Classical revealed preference theory postulates a connection between choices and revealed preferences. Political scientists have employed this theory in a wide variety of approaches and issues. For instance, comparativists predict parliamentary vote outcomes based on the preferences for legislators revealed in party manifestos. Social choice theorists initially expected on the basis of revealed preference theory that collective choice was based on collective preferences. In the previous chapter, we demonstrated that a maximal set may not exist under all conditions. This conclusion has led scholars to question the relationship between revealed social preferences and social choice. In particular, they have asked whether the choices made by collective actors are consistent with their collective social preference. In other words, if we assume that the preferences of a set of individuals are not cyclic, we would like to know if their collective choices are rationalizable. Formally, do their collective choices comprise a proper subset of the maximal set when one exists? The question is not a trivial one. For example, scholars often estimate the preferences of legislators based on roll-call votes [39]. If we do not assume that legislators’ roll-call votes are related to their preferences, then we must estimate their preferences by some other means.