Craig and Richeson’s second study, “On the Precipice of a ‘Majority-Minority’ America,” published last month, is even more directly relevant to the strategic choices facing Republicans. The authors found that whites – whether they called themselves liberals, centrists or conservatives — all moved to the right when exposed to the information about the approaching minority status of whites. This “suggests that the increasing diversity of the nation may engender a widening partisan divide,” Craig and Richeson write.

These findings led the two authors to observe that the future of the contemporary Republican Party may not be as bleak as some say. “Whites may be increasingly likely and motivated to support conservative candidates and policies in response to the changing racial demographics,” they write. “These results suggest that presumptions of the decline of the Republican Party due to the very same changing racial demographics may be premature.”

Responding to my emailed questions, Craig wrote, “Overall, making this racial shift salient could bring more moderate White Americans into the Republican Party, as well as increase turnout among White Americans who already consider themselves Republicans. “

The P.R.R.I. survey — conducted in 2013 of 1,028 respondents — was designed “to assess anxieties concerning the changing racial makeup of the country”; it was summarized in the May 2014 issue of The Atlantic by Robert Jones, the C.E.O. of P.R.R.I.

P.R.R.I. initially asked respondents a direct question: did they agree or disagree with the statement, “The idea of an America where most people are not white bothers me.” As you might expect, agreement was low, with just 13 percent saying they were bothered by the prospect of a majority-minority America. Then P.R.R.I. used a separate indirect technique to try to determine how many respondents were in fact disturbed by the growth of the minority population, but unwilling to admit it.

White respondents were divided into two demographically similar groups and then asked to describe how many of a list of short statements bothered them, but not to say exactly which ones, in what is known as a “list experiment.” One group was given three short statements unrelated to race and ethnicity, and the other group got the same three statements plus a fourth short statement which read: “An America that is not mostly white.”

This method allowed the institute to calculate the percentage of respondents who were actually bothered by the prospect of a white minority nation. The findings are striking.