J. L. García Lapresta, M. Martínez Panero
In this paper, we have considered the dense rank for assigning positions to objects in weak orders (or complete preorders). If we arrange the objects in tiers (i.e., indifference classes), the dense rank assigns position 1 to all the objects in the top tier, 2 to all the objects in the second tier, and so on. We have proposed a formal framework to analyze the dense rank when compared to other well-known position operators such as the (standard) rank and the mid-rank. As the main results, we have provided two different axiomatic characterizations which determine the dense rank by considering position invariance conditions along horizontal extensions (duplication), as well as through vertical reductions and movements (truncation, upwards or downwards independency).
Keywords: preferences; linear orders; weak orders; positions; ranking level; dense rank.
Scheduled
Data Analysis
November 7, 2023 6:40 PM
HC2: Canónigos Room 2