In linguistics, the theory that surface forms of language reflect resolutions of conflicts between competing constraints (i.e., specific restrictions on the forms of a structure).
Optimality Theory was introduced in the 1990s by linguists Alan Prince and Paul Smolensky (Optimality Theory: Constraint Interaction in Generative Grammar, 1993/2004). Though originally developed from generative phonology, the principles of Optimality Theory have also been applied in studies of syntax, morphology, pragmatics, language change, and other areas.
In Doing Optimality Theory (2008), John J. McCarthy points out that some of the most significant "work on OT is available for free on the Rutgers Optimality Archive. ROA, which was created by Alan Prince in 1993, is an electronic depository of 'work in, on, or about OT.' It's a fabulous resource for the student as well as the veteran scholar."
"At the heart of Optimality Theory lies the idea that language, and in fact every grammar, is a system of conflicting forces. These 'forces' are embodied by constraints, each of which makes a requirement about some aspect of grammatical output forms. Constraints are typically conflicting, in the sense that to satisfy one constraint implies the violation of another. Given the fact that no form can satisfy all constraints simultaneously, there must be some mechanism selecting forms that incur 'lesser' constraint violations from others that incur 'more serious' ones. This selectional mechanism involves hierarchical ranking of constraints, such that higher-ranked constraints have priority over lower-ranked ones. While constraints are universal, the rankings are not: differences in ranking are the source of cross-linguistic variation." (René Kager, Optimality Theory. Cambridge University Press, 1999)
Faithfulness and Markedness Constraints
"Optimality Theory holds that all languages have a set of constraints which produce the basic phonological and grammatical patterns of that particular language. In many cases, an actual utterance violates one or more of these constraints, so a sense of well-formedness applies to that utterance which violates the least number or least important constraints. Constraints can be classified in two types: faithfulness and markedness. The faithfulness principle constrains a word to match the underlying morphological form (such as plural tram +-s in trams). But words like buses or dogs do not follow this constraint (the first falls foul of the constraint that prevents the pronunciation of two consecutive /s/ sounds and the second places a /z/ instead of an /s/). These two examples, though, follow markedness constraints, and in these cases the particular markedness 'scores' higher than the faithfulness constraint, so the alternate forms are allowed. Differences between languages, then, are a matter of the relative importance given to particular constraints, and a description of these constitutes a description of the language." (R.L. Trask, Language and Linguistics: The Key Concepts, 2nd ed., ed. by Peter Stockwell. Routledge, 2007)
Constraint Interaction and the Domination Hierarchy
"We assert that the constraints operating in a particular language are highly conflicting and make sharply contrary claims about the well-formedness of most representations. The grammar consists of the constraints together with a general means of resolving their conflicts. We argue further that this conception is an essential prerequisite for a substantive theory of UG."
"How does a grammar determine which analysis of a given input best satisfies a set of consistent well-formedness conditions? Optimality Theory relies on a conceptually simple but surprisingly rich notion of constraint interaction whereby the satisfaction of one constraint can be designated to take absolute priority over the satisfaction of another. The means that a grammar uses to resolve conflicts is to rank constraints in a strict domination hierarchy. Each constraint has absolute priority over all the constraints lower in the hierarchy."
"Once the notion of constraint-precedence is brought in from the periphery and foregrounded, it reveals itself to be of remarkably wide generality, the formal engine driving many grammatical interactions. It will follow that much that has been attributed to narrowly specific constructional rules or to highly particularized conditions is actually the responsibility of very general well-formedness constraints. In addition, a diversity of effects, previously understood in terms of the triggering or blocking of rules by constraints (or merely by special conditions), will be seen to emerge from constraint interaction." (Alan Prince and Paul Smolensky, Optimality Theory: Constraint Interaction in Generative Grammar. Blackwell, 2004)
The Richness of the Base Hypothesis
"Optimality Theory (OT) does not allow for constraints on the inputs of phonological evaluation. Output constraints are the only mechanisms for expressing phonotactic patterns. This idea of OT is referred to as the Richness of the Base hypothesis. For instance, there is no input constraint that forbids the morpheme *bnik as a morpheme of English. The output constraints will penalize such a form, and evaluate this form in such a way that the optimal output form is not faithful to this form, but different, e.g. blik. Since forms such as bnik will never surface in English, it does not make sense to store an underlying form bnik for blik. This is the effect of lexicon optimization. Thus, the phonological output constraints of a language will be reflected by the input forms." (Geert Booij, "Morpheme Structure Constraints." The Blackwell Companion to Phonology: General Issues and Subsegmental Phonology, ed. by Marc van Oostendorp, Colin J. Ewen, Elizabeth Hume, Keren Rice. Blackwell, 2011)
"The emergence of OT syntax seems to fit into the general tendency in syntax to blame the ungrammaticality of a sentence on the existence of a better alternative. This view on grammaticality is also found in Noam Chomsky's Minimalist Program (Chomsky 1995), although Chomsky takes optimization to play a much more modest role than OT syntacticians do. Whereas Chomsky's only criterion for evaluation is derivational cost, the inventory of violable constraints assumed in OT syntax is richer. As a result, the OT constraints interact and conflict with each other. This interaction is exploited by the assumption that constraints are ranked, and that parametrization can be reduced to differences in ranking between languages. Chomsky's economic conditions, on the other hand, have no such direct parametrizing effect. In the Minimalist Program, the locus of the parametrization is the lexicon." (Introduction to Optimality Theory: Phonology, Syntax, and Acquisition, ed. by Joost Dekkers, Frank van der Leeuw, and Jeroen van de Weijer. Oxford University Press, 2000)