When more choice means less freedom: a note on candidate sets and typologies

This is perhaps the kind of thing that seems obvious in hindsight, but we initially thought that our typology generation algorithm had a bug when it produced the following results: (1) Using the constraints ONSET, NOCODA, DEP-C, DEP-V, MAX to model the CV-syllable theory of Prince and Smolensky (1993:ch 6) over the 14 forms in the input set CV 3 = 3 i=1 {C, V} i (i.e., all strings of C and V up to length three): i. the Optimality Theory (OT) typology has 12 languages, ii. the Harmonic Grammar (HG) typology has 23 languages (all 12 of the OT patterns plus 11 more patterns with cumulativity), iii. but, generating an HG typology using OT candidates yields 38 languages. For almost all inputs in CV 3 , the set of contenders (i.e., non-harmonically-bounded candidates) is the same under the ranked constraint interactions of Optimality Theory (OT; Prince and Smolensky 1993) and the weighted interactions of Harmonic Grammar (HG; Legendre et al. 1990). However, two of the input forms, /VVC/ and /CCC/, respectively have 1 and 2 extra contenders under weighting. These 1