The traditional single-candidate learning model for anaphora resolution considers the antecedent candidates of an anaphor in isolation, and thus cannot effectively capture the preference relationships between competing candidates for its learning and resolution. To deal with this problem, we propose a twin-candidate model for anaphora resolution. The main idea behind the model is to recast anaphora resolution as a preference classification problem. Specifically, the model learns a classifier that determines the preference between competing candidates, and, during resolution, chooses the antecedent of a given anaphor based on the ranking of the candidates. We present in detail the framework of the twin-candidate model for anaphora resolution. Further, we explore how to deploy the model in the more complicated coreference resolution task. We evaluate the twin-candidate model in different domains using the Automatic Content Extraction data sets. The experimental results indicate that our twin-candidate model is superior to the single-candidate model for the task of pronominal anaphora resolution. For the task of coreference resolution, it also performs equally well, or better.