It's sometimes said that most whites believe that America is a "colorblind society," or even think there is more discrimination against whites than against blacks. I've had several posts on this general issue, looking at questions that asked directly (see this post for links). This time I'll take another approach and look at responses to distinct questions about how much discrimination there is against blacks and against whites. In 2005, a survey sponsored by the National Conference for Community and Justice asked) "Would you say there is a great deal of discrimination, some discrimination, only a little discrimination, or none at all against. . ." various types of people. Blacks and whites were among those asked about, but were not close to each other. Among whites, 48% saw more discrimination against blacks, 10% against whites, and 43% chose the same category for both. In 2106, the American National Election Studies Pilot Survey asked "How much discrimination is there in the United States today against each of the following groups?" The possible responses were "a great deal," "a lot," "a moderate amount," "a little," and "none at all." This time, 52% saw more discrimination against blacks, 18% against whites, and 30% chose the same category for both.
The drop in the number choosing the same category is at least partly a result of the larger number of categories in 2016. However, there is a clear change in the ratio perceiving more against blacks to more against whites, from almost 5:1 in 2005 to about 3:1 in 2016. There were some differences in survey procedures--2005 was a random-digit phone sample and 2016 was a weighted opt-in internet panel. That could make a difference, although I'm not sure of the direction. Also, in 2016, the questions about blacks and whites were separated by only one item (Hispanics). My guess is that if this made any difference, proximity would reduce the number of whites saying there was more discrimination against whites, because some would regard it as something they "shouldn't" say.
The general result fits with others suggesting that white perceptions of discrimination against blacks fell somewhat in the early 21st century. The general estimate of the proportion seeing more discrimination against whites (10-20%) is about the same as with the direct questions.
PS: for blacks, the 2005 percentages were 64, 3, and 33 (more against blacks, whites, same); the 2016 percentages were 80, 4, 17.
PPS: The 2005 questions also were asked in 1996, but unfortunately the original data don't seem to have been preserved, so it's not possible to do a parallel analysis for that year.