“I want to be a J!”: Liberalism in group identification problems

We consider the problem of group identification in two different settings. In the first setting, there is a given number of classes in the society and each individual expresses his wishes about who should be in which class. We give two characterizations of the liberal collective identity function that aggregates the individual choices and assigns each individual to the class he wants to be in. In the second framework, individuals only express their wishes about who should be put together in the same classes. We show that in this case, different axioms of Liberalism together with standard axioms hardly lead to any liberal group identity function.