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Is proximity preservation rational in social choice theory?

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  • Wu-Hsiung Huang

Abstract

We establish a strong impossibility theorem of a rational social choice that the proximity preservation (also called weak proximorphism WPX) and the diagonal surjectivity are logically inconsistent. The result is valid for finite or infinite alternatives, discrete or continuous. It generalizes the Baigent theorem, largely weakening his antecedent. For continuum set of alternatives, we clarify the notion of WPX by showing (1) WPX almost implies the continuity, (2) WPX is almost rigid. These observations raise the issue whether WPX is a natural condition for a social welfare function. A splitting reformulation of the proximity preservation which is weaker but rational is suggested. Copyright Springer-Verlag 2004

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  • Wu-Hsiung Huang, 2004. "Is proximity preservation rational in social choice theory?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(3), pages 315-332, December.
    • Handle: RePEc:spr:sochwe:v:23:y:2004:i:3:p:315-332
    DOI: 10.1007/s00355-003-0224-z
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    Cited by:

    1. Michel Grabisch & Agnieszka Rusinowska, 2009. "A model of influence with a continuum of actions," Post-Print halshs-00464460, HAL.
    2. Stefano Vannucci, 2022. "Agenda manipulation-proofness, stalemates, and redundant elicitation in preference aggregation. Exposing the bright side of Arrow's theorem," Papers 2210.03200, arXiv.org.
    3. Wu-Hsiung Huang, 2014. "Singularity and Arrow’s paradox," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 671-706, March.
    4. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "A model of influence with a continuum of actions," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 576-587.

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