We introduce two first-order graph-based dependency parsers achieving a new state of the art. The first is a consensus parser built from an ensemble of independently trained greedy LSTM transition-based parsers with different random initializations. We cast this approach as minimum Bayes risk decoding (under the Hamming cost) and argue that weaker consensus within the ensemble is a useful signal of difficulty or ambiguity. The second parser is a "distillation" of the ensemble into a single model. We train the distillation parser using a structured hinge loss objective with a novel cost that incorporates ensemble uncertainty estimates for each possible attachment, thereby avoiding the intractable cross-entropy computations required by applying standard distillation objectives to problems with structured outputs. The first-order distillation parser matches or surpasses the state of the art on English, Chinese, and German.
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