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Random Dictatorship Domains

Author

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  • Shurojit Chatterji

    (School of Economics, Singapore Management University)

  • Arunava Sen

    (Indian Statistical Institute, New Delhi, India.)

  • Huaxia Zeng

    (Singapore Management University, Singapore.)

Abstract

A domain of preference orderings is a random dictatorship domain if every strategy- proof random social choice function satisfying unanimity de ned on the domain, is a random dictatorship. Gibbard (1977) showed that the universal domain is a random dictatorship domain. We investigate the relationship between dictatorial and random dictatorship domains. We show that there exist dictatorial domains that are not ran- dom dictatorship domains. We provide stronger versions of the linked domain condition (introduced in Aswal et al. (2003)) that guarantee that a domain is a random dicta- torship domain. A key step in these arguments that is of independent interest, is a ramification result that shows that under certain assumptions, a domain that is a ran- dom dictatorship domain for two voters is also a random dictatorship domain for an arbitrary number of voters.

Suggested Citation

  • Shurojit Chatterji & Arunava Sen & Huaxia Zeng, 2012. "Random Dictatorship Domains," Working Papers 27-2012, Singapore Management University, School of Economics.
    • Handle: RePEc:siu:wpaper:27-2012
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    Cited by:

    1. Chatterji, Shurojit & Zeng, Huaxia, 2018. "On random social choice functions with the tops-only property," Games and Economic Behavior, Elsevier, vol. 109(C), pages 413-435.
    2. Peters, Hans & Roy, Souvik & Sadhukhan, Soumyarup & Storcken, Ton, 2017. "An extreme point characterization of strategy-proof and unanimous probabilistic rules over binary restricted domains," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 84-90.
    3. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2016. "A characterization of single-peaked preferences via random social choice functions," Theoretical Economics, Econometric Society, vol. 11(2), May.
    4. Felix Brand & Patrick Lederer & Sascha Tausch, 2023. "Strategyproof Social Decision Schemes on Super Condorcet Domains," Papers 2302.12140, arXiv.org.
    5. Roy, Souvik & Sadhukhan, Soumyarup, 2023. "Committee formation under constraints through randomized voting rules on separable domains," Journal of Economic Theory, Elsevier, vol. 209(C).
    6. Chatterji, Shurojit & Roy, Souvik & Sadhukhan, Soumyarup & Sen, Arunava & Zeng, Huaxia, 2022. "Probabilistic fixed ballot rules and hybrid domains," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    7. Hans Peters & Souvik Roy & Soumyarup Sadhukhan, 2021. "Unanimous and Strategy-Proof Probabilistic Rules for Single-Peaked Preference Profiles on Graphs," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 811-833, May.
    8. Felix Brandt & Patrick Lederer & Ren'e Romen, 2022. "Relaxed Notions of Condorcet-Consistency and Efficiency for Strategyproof Social Decision Schemes," Papers 2201.10418, arXiv.org.
    9. Ehlers, Lars & Majumdar, Dipjyoti & Mishra, Debasis & Sen, Arunava, 2020. "Continuity and incentive compatibility in cardinal mechanisms," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 31-41.
    10. Gaurav, Abhishek & Picot, Jérémy & Sen, Arunava, 2017. "The decomposition of strategy-proof random social choice functions on dichotomous domains," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 28-34.
    11. Pycia, Marek & Ünver, M. Utku, 2015. "Decomposing random mechanisms," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 21-33.
    12. Aziz, Haris & Brandl, Florian & Brandt, Felix & Brill, Markus, 2018. "On the tradeoff between efficiency and strategyproofness," Games and Economic Behavior, Elsevier, vol. 110(C), pages 1-18.
    13. Peters, Hans & Roy, Souvik & Sadhukhan, Soumyarup, 2018. "Random social choice functions for single-peaked domains on trees," Research Memorandum 004, Maastricht University, Graduate School of Business and Economics (GSBE).
    14. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    15. Peters, Hans & Roy, Souvik & Sen, Arunava & Storcken, Ton, 2014. "Probabilistic strategy-proof rules over single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 123-127.
    16. Lars EHLERS & Dipjyoti MAJUMDAR & Debasis MISHRA & Arunava SEN, 2016. "Continuity and Incentive Compatibility in Cardinal Voting Mechanisms," Cahiers de recherche 04-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    17. EHLERS, Lars & MAJUMDAR, Dipjyoti & MISHRA, Debasis & SEN, Arunava, 2016. "Continuity and incentive compatibility," Cahiers de recherche 2016-04, Universite de Montreal, Departement de sciences economiques.
    18. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "Formation of committees under constraints through random voting rules," MPRA Paper 110873, University Library of Munich, Germany.
    19. Gopakumar Achuthankutty & Souvik Roy, 2018. "On single-peaked domains and min–max rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 753-772, December.
    20. Shurojit Chatterji & Souvik Roy & Soumyarup Sadhukhan & Arunava Sen & Huaxia Zeng, 2021. "Probabilistic Fixed Ballot Rules and Hybrid Domains," Papers 2105.10677, arXiv.org, revised Jan 2022.
    21. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "On Top-connected Single-peaked and Partially Single-peaked Domains," MPRA Paper 78102, University Library of Munich, Germany.
    22. Lê Nguyên Hoang, 2017. "Strategy-proofness of the randomized Condorcet voting system," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 679-701, March.

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    JEL classification:

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

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