We propose a new single-winner election method ("Schulze method") and prove that it satisfies many academic criteria (e.g. monotonicity, reversal symmetry, resolvability, independence of clones, Condorcet criterion, k-consistency, polynomial runtime). We then generalize this method to proportional representation by the single transferable vote ("Schulze STV") and to methods to calculate a proportional ranking ("Schulze proportional ranking"). Furthermore, we propose a generalization of the

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... rcet criterion to multi-winner elections. This paper contains a large number of examples to illustrate the proposed methods.