Should being a white man be a negative for Democratic presidential candidates?

Here’s a psychology experiment that I hope somebody will run:

Take a representative sample of potential Democratic voters, and break it up into six groups.

Group A gets asked this question:

All other things being equal, would it be a good thing in your view for the 2020 Democratic presidential nominee to be a woman?

Group B gets asked this question:

All other things being equal, would it be a bad thing in your view for the 2020 Democratic nominee to be a man?

Then ask the same parallel questions to Groups C and D, but replacing “woman” and “man” with “person of color” and “white.”

My hypothesis is that you would get a much higher percentage of “yes” answers from Group A relative to the number from Group B, and from Group C relative to Group D.

In other words, I would expect framing effects to be very powerful, with lots of people agreeing that it would be good for the candidate to be a woman, or a person of color, but much smaller numbers agreeing that it would be bad for the candidate to be a man, or white.

You could then ask Groups E and F, respectively, if it would be a good thing for the Democrats to nominate a woman of a color, or a bad thing for them to nominate a white man.  This would probably produce even a stronger framing effect, even though of course all the paired questions are logical equivalents.

As to the merits, it seems obvious to me at least that being a white man should be considered a significant negative for a Democratic presidential candidate, although not a dispositive one. And I would expect that many people who would find this statement objectionable would not object to the statement that it should be considered a significant positive for a candidate to be a woman, or non-white, or a non-white woman.

The reasons for my view are simple: The current Democratic coalition is made up very largely of people who would agree with the statement that it was a bad thing that the United States was run exclusively by and for white men for almost all of the nation’s history, and that it’s a bad thing that white men still have a vastly disproportionate amount of social, political, and economic power today.  The most obvious remedy for this state of affairs is to have a lot more people who are not men, or white, or in particular white men, running things.  This entails the conclusion that being a white man is not a good thing for a Democratic candidate to be, although again it shouldn’t be considered disqualifying by itself.  But it should be considered a negative.

My guess is that the best way to sugar this pill for white men who are inclined to vote for Democrats is to always frame the issue by arguing how great it would be for there to be more women and people of color in positions of power, while avoiding any hint of the fact that this conclusion logically entails having less whites, and men, and in particular white men, in those same positions.