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Mathematical Topics on Representations of Ordered Structures and Utility Theory

Part of the Studies in Systems, Decision and Control Book Series (volume 263)

Editors: Bosi, Gianni; Campión, María J.; Candeal, Juan C.; Indurain, Esteban

DOI: 10.1007/978-3-030-34226-5

ISBN: 978-3-030-34225-8

Publisher: Springer International Publishing - Springer Journals

Jan 24, 2020

1 - 10 of 19 Chapters

LitStream

Topology and Preference Relations

Beardon, A. F.

Pages: 3 –21

[In this essay we assume familiarity with the basic ideas in mathematical economics, and we discuss the influence of topological ideas on the theory of preference relations and utility functions.]
LitStream

The Existence and the Non-existence of Utility Functions in Order-Theoretic, Algebraic and Topological Environments

Candeal, Juan C.

Pages: 23 –45

[This paper reviews both the representation problem and the non-representation problem in utility theory. Beginning with the classical ordinal approach, I then move to also consider certain algebraic and topological environments. Some applications to social choice and measurement theory of the...
LitStream

Open Questions in Utility Theory

Campión, María J.; Indurain, Esteban

Pages: 47 –81

[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...
LitStream

Representations of Interval Orders on Connected Separable Topological Spaces

Rébillé, Yann

Pages: 85 –108

[We establish a partial continuous interval representation for interval orders preferences on connected separable topological spaces. Then we provide a generalization of interval representations of interval orders when a continuous strict weak order is given. This allows one to obtain for...
LitStream

Searching for a Debreu’s Open Gap Lemma for Semiorders

Estevan, Asier

Pages: 109 –128

[In 1956 R. D. Luce introduced the notion of a semiorder to deal with indifference relations in the representation of a preference. During several years the problem of finding a utility function was studied until a representability characterization was found. However, there was almost no results...
LitStream

A Note on Candeal and Induráin’s Semiorder Separability Condition

Bouyssou, Denis; Pirlot, Marc

Pages: 129 –141

[We show that the semiorder separability condition used by Candeal and Induráin in their characterization of semiorders having a strict representation with positive threshold can be factorized into two conditions. The first says that the trace of the semiorder must have a numerical...
LitStream

Chain Representations of Nested Families of Biorders

Bouyssou, Denis; Doignon, Jean-Paul

Pages: 143 –169

[Among the real-valued representations of nested families of biorders some representations reflect the nestedness of the family in a simple way. Calling them chain representations, we prove their existence in the finite and countably infinite cases. For the general case, we obtain chain...
LitStream

A Note on Representable Group Topologies

Chis, C.; Künzi, H.-P. A.; Sanchis, M.

Pages: 171 –186

[We study natural topologies in the sense of Debreu in the poset of topological group topologies on a topological group. We call this kind of topologies g-topologies. To be precise, groups admitting a non-totally disconnected g-natural topology as well as the non-totally disconnected g-topologies...
LitStream

Preferences in Abstract Convex Structures

Cardin, Marta

Pages: 187 –195

[Convexity of preferences is a canonical assumption in economic theory. In this paper we study a generalized definition of convex preferences that relies on the notion of a convex space, that is an abstraction of the standard notion of convexity in a linear space. We introduce also betweenness...
LitStream

Strictly Monotonic Preferences

Hervés-Beloso, Carlos; Monteiro, Paulo K.

Pages: 197 –209

[Monotonicity assumptions of preferences are natural and useful. A strictly monotonic preference is such that an increase in even only one commodity consumption is always strictly preferred. However, when we consider a continuum of commodities, it is not easy to find examples of strictly...

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