Stochastic OT as a model of constraint interaction

Stochastic OT is a set of specific assumptions about the mechanism of interaction between universal linguistic constraints: the choice of optimal candidates is determined by the rankings of constraint weights, but the rankings can be “perturbed” by a normally distributed “evaluation noise” (Boersma and Hayes 2001); the combined weight of a set of cooperating constraints is thus assumed to equal the maximum of their own weights. This implies that the combined effect of a set of cooperating constraints is only slightly stronger than the effect of the strongest constraint in this set. An interesting question is whether this hypothesis is correct, i.e. whether (and to which extent) it accurately predicts the universal properties of grammatical variation. Whereas this paper does not presume to answer this question, it provides necessary computational tools and defines a minimal condition on StOT grammars under which the StOT assumptions on the mechanism of constraint interaction can be tested against cross-linguistic data. Section 2 examines the general properties of StOT grammars viewed as parametric statistical models. Knowledge of these properties considerably facilitates all StOT-related computations (Section 3) and will, I hope, be useful independently of the theoretical agenda of this paper. Section 4 returns to the problem of typological predictions entailed by StOT grammars and shows that they can but need not be determined by the specific properties of the StOT mechanism of constraint interaction, depending on the configuration of constraint sets. Obviously, the plausibility of this mechanism can be corroborated or falsified by cross-linguistic evidence only insofar as StOT grammars do entail StOT-specific linguistic predictions. Finally, Section 5 establishes a minimal condition that must be satisfied by a StOT grammar in order to have this property and the corresponding criterion of linguistic plausibility of the StOT mechanism of constraint interaction.