Original title: Theory of SSB Representation of Preferences Revised
Authors: Pištěk, Miroslav
Document type: Papers
Conference/Event: Czech-Japan Seminar on Data Analysis and Decision Making 2019 (CJS’19) /22./, Nový Světlov (CZ), 20190925
Year: 2019
Language: eng
Abstract: 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\nthe 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.
Keywords: inductive linear topology; probability measures; topological vector space
Project no.: GA17-08182S (CEP)
Funding provider: GA ČR
Host item entry: Proceedings of the 22nd Czech-Japan Seminar on Data Analysis and Decision Making (CJS’19), ISBN 978-80-7378-400-3

Institution: Institute of Information Theory and Automation AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: http://library.utia.cas.cz/separaty/2019/MTR/pistek-0510321.pdf
Original record: http://hdl.handle.net/11104/0302533

Permalink: http://www.nusl.cz/ntk/nusl-407961


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