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Minimean optimality in sorting algorithms

We prove that an algorithm for selecting both the minimum and maximum element from an unordered set is minimean optimal. This algorithm had already been shown to be minimax optimal. The circumstances in which the same algorithm is optimum for both norms leads to a conjecture relating both norms. The method of proof utilizes a new idea in the theory of sorting optimality, namely degree information of the Hasse digraphs.