Abstract: | 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. |