Choice by Lexicographic Semiorders

We propose an extension of Tversky's lexicographic semiorder to a model of boundedly rational choice. We explore the connection with sequential rationalisability of choice, and we provide axiomatic characterisations of both models in terms of observable choice data.lexicographic semiorders, bounded rationality, revealed preference, choice

Biased quantitative measurement of interval ordered homothetic preferences

We represent interval ordered homothetic preferences with a quantitative homothetic utility function and a multiplicative bias. When preferences are weakly ordered (i.e. when indifference is transitive), such a bias equals 1. When indifference is intransitive, the biasing factor is a positive function smaller than 1 and measures a threshold of indifference. We show that the bias is constant if and only if preferences are semiordered, and we identify conditions ensuring a linear utility function. We illustrate our approach with indifference sets on a two dimensional commodity space.Weak order, semiorder, interval order, intransitive indifference, independence, homothetic, representation, linear utility

Choice by lexicographic semiorders

In Tversky's (1969) model of a lexicographic semiorder, preference is generated by the sequential application of numerical criteria, by declaring an alternative x better than an alternative y if the first criterion that distinguishes between x and y ranks x higher than y by an amount exceeding a fixed threshold. We generalize this idea to a fully-fledged model of boundedly rational choice. We explore the connection with sequential rationalizability of choice (Apesteguia and Ballester 2009, Manzini and Mariotti 2007), and we provide axiomatic characterizations of both models in terms of observable choice data.Lexicographic semiorders, bounded rationality, revealed preference, choice

Multiattribute preference models with reference points

In the context of multiple attribute decision making, preference models making use of reference points in an ordinal way have recently been introduced in the literature. This text proposes an axiomatic analysis of such models, with a particular emphasis on the case in which there is only one reference point. Our analysis uses a general conjoint measurement model resting on the study of traces induced on attributes by the preference relation and using conditions guaranteeing that these traces are complete. Models using reference points are shown to be a particular case of this general model. The number of reference points is linked to the number of equivalence classes distinguished by the traces. When there is only one reference point, the in- duced traces are quite rough, distinguishing at most two distinct equivalence classes. We study the relation between the model using a single reference point and other preference models proposed in the literature.

Open questions in utility theory

Throughout this paper, our main idea is to explore different classical questions arising in Utility Theory, with a particular attention to those that lean on numerical representations of preference orderings. We intend to present a survey of open questions in that discipline, also showing the state-of-art of the corresponding literature.This work is partially supported by the research projects ECO2015-65031-R, MTM2015-63608-P (MINECO/ AEI-FEDER, UE), and TIN2016-77356-P (MINECO/ AEI-FEDER, UE)

Continuous representability of interval orders: The topological compatibility setting

In this paper, we go further on the problem of the continuous numerical representability of interval orders defined on topological spaces. A new condition of compatibility between the given topology and the indifference associated to the main trace of an interval order is introduced. Provided that this condition is fulfilled, a semiorder has a continuous interval order representation through a pair of continuous real-valued functions. Other necessary and sufficient conditions for the continuous representability of interval orders are also discussed, and, in particular, a characterization is achieved for the particular case of interval orders defined on a topological space of finite support