RT info:eu-repo/semantics/article
T1 Characterizing competition ranks within a comprehensive family of position operators
A1 Martínez Panero, Miguel
A1 García Lapresta, José Luis
K1 Preference learning
K1 Linear orders
K1 Weak orders
K1 Positions
K1 Ranks
K1 12 Matemáticas
AB There is only one way to assign positions to objects arranged in linear orders: following the sequence of naturalnumbers (1, 2, 3, 4, …). However, in weak orders, where ties arise, there are different possibilities to assignpositions to tied objects. In this paper, we focus mainly on three relevant cases: the standard, modified, andfractional ranks. They are differentiated by the spaces that appear after, before, or on either side of the positionvalues corresponding to the objects that are in a tie. For instance, if two objects are tied and are located immedi-ately below the top object, these ranks assign the positions (1, 2, 2, 4, …), (1, 3, 3, 4, …), and (1, 2.5, 2.5, 4, …),respectively. Collectively, and because of the common properties shown here, we call them “competition ranks”.In this paper, we characterize a parameterized family of position operators which includes the competition ranks.We also provide specific axiomatizations of each of them, taking into account the spaces in the sequence of as-signed position numbers. It is shown why the dense rank (1, 2, 2, 3, …), another position operator where gapsdo not appear, is an essentially different approach. Furthermore, interesting duality relationships are revealedbetween the competition ranks and between the properties introduced to characterize them, which allow usto understand their internal logic and connections. Different examples, mainly from sports, bibliometrics, etc.,illustrate the introduced concepts
PB Elsevier
SN 0377-2217
YR 2025
FD 2025
LK https://uvadoc.uva.es/handle/10324/79452
UL https://uvadoc.uva.es/handle/10324/79452
LA eng
NO European Journal of Operational Research, 2025.
NO Producción Científica
DS UVaDOC
RD 02-dic-2025