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