Some 11.7% of Republicans and 10.5% independents said they would not give their true opinion, vs. 5.4% of Democrats, according to the study by CloudResearch LLC, a Queens, N.Y.-based company that conducts online market research and data collection for clients. Among the reasons they gave was that “it’s dangerous to express an opinion outside of the current liberal viewpoint,” according to Leib Litman, the co-chief executive officer and chief research officer.

CloudResearch conducted the survey online but inquired about surveys that are conducted by phone. It first asked participants for their political preference, then asked how they felt about divulging their preference for president in a phone poll. Later, it asked whom they actually did support for president.

Political party preference was the only characteristic that correlated consistently with reluctance to share presidential preference, Leib says. There was no correlation with age, race, education, or income. Cloud Research conducted the study two ways and got basically the same result both times, he says: In one, 1,000 respondents were evenly divided among Democrats, Republicans, and independents, and the second asked a different set of 1,000 respondents picked to precisely match the demographics of likely voters, regardless of party.