Theory of SSB Representation of Preferences Revised

0510321 - ÚTIA 2020 RIV CZ eng K - Conference Paper (Czech conference)
Pištěk, Miroslav
Theory of SSB Representation of Preferences Revised.
Proceedings of the 22nd Czech-Japan Seminar on Data Analysis and Decision Making (CJS’19). Praha: MatfyzPress, 2019 - (Inuiguchi, M.; Jiroušek, R.; Kratochvíl, V.), s. 145-149. ISBN 978-80-7378-400-3.
[Czech-Japan Seminar on Data Analysis and Decision Making 2019 (CJS’19) /22./. Nový Světlov (CZ), 25.09.2019-28.09.2019]
R&D Projects: GA ČR GA17-08182S
Institutional support: RVO:67985556
Keywords : probability measures * inductive linear topology * topological vector space
OECD category: Pure mathematics
http://library.utia.cas.cz/separaty/2019/MTR/pistek-0510321.pdf

A continuous skew-symmetric bilinear (SSB) representation of preferences has recently been proposed in a topological vector space, assuming a weaker notion of convexity of preferences than in the classical (algebraic) case. Equipping a linear vector space with the so-called inductive linear topology, we derive the algebraic SSB representation on a topological basis, thus weakening
the convexity assumption. Such a unifying approach to SSB representation permits also to fully discuss the relationship of topological and algebraic axioms of continuity, and leads to a stronger existence result for a maximal element. 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 in this context.
Permanent Link: http://hdl.handle.net/11104/0302533