Writing in the New Yorker a few weeks ago, Jill Lepore noted that polls now show that people overwhelmingly say yes when asked if they would vote for a qualified woman for president. She adds, "But the question requires respondents to self-report on the kind of thing, like church attendance, that they tend to overstate. In 2005, Gallup asked a different question: Do you think most of your neighbors would vote for a woman for President? Thirty-four per cent said no." From the context, it seems that she is interpreting the answers about what "your neighbors" would do as a more accurate measure of real opinions.
Is this a reasonable interpretation? I did a cross-tabulation of gender by ideology by answers to two questions, one about what you would do, the other about your neighbors (each question was asked to a randomly selected half of the sample). The numbers below are the percent saying "yes":
Conservative men 88% 61%
Conservative women 72% 55%
Moderate men 93% 77%
Moderate women 90% 66%
Liberal men 94% 67%
Liberal women 98% 67%
Answers about whether you would vote for a women have a strong relation to self-described ideology, especially among women. Opinions about what your neighbors would do have a weaker relationship. In fact, moderates are more likely to say that their neighbors would support a woman for president than liberals are.
If you think that the answers to the question about neighbors is a more accurate measure of true beliefs, you have to conclude that a lot of liberal women would not vote for a woman for president, which seems very unlikely. The more plausible interpretation is that people are answering the question about neighbors in a straightforward way, and people generally think that they are less prejudiced than most other people.
[Note: data from the Roper Center for Public Opinion Research]