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SSB representation of preferences: Weakening of convexity assumptions

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  • Pištěk, Miroslav

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 such topological basis, thus weakening the convexity assumption. Such a unifying approach to SSB representation leads, moreover, to a stronger existence result for a maximal element and opens a way for a non-probabilistic interpretation of the algebraic theory. Note finally that our method of using powerful topological techniques to derive purely algebraic result may be of general interest.

Suggested Citation

  • Pištěk, Miroslav, 2019. "SSB representation of preferences: Weakening of convexity assumptions," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 84-88.
    • Handle: RePEc:eee:mateco:v:83:y:2019:i:c:p:84-88
    DOI: 10.1016/j.jmateco.2019.04.006
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