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Further results on dictatorial domains

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  • Anup Pramanik

Abstract

This paper generalizes the results in Aswal et al. (Econ Theory 22:45–62, 2003 ) on dictatorial domains. This is done in two ways. In the first, the notion of connections between pairs of alternatives in Aswal et al. ( 2003 ) is weakened to weak connectedness. This notion requires the specification of four preference orderings for every alternative pair. Domains that are linked in the sense of Aswal et al. ( 2003 ) with weak connectedness replacing connectedness, are shown to be dictatorial. In the second, the notion of connections for alternative pairs is strengthened relative to its counterpart in Aswal et al. ( 2003 ). However, a domain is shown to be dictatorial if the induced graph is merely connected rather than linked. This result generalizes the result in Sato (Rev Econ Design 14:331–342, 2010 ) on circular domains. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Anup Pramanik, 2015. "Further results on dictatorial domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 379-398, September.
    • Handle: RePEc:spr:sochwe:v:45:y:2015:i:2:p:379-398
    DOI: 10.1007/s00355-015-0889-0
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    References listed on IDEAS

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    1. Shin Sato, 2010. "Circular domains," Review of Economic Design, Springer;Society for Economic Design, vol. 14(3), pages 331-342, September.
    2. 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.
    3. Dogan, Emre & Sanver, M. Remzi, 2007. "On the alternating use of "unanimity" and "surjectivity" in the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 96(1), pages 140-143, July.
    4. Sen, Arunava, 2001. "Another direct proof of the Gibbard-Satterthwaite Theorem," Economics Letters, Elsevier, vol. 70(3), pages 381-385, March.
    5. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    Cited by:

    1. Erdamar, Bora & Sanver, M. Remzi & Sato, Shin, 2017. "Evaluationwise strategy-proofness," Games and Economic Behavior, Elsevier, vol. 106(C), pages 227-238.
    2. Anup Pramanik & Arunava Sen, 2016. "Pairwise partition graphs and strategy-proof social choice in the exogenous indifference class model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(1), pages 1-24, June.
    3. Gopakumar Achuthankutty & Souvik Roy, 2018. "Dictatorship on top-circular domains," Theory and Decision, Springer, vol. 85(3), pages 479-493, October.
    4. Bandhu, Sarvesh & Mondal, Bishwajyoti & Pramanik, Anup, 2022. "Strategy-proofness of the unanimity with status-quo rule over restricted domains," Economics Letters, Elsevier, vol. 210(C).
    5. Roy, Souvik & Storcken, Ton, 2019. "A characterization of possibility domains in strategic voting," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 46-55.
    6. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    7. Gori, Michele, 2021. "Manipulation of social choice functions under incomplete information," Games and Economic Behavior, Elsevier, vol. 129(C), pages 350-369.
    8. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "Strategy-proof Rules on Partially Single-peaked Domains," MPRA Paper 82267, University Library of Munich, Germany.
    9. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "On Top-connected Single-peaked and Partially Single-peaked Domains," MPRA Paper 78102, University Library of Munich, Germany.
    10. Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Oct 2022.

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    Keywords

    D71;

    JEL classification:

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

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