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Preferences can be aggregated using voting rules. We consider here the family of rules which perform a sequence of pairwise majority comparisons between two candidates. The winner thus depends on the chosen sequence of comparisons, which can be represented by a binary tree. We address the difficulty of computing candidates that win for some trees, and then introduce and study the notion of fair winner, ie candidates who win in a balanced tree. We then consider the situation where we lack complete informations about preferences, and determine the computational complexity of computing winners in this case.