In this contribution, we analyze, from a formal perspective, the dense, standard, modified and fractional ranks. They assign a position to each alternative of a weak order from different points of view, generalizing the natural positions of linear orders. We show that the standard, modified and fractional ranks belong to a family of parameterized ranks. However, the dense rank has a different behavior, and it does not belong to that family. We provide some properties that all the mentioned ranks satisfy and we also show a characterization of the dense rank through two independent properties.

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A Positional Analysis of Ranking Procedures

  • José Luis García-Lapresta,
  • Miguel Martínez-Panero

摘要

In this contribution, we analyze, from a formal perspective, the dense, standard, modified and fractional ranks. They assign a position to each alternative of a weak order from different points of view, generalizing the natural positions of linear orders. We show that the standard, modified and fractional ranks belong to a family of parameterized ranks. However, the dense rank has a different behavior, and it does not belong to that family. We provide some properties that all the mentioned ranks satisfy and we also show a characterization of the dense rank through two independent properties.