to avoid biased responses

Conventional surveys on sensitive issues are susceptible to various biases. If those who choose not to answer the survey have different opinions from those who do, the results won’t accurately reflect group opinion. Even those who do participate may adjust their responses to harmonize with what they think the researchers want to hear — a phenomenon known as “social desirability bias.”

To mitigate these problems, we used a technique known as fully randomized conjoint analysis, recently developed by political scientists. A respondent is presented with a pair of hypothetical candidates for a position — say, a faculty slot — and asked which one should be appointed. Each hypothetical candidate is described with a bundle of attributes that include race/ethnicity and gender identification, but also many others, such as academic discipline, undergraduate and graduate degrees, research record, teaching reputation, rank and even whether the candidate’s spouse or partner is already on the faculty.

The particulars of each attribute (say, whether race/ethnicity is white, black or African American, Asian, Hispanic or Latino, or Native American, etc.) are randomly assigned for each candidate. The order in which the attributes themselves are presented is also randomly shuffled for each respondent. That way no attribute is inadvertently made to seem especially important just by being placed first.

Each respondent chooses among about half a dozen pairs of candidates (five in one survey, eight in the other). Using the answers of hundreds of respondents and thousands of decisions with the attributes randomized, we can estimate whether, and how much, respondents care about hiring a black candidate rather than a white one, a Latino rather than an Asian American, an engineer rather than an economist, or a candidate with a degree from the University of Georgia rather than one from Yale.

Better yet, we can estimate whether preferences about these attributes differ across groups of respondents. So we can measure how priorities differ among students who self-identify as men, women and gender nonbinary, or among whites, African Americans, Asians and Native Americans, and so on.

Most important, it allows us to do these analyses without ever mentioning diversity when we recruit survey-takers or within our survey. Some participants may guess what the study is about, but not all will. Students have plenty of other reasons to care about what kind of faculty are recruited and what kind of students are admitted — and most of the attributes we ask them to evaluate have nothing to do with diversity demographics.

Here’s who we asked and what we found

Collaborating with two student partners, we designed randomized conjoint surveys for the 4,508 undergraduate students enrolled at Dartmouth College in Hanover, N.H. We invited half to take a survey on faculty recruitment in October 2015; 501 did. We invited the other half to take a survey on undergraduate admissions between December 2015 and January 2016; 607 did.

Although our samples are fairly representative, to account for any remaining imbalance, we re-weighted each sample to known demographic characteristics from the targeted population based on the procedure called entropy balancing.

So what did we find? First, Dartmouth students broadly support more demographic diversity in faculty recruitment and in undergraduate admissions. Second, some groups of students want a diverse faculty more than others, but effectively all groups want a diverse student body. Third, we found no evidence that groups are polarized about diversity. We never found one group — say, African American students — whose preferences directly oppose students from another group — say, whites.

Dartmouth students agree that they want a diverse student body

On admissions, Dartmouth students had a few particular preferences that stood out. For instance, they heavily favored bringing in students with strong academic records and high SAT scores, and they had a predilection for recruited varsity athletes.

But on the attitudes relevant to current news — race, ethnicity, gender and socioeconomic status — they wanted diversity. Holding all else equal, students preferred an African American or Native American applicant by 15 percentage points over a white applicant, and a Hispanic or Latino applicant over a white applicant by about 7 percentage points. They slightly preferred a woman over a man; strongly preferred a socioeconomically disadvantaged student over the affluent; and a first-generation college applicant over one coming from a family where college has been the norm.

Most important, there were almost no statistically significant differences in these preferences across various groups of students. Responses from whites, blacks, Latinos and Asian Americans, from men and women, and from students across a range of socioeconomic backgrounds were similar.

African American and female students think faculty diversity is a priority

Different groups of Dartmouth students did have different ideas about what types of faculty should be recruited. Once again, candidates’ academic bona fides matter a lot. Beyond that, students consider recruiting faculty from underrepresented groups to be a strong priority. All else equal, they preferred an African American candidate by 12 percentage points over a white candidate; an American Indian or Hispanic by 9 percentage points; and an Asian American by 5 percentage points.

But that preference varied by the demographics of the students. African American students place tremendous priority on recruiting non-white — and especially black — faculty, preferring an African American faculty candidate by 51 percentage points over an equivalent white applicant, holding all other attributes equal. (White students are also more likely to select the African American faculty candidate than the white one, but by a far lesser degree.)

And Dartmouth women consider diversity a higher priority than do men. Yes, they want more female faculty members, but they’re just as committed to more faculty members from all underrepresented race and ethnicity categories.

No group opposed diversity. White students overall, male students overall, and white males in particular are effectively indifferent to a candidate’s race and gender.

There may be differences in opinion about how to address campus climate

We suspect that opinion about how to address campus climate issues — about mandatory diversity training, for example, or the regulation of speech — is more divided than opinion about the value of diversity itself.

Still, we are struck by the levels of agreement — or the lack of clear cleavages — for giving priority in admissions to applicants from traditionally underrepresented groups in a manner consistent with affirmative action programs already in place, and ratified by the Supreme Court’s recent decision in Fisher v. University of Texas.

We also found support for prioritizing diversity in faculty recruitment decisions, driven primarily by demand among the groups most profoundly underrepresented among university faculties.

We look forward to giving our survey on campuses whose students have different backgrounds than those at Dartmouth. To think about what comes next for universities, it’s important to ask the right questions, the right way.

John M. Carey is the Wentworth Professor in the Social Sciences and professor of government at Dartmouth College.

Yusaku Horiuchi is the Mitsui Professor of Japanese Studies and professor of government at Dartmouth College.