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On the ultrafilter representation of coalitionally strategy-proof social choice functions

Author

Listed:
  • Surekha Rao

    (Indiana University Northwest)

  • Achille Basile

    (Università Federico II)

  • K. P. S. Bhaskara Rao

    (Indiana University Northwest)

Abstract

By means of a simple new characterization of ultrafilters, we elementarily prove, in the case of finitely many alternatives and arbitrarily large societies, that every coalitionally strategy-proof social choice function with at least three alternatives in its range is given by an ultrafilter. This provides an alternate and simple proof of results in Mihara (Soc Choice Welf 17:393–402, 2000). In case there are only two alternatives in the range of a coalitionally strategy-proof social choice function, we describe its structure, supplementing the work of Barberà et al. (Int J Game Theory 41:791–808, 2012).

Suggested Citation

  • Surekha Rao & Achille Basile & K. P. S. Bhaskara Rao, 2018. "On the ultrafilter representation of coalitionally strategy-proof social choice functions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(1), pages 1-13, April.
    • Handle: RePEc:spr:etbull:v:6:y:2018:i:1:d:10.1007_s40505-017-0129-0
    DOI: 10.1007/s40505-017-0129-0
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    References listed on IDEAS

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    1. H. Reiju Mihara, 2000. "Coalitionally strategyproof functions depend only on the most-preferred alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(3), pages 393-402.
    2. H. Reiju Mihara, 2001. "Existence of a coalitionally strategyproof social choice function: A constructive proof," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(3), pages 543-553.
    3. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2012. "Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(4), pages 791-808, November.
    4. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    5. Kirman, Alan P. & Sondermann, Dieter, 1972. "Arrow's theorem, many agents, and invisible dictators," Journal of Economic Theory, Elsevier, vol. 5(2), pages 267-277, October.
    6. Pazner, Elisha A. & Wesley, Eugene, 1977. "Stability of social choices in infinitely large societies," Journal of Economic Theory, Elsevier, vol. 14(2), pages 252-262, April.
    7. Ishikawa, Shin & Nakamura, Kenjiro, 1979. "The strategy-proof social choice functions," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 283-295, December.
    8. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    9. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, June.
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    Cited by:

    1. Makoto Hagiwara & Hirofumi Yamamura, 2020. "Upper set rules with binary ranges," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 657-666, April.
    2. Achille Basile & Anna De Simone & Ciro Tarantino, 2022. "A Note on Binary Strategy-Proof Social Choice Functions," Games, MDPI, vol. 13(6), pages 1-19, November.
    3. Basile, Achille & Rao, Surekha & Bhaskara Rao, K.P.S., 2021. "The structure of two-valued coalitional strategy-proof social choice functions," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    4. Achille Basile & Surekha Rao & K. P. S. Bhaskara Rao, 2020. "The structure of two-valued strategy-proof social choice functions with indifference," Papers 2002.06341, arXiv.org, revised Jul 2020.
    5. Achille Basile & Surekha Rao & K. P. S. Bhaskara Rao, 2022. "Binary strategy-proof social choice functions with indifference," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 807-826, April.
    6. 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.
    7. Anna De Simone & Ciro Tarantino, 2021. "Functional Form of Nonmanipulable Social Choice Functions with Two Alternatives," Mathematics, MDPI, vol. 9(21), pages 1-14, November.

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    More about this item

    Keywords

    Social choice functions; Coalitional strategy proofness; Gibbard–Satterthwaite theorem; Ultrafilters;
    All these keywords.

    JEL classification:

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

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