Information about the ideological positions of different political actors is crucial in answering questions regarding political representation, polarization, and voting behavior. One way to obtain such information is to ask survey respondents to place actors on a common ideological scale, but, unfortunately, respondents typically display a set of biases when performing such placements. Key among these are rationalization bias and differential item functioning (DIF). While Aldrich–McKelvey (AM) scaling offers a useful solution to DIF, it ignores the issue of rationalization bias, and this study presents Monte Carlo simulations demonstrating that AM-type models thus can give inaccurate results. As a response to this challenge, this study develops an alternative Bayesian scaling approach, which simultaneously estimates DIF and rationalization bias, and therefore performs better when the latter bias is present.