On the priority vector associated with a fuzzy preference relation and a multiplicative preference relation.

We propose two straightforward methods for deriving the priority vector associated with a fuzzy preference relation. Then, using transformations between multiplicative preference relations and fuzzy preference relations, we study the relationships between the priority vectors associated with these two types of preference relations.pairwise comparison matrix; fuzzy preference relation; priority vector

Can intergenerational equity be operationalized?

A long Utilitarian tradition has the ideal of equal regard for all individuals, both those now living and those yet to be born. The literature formalizes this ideal as asking for a preference relation on the space of infinite utility streams that is complete, transitive, invariant to finite permutations, and respects the Pareto ordering; an ethical preference relation, for short. This paper argues that operationalizing this ideal is problematic. Most simply, every ethical preference relation has the property that almost all (in the sense of outer measure) pairs of utility streams are indifferent. Even if we abandon completeness and respect for the Pareto ordering, every irreflexive preference relation that is invariant to finite permutations has the property that almost all pairs of utility streams are incomparable (not strictly ranked). Moreover, no ethical preference relation can be measurable. As a consequence, the existence of an ethical preference relation is independent of the axioms used in almost all of formal economics and all of classical analysis. Finally, even if an ethical preference relation exists, it cannot be "explicitly described." These results have implications for game theory, for macroeconomics, and for economic development.Intergenerational equity, infinite utility streams, long run averages, overtaking criterion, Utilitarianism

The Fundamental Theorems of Welfare Economics in a Non-Welfaristic Approach

This paper investigates extensions of the two fundamental theorems of welfare economics to the framework in which each agent is endowed with three types of preference relations: an allocation preference relation, an opportunity preference relation, and an overall preference relation. It is shown that, under certain conditions, the two theorems can be extended. It is also pointed out that the conditions underlying the positive results are restrictive.

A utility representation theorem with weaker continuity condition

We prove that a preference relation which is continuous on every straight line has a utility representation if its domain is a convex subset of a finite dimensional vector space. Our condition on the domain of a preference relation is stronger than Eilenberg (1941) and Debreu (1959, 1964), but our condition on the continuity of a preference relation is strictly weaker than theirs.linear continuity, utility representation

Towards an Ontological Modelling of Preference Relations

Preference relations are intensively studied in Economics, but they are also approached in AI, Knowledge Representation, and Conceptual Modelling, as they provide a key concept in a variety of domains of application. In this paper, we propose an ontological foundation of preference relations to formalise their essential aspects across domains. Firstly, we shall discuss what is the ontological status of the relata of a preference relation. Secondly, we investigate the place of preference relations within a rich taxonomy of relations (e.g. we ask whether they are internal or external, essential or contingent, descriptive or nondescriptive relations). Finally, we provide an ontological modelling of preference relation as a module of a foundational (or upper) ontology (viz. OntoUML). The aim of this paper is to provide a sharable foundational theory of preference relation that foster interoperability across the heterogeneous domains of application of preference relations

Expected Utility Theory without the Completeness Axiom

We study axiomatically the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteries by means of a set of von Neumann-Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well-defined sense.Expected utility, incomplete preferences