Strategy-proof social choice with continuous separable preferences

Article Abstract:

A study has been conducted to determine whether a set of alternatives can be considered a product of Tychonoff spaces that satisfy the first axiom of countability and that any subset of a Euclidean space can satisfy these topological assumptions. Four possibilities for the set of admissible individual preferences must be considered namely, the set of all continuous separable preferences with unique tops, the set of all continuous top-separable preferences with unique tops, the set of continuous separable preferences and the set of all continuous top-separable preferences.

Analysis, Economic aspects, Externalities (Economics), Social choice, Separable algebras

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On the existence of continuous preference orderings without utility representations

Article Abstract:

Continuous preference orderings on a connected and separable topological space always have utility representations. However, only the assumption of separability is crucial to continuous preference orderings' representability by utility functions. Furthermore, continuous preference orderings on a metric space can be represented only if the assumption of separability is present.

Evaluation, Topological spaces, Metric spaces

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The construction of a continuous demand function for uniformly rotund preferences

Article Abstract:

Mathematical computations proving the existence and continuity of the demand function for consumer behavior are presented. The consumption set is ordered by a continuous, uniformly rotund preference relation. The purpose of the proof is to illustratethe mathematical basis of economic theory and the extent of mathematical applications in economic theory.

Models, Consumer behavior, Demand (Economics)

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