Lexicographic decomposition of chains and the concept of a planar chain

In an earlier paper [Journal of Mathematical Economics, 37 (2002) 17-38], we proved that if a preference relation on a commodity space is non-representable by a real-valued function then that chain is necessarily a long chain, a planar chain, an Aronszajn-like chain or a Souslin chain. In this paper, we study the class of planar chains, the simplest example of which is the Debreu chain (R-2, <(l)). (C) 2002 Elsevier Science B.V. All rights reserved.

Multiple Public Goods and Lexicographic Preferences Replacement Principle.

We study the problem of locating two public goods for a group of agents with single-peaked preferences over an interval. An alternative specifies a location for each public good. In Miyagawa (1998), each agent consumes only his most preferred public good without rivalry. We extend preferences lexicographically and characterize the class of single-peaked preference rules by Pareto-optimality and replacement-domination. This result is considerably different from the corresponding characterization by Miyagawa (2001a).

Evolving decision trees with beam search-based initialization and lexicographic multi-objective evaluation

Decision tree induction algorithms represent one of the most popular techniques for dealing with classification problems. However, traditional decision-tree induction algorithms implement a greedy approach for node splitting that is inherently susceptible to local optima convergence. Evolutionary algorithms can avoid the problems associated with a greedy search and have been successfully employed to the induction of decision trees. Previously, we proposed a lexicographic multi-objective genetic algorithm for decision-tree induction, named LEGAL-Tree. In this work, we propose extending this approach substantially, particularly w.r.t. two important evolutionary aspects: the initialization of the population and the fitness function. We carry out a comprehensive set of experiments to validate our extended algorithm. The experimental results suggest that it is able to outperform both traditional algorithms for decision-tree induction and another evolutionary algorithm in a variety of application domains.

Lexicographic allocations and extreme core payoffs: the case of assignment games

We consider various lexicographic allocation procedures for coalitional games with transferable utility where the payoffs are computed in an externally given order of the players. The common feature of the methods is that if the allocation is in the core, it is an extreme point of the core. We first investigate the general relationship between these allocations and obtain two hierarchies on the class of balanced games. Secondly, we focus on assignment games and sharpen some of these general relationship. Our main result is the coincidence of the sets of lemarals (vectors of lexicographic maxima over the set of dual coalitionally rational payoff vectors), lemacols (vectors of lexicographic maxima over the core) and extreme core points. As byproducts, we show that, similarly to the core and the coalitionally rational payoff set, also the dual coalitionally rational payoff set of an assignment game is determined by the individual and mixed-pair coalitions, and present an efficient and elementary way to compute these basic dual coalitional values. This provides a way to compute the Alexia value (the average of all lemacols) with no need to obtain the whole coalitional function of the dual assignment game.

Spectra and Laplacian spectra of arbitrary powers of lexicographic products of graphs

Consider two graphs G and H. Let H^k[G] be the lexicographic product of H^k and G, where H^k is the lexicographic product of the graph H by itself k times. In this paper, we determine the spectrum of H^k[G]H and H^k when G and H are regular and the Laplacian spectrum of H^k[G] and H^k for G and H arbitrary. Particular emphasis is given to the least eigenvalue of the adjacency matrix in the case of lexicographic powers of regular graphs, and to the algebraic connectivity and the largest Laplacian eigenvalues in the case of lexicographic powers of arbitrary graphs. This approach allows the determination of the spectrum (in case of regular graphs) and Laplacian spectrum (for arbitrary graphs) of huge graphs. As an example, the spectrum of the lexicographic power of the Petersen graph with the googol number (that is, 10^100 ) of vertices is determined. The paper finishes with the extension of some well known spectral and combinatorial invariant properties of graphs to its lexicographic powers.

Determining when the absolute state complexity of a Hermitian code achieves its DLP bound

Let g be the genus of the Hermitian function field H/F(q)2 and let C-L(D,mQ(infinity)) be a typical Hermitian code of length n. In [Des. Codes Cryptogr., to appear], we determined the dimension/length profile (DLP) lower bound on the state complexity of C-L(D,mQ(infinity)). Here we determine when this lower bound is tight and when it is not. For m less than or equal to n-2/2 or m greater than or equal to n-2/2 + 2g, the DLP lower bounds reach Wolf's upper bound on state complexity and thus are trivially tight. We begin by showing that for about half of the remaining values of m the DLP bounds cannot be tight. In these cases, we give a lower bound on the absolute state complexity of C-L(D,mQ(infinity)), which improves the DLP lower bound. Next we give a good coordinate order for C-L(D,mQ(infinity)). With this good order, the state complexity of C-L(D,mQ(infinity)) achieves its DLP bound (whenever this is possible). This coordinate order also provides an upper bound on the absolute state complexity of C-L(D,mQ(infinity)) (for those values of m for which the DLP bounds cannot be tight). Our bounds on absolute state complexity do not meet for some of these values of m, and this leaves open the question whether our coordinate order is best possible in these cases. A straightforward application of these results is that if C-L(D,mQ(infinity)) is self-dual, then its state complexity (with respect to the lexicographic coordinate order) achieves its DLP bound of n /2 - q(2)/4, and, in particular, so does its absolute state complexity.

On the iteration of Katsuno and Mendelzon update

In this dissertation we present a model for iteration of Katsuno and Mendelzon’s Update, inspired in the developments for iteration in AGM belief revision. We adapt Darwiche and Pearls’ postulates of iterated belief revision to update (as well as the independence postulate proposed in [BM06, JT07]) and show two families of such operators, based in natural [Bou96] and lexicographic revision [Nay94a, NPP03]. In all cases, we provide a possible worlds semantics of the models.

Colocaciones léxicas en dicconarios monolingües generales del español

El objetivo de la presente investigación es analizar el tratamiento que algunos de los diccionarios generales monolingües del español aparecidos en los últimos diez años han dado al fenómeno de las colocaciones léxicas, a saber, aquellas combinaciones de palabras que, desde el punto de vista de la norma, presentan ciertas restricciones combinatorias, esencialmente de carácter semántico, impuestas por el uso (Corpas: 1996). Los repertorios objeto de análisis han sido: el "Diccionario Salamanca de la lengua española", dirigido por Juan Gutiérrez (1996); el "Diccionario del español actual", de Manuel Seco, Olimpia Andrés y Gabino Ramos (1999); la vigésima segunda edición del diccionario de la RAE (2001); y el "Gran diccionario de uso del español actual. Basado en el corpus Cumbre", dirigido por Aquilino Sánchez (2001). Nuestro estudio se ha fundamentado en un corpus de 52 colocaciones léxicas confeccionado a partir del análisis de las subentradas contenidas en la letra "b" de cada uno de los diccionarios seleccionados. Posteriormente, hemos examinado las entradas correspondientes a cada uno de los elementos que constituyen la colocación (base y colocativo) con el fin de observar si los diccionarios estudiados dan cuenta de estas mismas combinaciones en otras partes del artículo lexicográfico, como son las definiciones o los ejemplos. A la hora de analizar la información lexicográfica hemos centrado nuestra atención en cuatro aspectos: a) la información contenida en las páginas preliminares de cada una de las obras; b) la ubicación de las colocaciones en el artículo lexicográfico; c) la asignación de la colocación a un artículo determinado; y d) la marcación gramatical.

Regions of rationality: Maps for bounded agents

An important problem in descriptive and prescriptive research in decision making is to identify regions of rationality, i.e., the areas for which heuristics are and are not effective. To map the contours of such regions, we derive probabilities that heuristics identify the best of m alternatives (m > 2) characterized by k attributes or cues (k > 1). The heuristics include a single variable (lexicographic), variations of elimination-by-aspects, equal weighting, hybrids of the preceding, and models exploiting dominance. We use twenty simulated and four empirical datasets for illustration. We further provide an overview by regressing heuristic performance on factors characterizing environments. Overall, sensible heuristics generally yield similar choices in many environments. However, selection of the appropriate heuristic can be important in some regions (e.g., if there is low inter-correlation among attributes/cues). Since our work assumes a hit or miss decision criterion, we conclude by outlining extensions for exploring the effects of different loss functions.

Simple models for multi-attribute choice with many alternatives: When it does and does not pay to face tradeoffs with binary attributes

Working Paper no longer available. Please contact the author.

Take-the-best and other simple strategies: Why and when they work 'well' in binary choice

The effectiveness of decision rules depends on characteristics of bothrules and environments. A theoretical analysis of environments specifiesthe relative predictive accuracies of the lexicographic rule 'take-the-best'(TTB) and other simple strategies for binary choice. We identify threefactors: how the environment weights variables; characteristics of choicesets; and error. For cases involving from three to five binary cues, TTBis effective across many environments. However, hybrids of equal weights(EW) and TTB models are more effective as environments become morecompensatory. In the presence of error, TTB and similar models do not predictmuch better than a naïve model that exploits dominance. We emphasizepsychological implications and the need for more complete theories of theenvironment that include the role of error.