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Impossibility theorems with countably many individuals

Author

Listed:
  • Uuganbaatar Ninjbat

    (The National University of Mongolia)

Abstract

The problem of social choice is studied on a domain with countably many individuals. In contrast to most of the existing literature which establish either non-constructive possibilities or approximate (i.e. invisible) dictators, we show that if one adds a continuity property to the usual set of axioms, the classical impossibilities persist in countable societies. Along the way, a new proof of the Gibbard–Satterthwaite theorem in the style of Peter Fishburn’s well known proof of Arrow’s impossibility theorem is obtained.

Suggested Citation

  • Uuganbaatar Ninjbat, 2018. "Impossibility theorems with countably many individuals," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 9(3), pages 333-350, August.
    • Handle: RePEc:spr:series:v:9:y:2018:i:3:d:10.1007_s13209-018-0182-4
    DOI: 10.1007/s13209-018-0182-4
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    References listed on IDEAS

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    More about this item

    Keywords

    Arrow’s impossibility theorem; The Gibbard–Satterthwaite theorem; Infinite society; Continuity;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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