In a recent paper Samek-Lodovici and Prince (1999) show: (i) that all the potential winners (harmonically unbounded candidates) can be determined in a ranking independent way, and (ii) that this set of potential winners is finite in number. However, they did not consider the influence of sympathetic constraints (McCarthy, 1999, 2003) on their results. These constraints can promote perpetual losers to the set of potential winners. With sympathetic constraints, the finiteness of the set of potential winners is therefore in question. Also, the violations assigned by sympathetic constraints are indirectly ranking dependent (via the choice of the sympathetic candidate). This paper shows that: (i) the set of potential winners is still finite even in a version of OT with sympathetic constraints, and (ii) that the harmonically bounded candidates that sympathetic constraints can promote to the set of potential winners, can be determined in a ranking independent way. It follows that Samek-Lodovici and Prince’s results are also valid in an OT grammar with sympathy constraints.
 

This is an important result for two reasons: (i) If for any given input the set of potential winners were to be infinite, then an infinite typology would be predicted—there will be infinitely many possible languages. However, if the set of potential winners is finite, then only a finite typology is predicted—i.e. it results in a much more restrictive theory. (ii) If the set of potential winners can only be determined in a ranking dependent manner, then the grammar of every language (a ranking of CON) has to consider the full infinite candidate set. However, if the finite set of potential winners can be determined without recourse to a specific grammar (a specific ranking of CON), then it is in principle possible to weed out the perpetual losers before the grammar of a specific language comes into play. The grammar of any given language then needs to consider only the finite set of potential winners.