Dylan Matthews flags a new working paper (pdf) by David Broockman and Christopher Skovron:
Broockman and Skovron find that all legislators consistently believe their constituents are more conservative than they actually are. This includes Republicans and Democrats, liberals and conservatives. But conservative legislators generally overestimate the conservatism of their constituents by 20 points. “This difference is so large that nearly half of conservative politicians appear to believe that they represent a district that is more conservative on these issues than is the most conservative district in the entire country,” Broockman and Skovron write. This finding held up across a range of issues.