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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. (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 (2010) on circular domains.

Suggested Citation

  • Anup Pramanik, 2014. "Further Results on Dictatorial Domains," ISER Discussion Paper 0899, Institute of Social and Economic Research, Osaka University.
    • Handle: RePEc:dpr:wpaper:0899
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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. Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Oct 2022.
    2. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "Strategy-proof Rules on Partially Single-peaked Domains," MPRA Paper 82267, University Library of Munich, Germany.
    3. Erdamar, Bora & Sanver, M. Remzi & Sato, Shin, 2017. "Evaluationwise strategy-proofness," Games and Economic Behavior, Elsevier, vol. 106(C), pages 227-238.
    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. Gori, Michele, 2021. "Manipulation of social choice functions under incomplete information," Games and Economic Behavior, Elsevier, vol. 129(C), pages 350-369.
    6. 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.
    7. Gopakumar Achuthankutty & Souvik Roy, 2018. "Dictatorship on top-circular domains," Theory and Decision, Springer, vol. 85(3), pages 479-493, October.
    8. Roy, Souvik & Storcken, Ton, 2019. "A characterization of possibility domains in strategic voting," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 46-55.
    9. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    10. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "On Top-connected Single-peaked and Partially Single-peaked Domains," MPRA Paper 78102, University Library of Munich, Germany.

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    JEL classification:

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

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