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Restricted Probabilistic Fixed Ballot Rules and Hybrid Domains

Author

Listed:
  • Chatterji, Shurojit

    (School of Economics, Singapore Management University)

  • Roy, Souvik

    (Indian Statistical Institute)

  • Sadhukhan, Soumyarup

    (Indian Statistical Institute)

  • Sen, Arunava

    (Indian Statistical Institute)

  • Zeng, Huaxia

    (Shanghai University of Finance and Economics)

Abstract

We study Random Social Choice Functions (or RSCFs) in a standard ordinal mech-anism design model. We introduce a new preference domain called a hybrid domain which includes as special cases as the complete domain and the single-peaked domain. We characterize the class of unanimous and strategy-proof RSCFs on these domains and refer to them as Restricted Probabilistic Fixed Ballot Rules (or RPFBRs). These RSCFs are not necessarily decomposable, i.e., cannot be written as a convex combina-tion of their deterministic counterparts. We identify a necessary and sufficient condition under which decomposability holds for anonymous RPFBRs. Finally, we provide an axiomatic justification of hybrid domains and show that every connected domain satis-fying some mild conditions is a hybrid domain where the RPFBR characterization still prevails.

Suggested Citation

  • Chatterji, Shurojit & Roy, Souvik & Sadhukhan, Soumyarup & Sen, Arunava & Zeng, Huaxia, 2020. "Restricted Probabilistic Fixed Ballot Rules and Hybrid Domains," Economics and Statistics Working Papers 3-2020, Singapore Management University, School of Economics.
    • Handle: RePEc:ris:smuesw:2020_003
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    Citations

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    Cited by:

    1. Karmokar, Madhuparna & Roy, Souvik, 2020. "The structure of (local) ordinal Bayesian incentive compatible random rules," MPRA Paper 103494, University Library of Munich, Germany.
    2. Roy, Souvik & Sadhukhan, Soumyarup, 2022. "On the equivalence of strategy-proofness and upper contour strategy-proofness for randomized social choice functions," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    3. Madhuparna Karmokar & Souvik Roy, 2023. "The structure of (local) ordinal Bayesian incentive compatible random rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 111-152, July.

    More about this item

    Keywords

    Strategy-proofness; hybrid domain; restricted probabilistic fixed ballot rule; decomposability; connectedness;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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