Anything Goes

Representing OT hierarchies in terms of weighted sums of violations requires in the general case exponential growth of weights; and any such weight system will only work for finite fragments of grammars in which the quantity of violations incurred by optima does not grow without bound (typically, those fragments in which input size is bounded). This conclusion is based on a worst-case analysis, and the worst is not always at hand. Noting that greater dominance can be minimally respected as greater weight without conditions on rate of weight growth, Paul Smolensky poses the following question: what OT systems are such that any dominance-respecting weighting whatever will recover the OT optima? These are systems in which ‘anything goes’ in the weighting systems (within the overarching restriction of weight-dominance concord). This note provides an answer to that question, and explores some systems in which anything goes and others in which it does not. 0. Introduction: OT and Weighting OT works by strict domination: constraints are ranked into a total domination order; candidate q is better than candidate z iff q is better than z on the highest-ranking constraint that distinguishes them. (On a constraint, the candidate with fewer violations is the better one.) Strictness comes in because no matter how poorly the better candidate fares on constraints ranked lower than the decisive constraint — no matter how massively it violates them — its failed competitor cannot be redeemed: the contest is over. From the OT point of view, there is no distinction between these comparisons: (1) Different Violations, Same Relations a. b. qTMz C1 C2 qNTMzN C1 C2 q 0 1 qN 0 77