Tuesday, November 13, 2007

This series is part of the Politics and the Election series
The Kemeny-Young method is a voting system that uses preferential ballots, pairwise comparison counts, and sequence scores to identify the most popular choice, and also identify the second-most popular choice, the third-most popular choice, and so on down to the least-popular choice. This is a Condorcet method because if there is a Condorcet winner it is always the most popular choice.
The system was developed

Single member

  • Plurality (first-past-the-post)
    Two-round system
    Exhaustive ballot
    Preferential systems

    • Satisfy Condorcet criterion

      • Condorcet method
        Copeland's method
        Kemeny-Young method
        Minimax Condorcet
        Nanson's method
        Ranked Pairs
        Schulze method
        Runoff voting

        • Bucklin voting
          Coombs' method
          Non-rank methods

          • Approval voting
            Range voting

            • Proportional representation

              • Cumulative voting
                Party-list (Open and Closed)

                • D'Hondt method
                  Highest averages method
                  Largest remainder method
                  Sainte-Laguë method
                  Single transferable vote
                  Semi-proportional representation

                  • Additional Member System

                    • Parallel voting
                      Cumulative voting
                      Single non-transferable vote
                      Non-proportional multi-memberKemeny-Young method representation

                      • Bloc voting
                        Limited voting
                        Random Selection

                        • Sortition Characteristics
                          Calculating all sequence scores requires time proportional to N!, where N is the number of choices. This is significantly more time than required for most other voting methods. This calculation time is superpolynomial in the number of choices, so it does not meet the polynomial runtime criteria.
                          Not every sequence score needs to be calculated to identify the Kemeny ranking. Fast calculation methods, including those based on linear programming, allow the computation of the Kemeny ranking for as many as 40 choices.

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