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Social evaluation functionals with an arbitrary set of alternatives

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  • Juan C. Candeal

    (Universidad de Zaragoza)

Abstract

This paper explores the concept of a social evaluation functional in the case of an arbitrary set of alternatives. In the first part, a characterization of projective social evaluations functionals is shown whenever the common restricted domain is the set of all bounded utility functions equipped with the supremum norm topology. The result makes a crucial use, among others, of a continuity axiom. In the second part, a comparison meaningful property is introduced for a social evaluation functional which allows us for obtaining a more general result with no continuity requirements. Finally, an impossibility theorem, which is reminiscent of that is obtained by Chichilnisky in (Q J Econ 97:337–352, 1982) but without using topological conditions, is offered.

Suggested Citation

  • Juan C. Candeal, 2023. "Social evaluation functionals with an arbitrary set of alternatives," Theory and Decision, Springer, vol. 95(2), pages 255-271, August.
    • Handle: RePEc:kap:theord:v:95:y:2023:i:2:d:10.1007_s11238-022-09923-7
    DOI: 10.1007/s11238-022-09923-7
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    References listed on IDEAS

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    3. Graciela Chichilnisky, 1982. "Social Aggregation Rules and Continuity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 97(2), pages 337-352.
    4. Juan Candeal, 2015. "Social evaluation functionals: a gateway to continuity in social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 369-388, February.
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    7. Kevin W. S. Roberts, 1980. "Possibility Theorems with Interpersonally Comparable Welfare Levels," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(2), pages 409-420.
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