We describe the first automatic approach for merging coreference annotations obtained from multiple annotators into a single gold standard. This merging is subject to certain linguistic hard constraints and optimisation criteria that prefer solutions with minimal divergence from annotators. The representation involves an equivalence relation over a large number of elements. We use Answer Set Programming to describe two representations of the problem and four objective functions suitable for different data-sets. We provide two structurally different real-world benchmark data-sets based on the METU-Sabanci Turkish Treebank and we report our experiences in using the Gringo, Clasp and Wasp tools for computing optimal adjudication results on these data-sets.