We show that MaxEnt is so rich that it can distinguish between any two different mappings: there always exists a nonnegative weight vector which assigns them different MaxEnt probabilities. Stochastic HG instead does admit equiprobable mappings and we give a complete formal characterization of them.

This paper focuses on the most basic implicational universals in phonological theory, called T-orders after Anttila and Andrus (2006). It shows that the T-orders predicted by stochastic (and partial order) Optimality Theory coincide with those predicted by categorical OT. Analogously, the T-orders predicted by stochastic Harmonic Grammar coincide with those predicted by categorical HG. In other words, these stochastic constraint-based frameworks do not tamper with the typological structure induced by the original categorical frameworks.

This paper focuses on the most basic implicational universals in phonological theory, called T-orders after Anttila and Andrus (2006). It develops necessary and sufficient constraint characterizations of T-orders within Harmonic Grammar and Optimality Theory. These conditions rest on the rich convex geometry underlying these frameworks. They are phonologically intuitive and have significant algorithmic implications.