Semiorders and continuous Scott–Suppes representations. Debreu’s Open Gap Lemma with a threshold
Fecha
2023Autor
Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión publicada / Argitaratu den bertsioa
Identificador del proyecto
AEI//PID2020-119703RB-I00 AEI//PID2021-127799NB-I00
Impacto
|
10.1016/j.jmp.2023.102754
Resumen
The problem of finding a utility function for a semiorder has been studied since 1956, when the notion of semiorder was introduced by Luce. But few results on continuity and no result like Debreu’s Open Gap Lemma, but for semiorders, was found. In the present paper, we characterize semiorders that accept a continuous representation (in the sense of Scott–Suppes). Two weaker theorems are also prov ...
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The problem of finding a utility function for a semiorder has been studied since 1956, when the notion of semiorder was introduced by Luce. But few results on continuity and no result like Debreu’s Open Gap Lemma, but for semiorders, was found. In the present paper, we characterize semiorders that accept a continuous representation (in the sense of Scott–Suppes). Two weaker theorems are also proved, which provide a programmable approach to Open Gap Lemma, yield a Debreu’s Lemma for semiorders, and enable us to remove the open-closed and closed-open gaps of a set of reals while keeping the threshold. [--]
Materias
Continuity,
Debreu's Open Gap Lemma,
Scott-Suppes representation,
Semiorders
Editor
Elsevier
Publicado en
Journal of Mathematical Psychology 113 (2023) 102754
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Research in Business and Economics - INARBE
Versión del editor
Entidades Financiadoras
Asier Estevan acknowledges financial support from the Ministry of Science and Innovation of Spain under grants PID2020-119703RB-I00 and PID2021-127799NB-I00 as well as from the UPNA, Spain under grant JIUPNA19-2022.