HAL CCSD Lexicographic decomposition of preferences Charon, Irène Hudry, Olivier Laboratoire Traitement et Communication de l'Information (LTCI) ; Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS) Mathématiques discrètes, Codage et Cryptographie (MC2) ; Laboratoire Traitement et Communication de l'Information (LTCI) ; Institut Mines-Télécom [Paris] (IMT)-Télécom Paris-Institut Mines-Télécom [Paris] (IMT)-Télécom Paris Département Informatique et Réseaux (INFRES) ; Télécom ParisTech International audience Electronic Notes in Discrete Mathematics hal-02286383 https://telecom-paris.hal.science/hal-02286383 https://telecom-paris.hal.science/hal-02286383 Electronic Notes in Discrete Mathematics, 2013, 42, pp.25-32 en Preferences Intransitivities Lexicographic Sum Lexicographic Model Lexicographic Decomposition Lexicographic Dimension [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA] info:eu-repo/semantics/article Journal articles The Ordinal Lexicographic Model, based on the lexicographic sum of relations, provides an explanation to intransitivities in preferences as shifts in choice criteria. The lexicographic sum R + R' between two preferences R and R' on a same finite set X is defined as follows: x is preferred to y with respect to R + R' when x is preferred to y with respect to R, or there is a tie between x and y with respect to R but x is preferred to y with respect to R'. If a preference R can be written as R = R1 + R2 + ... + Rk, (R1, R2, ..., Rk) is said to be a lexicographic decomposition (LD) of R. It means that a first criterion, expressed by R1, explains a part of R, a second criterion, expressed by R2, explains a part of R which is not explained by R1, and so on. Each relation Ri of the LD can be interpreted as a point of view, and the number k is the number of shifts in point of view in the decomposition. It is usually required from the relations of the LD to fulfil some structural properties,for instance to be partial orders. When a LD is possible, the usual question consists in computing, for any preference R, the minimum number d(R), called the lexicographic dimension of R, of relations involves in the LD in order to explain R. The aim of this paper is to provide some algebraic properties of the lexicographic sum +. 2013-06