This course deals with theoretical and empirical questions in the study of individual political preferences over alternatives (candidates, parties, legislative bills, etc.). The emphasis is on the default scenario that the analyst has finite data on choices/preferences over political alternatives that are themselves (partially) unobserved. On the theoretical side, the goal is to thoroughly study the reach of joint restrictions leveraged from such data under various shape and dimensionality assumptions. On the empirical side, the theoretical results are connected with existing and novel estimation strategies, both non-parametric and parametric (including the classic IRT model), along with specification tests of the various assumptions that underpin these methods and with (select) applications to questions of collective choice.