Constraint summation in phonological theory

The classical constraints used in phonological theory apply to a single candidate at a time. Yet, some proposals in the phonological literature have enriched the classical constraint toolkit with constraints that instead apply to multiple candidates simultaneously. For instance, Dispersion Theory (Flemming 2002, 2004, 2008) adopts distinctiveness constraints that penalize pairs of surface forms which are not sufficiently dispersed. Also, some approaches to paradigm uniformity effects (Kenstowicz 1997; McCarthy 2005) adopt Optimal Paradigm faithfulness constraints that penalize pairs of stems in a paradigm which are not sufficiently similar. As a consequence, these approaches need to “lift” the classical constraints from a single candidate to multiple candidates by summing constraint violations across multiple candidates.Is this assumption of constraint summation typologically innocuous? Or do the classical constraints make different typological predictions when they are summed, independently of the presence of distinctiveness or optimal paradigm faithfulness constraints? The answer depends on the underlying model of constraint optimization, namely on how the profiles of constraint violations are ordered to determine the smallest one. Extending an independent result by Prince (2015), this paper characterizes those orderings for which the assumption of constraint summation is typologically innocuous. As a corollary, the typological innocuousness of constraint summation is established within both Optimality Theory and Harmonic Grammar.