We apply latent class analysis (LCA) to build typologies of response profiles underlying variation in attitudes. LCA is directly suited for identifying categories of people who have distinct representational profiles, that is, discretely measureable patterns of attitudes that are bound together by a common system of interpretation used by the group to make sense of and communicate about a social object within a social context. This novel application extends social representations theory and provides a way to simultaneously examine the relevant content of important representations and their prevalence across a priori social categories and demographics within a given society. We identify four distinct representational profiles underlying bicultural policy attitudes in a nationally representative New Zealand sample (N = 6150). We map the prevalence of these four profiles across the population, show how they vary demographically across indicators of social class, immigration status, and ethnicity, and predict distinct patterns of voting behavior, political party support, social identification, and in-group and out-group attitudes. Guidelines for the use of LCA in the study of social representations are discussed, including a three-step model of the following: (i) profile prediction and derivation; (ii) profile validation; and (iii) prevalence mapping of profile distributions across strata within the population. Copyright © 2013 John Wiley & Sons, Ltd.