Continuous SSB representation of preferences

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00491011" target="_blank" >RIV/67985556:_____/18:00491011 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1016/j.jmateco.2018.06.005" target="_blank" >http://dx.doi.org/10.1016/j.jmateco.2018.06.005</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmateco.2018.06.005" target="_blank" >10.1016/j.jmateco.2018.06.005</a>

Result language

angličtina

Original language name

Continuous SSB representation of preferences

Original language description

We propose a topological variant of skew-symmetric bilinear (SSB) representation of preferences. First, semi-Fishburn relations are defined by assuming convexity and coherence, a newly considered topological property. We show that lower and upper semi-Fishburn relations admit the existence of a minimal element and a maximal element, respectively. Then axiom of ‘‘balance’’ is stated and we prove that a binary relation has a continuous SSB representation if and only if it is a balanced (lower and upper semi-)Fishburn relation. The relationship between the above definitions and the original axioms of (algebraic) SSB representation is fully discussed. Finally, by applying this theory to probability measures, we show the existence of a maximal preferred measure for an infinite set of pure outcomes, thus generalizing all available existence theorems of (algebraic) SSB representation. Note that by using this framework to, e.g., finitely additive measures, one may develop a non-probabilistic variant of SSB representation as well.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

50201 - Economic Theory

Project

<a href="/en/project/GA17-08182S" target="_blank" >GA17-08182S: Mathematical Modelling of Intransitive Preferences</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Mathematical Economics

ISSN

0304-4068

e-ISSN

—

Volume of the periodical

77

Issue of the periodical within the volume

1

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

7

Pages from-to

59-65

UT code for WoS article

000442713800007

EID of the result in the Scopus database

2-s2.0-85049434709