The paper proposes a variant of Boersma's Gradual Learning
 Algorithm for Stochastic Optimality Theory. While in the
 original version the learner is always (or tries to become)
 a speaker, I assume that the learner is both speaker and
 hearer. This learning theory is applied to the OT system
 from Aissen (2000), which was developed to explain the
 typology of differential case marking. It can be shown
 that the constraint sub-hierarchies that Aissen assumes to
 be universal follow from the statistical patterns of
 language use that have been uncovered in several corpus
 studies, if one adopts the bidirectional learning approach.
 The paper finally reports some tentative considerations on
 the repercussions of this learning theory for typology and
 diachrony.