The rationalizability of survey responses

We propose and study the concept of survey rationalizability. In the simplest scenario of dichotomous attitudinal surveys, survey rationalizability means that both questions and individuals'views can be positioned on the real line in such a way that individuals endorse only the questions that closely align with their views. We demonstrate how the relative positioning of questions can be learned through a revelation mechanism involving pairs of individuals and triplets of questions. We also establish that the acyclicity of these revelations is necessary and sufficient for rationalizability. Additionally, we show that our analysis readily extends to polytomous surveys and probabilistic data. Furthermore, we investigate the identification of the parameters in these models and prove that even the cardinal locations can be fully determined in an exponential version of the probabilistic model. Finally, we conclude by examining an alternative model of survey responses for aptitudes.