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Functional Form of Nonmanipulable Social Choice Functions with Two Alternatives

Author

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  • Anna De Simone

    (Dipartimento di Matematica e Applicazioni R. Caccioppoli, Università Federico II di Napoli (ITALY), 80126 Napoli, Italy)

  • Ciro Tarantino

    (Dipartimento di Scienze Economiche e Statistiche, Università Federico II di Napoli (ITALY), 80126 Napoli, Italy)

Abstract

We propose a new functional form characterization of binary nonmanipulable social choice functions on a universal domain and an arbitrary, possibly infinite, set of agents. In order to achieve this, we considered the more general case of two-valued social choice functions and describe the structure of the family consisting of groups of agents having no power to determine the values of a nonmanipulable social choice function. With the help of such a structure, we introduce a class of functions that we call powerless revealing social choice functions and show that the binary nonmanipulable social choice functions are the powerless revealing ones.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2827-:d:673912
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    References listed on IDEAS

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    1. Abhinaba Lahiri & Anup Pramanik, 2020. "On strategy-proof social choice between two alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 581-607, April.
    2. 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.
    3. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2011. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 2, number 2.
    4. 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.
    5. 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.
    6. Manjunath, Vikram, 2012. "Group strategy-proofness and voting between two alternatives," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 239-242.
    7. 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.
    8. Larsson, Bo & Svensson, Lars-Gunnar, 2006. "Strategy-proof voting on the full preference domain," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 272-287, December.
    9. 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).
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    Cited by:

    1. 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.

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