A Characterization of Lexicographic Preferences

This paper characterizes lexicographic preferences over alternatives that are identified by a finite number of attributes. Our characterization is based on two key concepts: a weaker notion of continuity called “mild continuity” (strict preference order between any two alternatives that are different with respect to every attribute is preserved around their small neighborhoods) and an “unhappy set” (any alternative outside such a set is preferred to all alternatives inside). Three key aspects of our characterization are as follows: (i) we use continuity arguments; (ii) we use the stepwise approach of looking at two attributes at a time; and (iii) in contrast with the previous literature, we do not impose noncompensation on the preference and consider an alternative weaker condition.

A Many-valued Logic for Lexicographic Preference Representation

We introduce lexicographic logic, an extension of propositional logic that can represent a variety of preferences, most notably lexicographic ones. The proposed logic supports a simple new connective whose semantics can be defined in terms of finite lists of truth values. We demonstrate that, despite the well-known theoretical limitations that pose barriers to the quantitative representation of lexicographic preferences, there exists a subset of the rational numbers over which the proposed new connective can be naturally defined. Lexicographic logic can be used to define in a simple way some well-known preferential operators, like "A and if possible B", and "A or failing that B". We argue that the new logic is an effective formalism for ranking query results according to the satisfaction level of user preferences.

A neutral core of degressively proportional allocations under lexicographic preferences of agents

One of the main problems of practical applications of degressively proportional allocations of goods and burdens is lack of uniqueness of this principle. Even under given boundary conditions of allocation, i.e. determined minimal and maximal amounts of a good that can be assigned in a given allocation, there are usually many feasible solutions. The lack of formal rules of allocation is the reason why the allocation is typically a result of negotiations among its agents. A number of allocations favor some of agents or their groups, therefore other agents cannot accept them. The aim of this paper is to indicate a way of reducing the set of all feasible solutions exclusively to those that are neutral to all agents. As a result of the term of lexicographic preference of allocation agents defined on the basis of the relation theory followed by a numerical analysis of sets of all feasible solutions, it is possible to determine a core of this set in the form of a subset of all feasible solutions that are acceptable by all agents. In addition, this subset can be further divided into smaller subsets with regard to the degree of acceptance of their elements. Theoretical analysis is complemented by case studies, one of which is application of this idea to the allocation of seats in the European Parliament among the member states of the European Union.

Econometric Modelling: Extensions

This chapter is devoted to advanced issues of econometric modelling. The topics covered are, among others, models in willingness to pay space, the meaning of scale heterogeneity in discrete choice models and the application of various information processing rules such as random regret minimisation or attribute non-attendance. Other topics are anchoring and learning effects when respondents move through a sequence of choice tasks as well as different information processing strategies such as lexicographic preferences or choices based on elimination-by-aspects.

Experimental Evaluation of Three Value Recommendation Methods in Interactive Configuration

The present work deals with the recommendation of values in interactive configuration, with no prior knowledge about the user, but given a list of products previously configured and bought by other users ("sales histories"). The basic idea is to recommend, for a given variable at a given step of the configuration process, a value that has been chosen by other users in a similar context, where the context is defined by the variables that have already been decided, and the values that the current user has chosen for these variables. From this point, two directions have been explored. The first one is to select a set of similar configurations in the sales history (typically, the k closest ones, using a distance measure) and to compute the best recommendation from this set - this is the line proposed by [Coster et al., 2002]. The second one, that we propose here, is to learn a model from the entire sample as representation of the users' preferences, and to use it to recommend a pertinent value; three families of models are experimented: the Bayesian networks, the naive Bayesian networks and the lexicographic preferences trees.

On the clock of the combinatorial clock auction

The combinatorial clock auction (CCA) has frequently been used in recent spectrum auctions. It combines a dynamic clock phase and a one‐off supplementary round. The winning allocation and the corresponding prices are determined by the Vickrey–Clarke–Groves rules. These rules should encourage truthful bidding, whereas the clock phase is intended to reveal information. We inquire into the role of the clock when bidders have lexicographic preferences for raising rivals' costs. We show that in an efficient equilibrium, the clock cannot fully reveal bidders' types. In the spirit of the ratchet effect, in the supplementary round competitors extract surplus from strong bidders whose type is revealed. We also show that if there is substantial room for information revelation, that is, if the uncertainty about the final allocation is large, all equilibria of the CCA are inefficient. Qualitative features of our equilibria are in line with evidence concerning bidding behavior in some recent CCAs.