Optimality Theory (OT, cf. [Prince and Smolensky(1993), Grimshaw(1995)]) assumes that a grammar consists of ranked, violable constraints. In OT, the linguistic structure of an utterance is computed as the optimal structure of a set of possible candidates, where ``optimal'' is defined as satisfying most of the most highly ranked constraints. Like traditional linguistic theories, OT is based on a binary notion of grammaticality: the optimal candidate is grammatical; no assumptions are made about the relative grammaticality of suboptimal candidates.
To account for graded data, we propose to extend OT such that degrees
of grammaticality are assigned to competing candidates according to the number
and ranks of the constraints they violate. More precisely, we
postulate that the optimality theoretic harmony of a candidate
corresponds to its relative grammaticality in the candidate set. Under this
assumption, evidence for constraint rankings can be obtained from
judgments for suboptimal candidates. While a standard OT grammar makes
predictions of the form: a structure 
is grammatical, but
is ungrammatical, graded OT predicts that a structure more
or less grammatical than , a claim that can be tested against
graded experimental data.