As I mentioned last time, many people seem to have incorrect or idiosyncratic understandings of "liberal" and "conservative." A December 2007 USA Today/Gallup Poll asked people to rate the leading Democratic and Republican candidates. The original data for this survey are available, so it is possible to see who got things "wrong." First, the average ratings of the candidates, which are on a scale of 1-5, with higher meaning more liberal.
Mike Huckabee 2.27
Fred Thompson 2.35
Mitt Romney 2.39
John McCain 2.51
Rudy Giuliani 2.76
John Edwards 3.47
Barack Obama 3.59
Hillary Clinton 3.74
There are no major surprises here--there's a clear separation between the Democratic and Republican candidates, and the ratings within each party are reasonable too. However, these are averages--the individual ratings for each candidate covered the whole range. I divided people into three groups--those who rated the top three Republican candidates (Giuliani, McCain, and Huckabee) as, on the average, more conservative than the three Democrats; those who rated them as more liberal; and those who rated them as exactly the same. (I just used three Republicans to reduce the number of people who had to be excluded because they didn't rate all of the candidates used). So one group got the rough placement right, as conventionally defined, and the other two didn't.
Comparing ratings of own ideological position:
correct (83%): 41% said they were conservative, 37% moderate, 22% liberal
no difference (7%): 33% conservative, 51% moderate, 16% liberal
backwards (11%): 59% conservative, 32% moderate, and 9% liberal
Comparing party preference:
correct: 45% Republican, 48% Democrat, 7% independent
no difference: 33% Republican, 53% Democrat, 14% independent
backwards: 22% Republican, 74% Democrat, 4% independent
So a significant group of people seem to be working on the following principles: they like the Democrats, they hear that it's good to be conservative and bad to be liberal, so they conclude the Democrats are more conservative. Although they definitely a minority, there are enough of them so that they might make up a major part of the shift in self-identification. That is, we've gone from 35-40% of people calling themselves liberals to 20-25%, or a drop of about 15%. That's close to the size of the "backwards" group.