Continuous SSB representation of preferences

Kód výsledku v IS VaVaI

RIV/67985556:_____/18:00491011 - isvavai.cz

Výsledek na webu

http://dx.doi.org/10.1016/j.jmateco.2018.06.005

DOI - Digital Object Identifier

10.1016/j.jmateco.2018.06.005

Jazyk výsledku

angličtina

Název v původním jazyce

Continuous SSB representation of preferences

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Continuous SSB representation of preferences

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50201 - Economic Theory

Projekt

GA17-08182S: Matematické modelování netranzitivních preferencí

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Economics

ISSN

0304-4068

e-ISSN

—

Svazek periodika

77

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

7

Strana od-do

59-65

Kód UT WoS článku

000442713800007

EID výsledku v databázi Scopus

2-s2.0-85049434709