Optimality Theory - EVAL: Definition of Optimality

EVAL: Definition of Optimality

Given two candidates, A and B, A is better than B on a constraint if A incurs fewer violations than B. Candidate A is better than B on an entire constraint hierarchy if A incurs fewer violations of the highest-ranked constraint distinguishing A and B. A is optimal in its candidate set if it is better on the constraint hierarchy than all other candidates. For example, given constraints C1, C2, and C3, where C1 dominates C2, which dominates C3 (C1 >> C2 >> C3), A is optimal if it does better than B on the highest ranking constraint which assigns them a different number of violations. If A and B tie on C1, but A does better than B on C2, A is optimal, even if A has 100 more violations of C3 than B. This comparison is often illustrated with a tableau. The pointing finger marks the optimal candidate, and each cell displays an asterisk for each violation for a given candidate and constraint. Once a candidate does worse than another candidate on the highest ranking constraint distinguishing them, it incurs a crucial violation (marked in the tableau by an exclamation mark). Once a candidate incurs a crucial violation, there is no way for it to be optimal, even if it outperforms the other candidates on the rest of CON.

Constraints are ranked in a hierarchy of strict domination. The strictness of strict domination means that a candidate who violates only a high-ranked constraint does worse on the hierarchy than one that doesn't, even if the second candidate fared worse on every other lower-ranked constraint. This also means that constraints are violable; the winning candidate need not satisfy all constraints. Within a language, a constraint may be ranked high enough that it is always obeyed; it may be ranked low enough that it has no observable effects; or, it may have some intermediate ranking. The term the emergence of the unmarked describes situations in which a markedness constraint has an intermediate ranking, so that it is violated in some forms, but nonetheless has observable effects when higher-ranked constraints are irrelevant.

An early example proposed by McCarthy & Prince (1994) is the constraint NoCoda, which prohibits syllables from ending in consonants. In Balangao, NoCoda is not ranked high enough to be always obeyed, as witnessed in roots like taynan (faithfulness to the input prevents deletion of the final /n/). But, in the reduplicated form ma-tayna-taynan 'repeatedly be left behind', the final /n/ is not copied. Under McCarthy & Prince's analysis, this is because faithfulness to the input does not apply to reduplicated material, and NoCoda is thus free to prefer ma-tayna-taynan over hypothetical ma-taynan-taynan (which has an additional violation of NoCoda). Constraints are also violable; the winning candidate need not satisfy all constraints, as long as for any rival candidate that does better than the winner on some constraint, there is a higher ranked constraint on which the winner does better than that rival.

Some optimality theorists prefer the use of comparative tableaux, as described in Prince (2002). Comparative tableaux display the same information as the classic or "flyspeck" tableaux, but the information is presented in such a way that it highlights the most crucial information. For instance, the tableau above would be rendered in the following way.

Each row in a comparative tableau represents a winner-loser pair, rather than an individual candidate. In the cells where the constraints assess the winner-loser pairs, there is a W if the constraint in that column prefers the winner, an L if the constraint prefers the loser, and an e if the constraint does not differentiate between the pair. Presenting the data in this way makes it easier to make generalizations. For instance, in order to have a consistent ranking some W must dominate all L's. Brasoveanu and Prince (2005) describe a process known as fusion and the various ways of presenting data in a comparative tableau in order to achieve the necessary and sufficient conditions for a given argument.