Several NLP tasks are characterized by asymmetric data where one class label NONE, signifying the absence of any structure (named entity, coreference, relation, etc.) dominates all other classes. Classifiers built on such data typically have a higher precision and a lower recall and tend to overproduce the NONE class. We present a novel scheme for voting among a committee of classifiers that can significantly boost the recall in such situations. We demonstrate results showing up to a 16% relative improvement in ACE value for the 2004 ACE relation extraction task for English, Arabic and Chinese.