Continuity postulates and solvability axioms in economic theory and in mathematical psychology: a consolidation of the theory of individual choice

Aniruddha Ghosh (), M. Khan and Metin Uyanık
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Aniruddha Ghosh: Johns Hopkins University

Theory and Decision, 2023, vol. 94, issue 2, No 2, 189-210

Abstract: Abstract This paper presents four theorems that connect continuity postulates in mathematical economics to solvability axioms in mathematical psychology, and ranks them under alternative supplementary assumptions. Theorem 1 connects notions of continuity (full, separate, Wold, weak Wold, Archimedean, mixture) with those of solvability (restricted, unrestricted) under the completeness and transitivity of a binary relation. Theorem 2 uses the primitive notion of a separately continuous function to answer the question when an analogous property on a relation is fully continuous. Theorem 3 provides a portmanteau theorem on the equivalence between restricted solvability and various notions of continuity under weak monotonicity. Finally, Theorem 4 presents a variant of Theorem 3 that follows Theorem 1 in dispensing with the dimensionality requirement and in providing partial equivalences between solvability and continuity notions. These theorems are motivated for their potential use in representation theorems.

Keywords: Wold-continuity; Separate continuity; Restricted solvability; Conjoint measurement (search for similar items in EconPapers)
Date: 2023
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Working Paper: Continuity Postulates and Solvability Axioms in Economic Theory and in Mathematical Psychology: A Consolidation of the Theory of Individual Choice (2022)
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DOI: 10.1007/s11238-022-09890-z

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