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An extreme point characterization of strategy-proof and unanimous probabilistic rules over binary restricted domains

Author

Listed:
  • Peters, H.J.M.

    (Quantitative Economics)

  • Roy, S.

    (Quantitative Economics)

  • Sadhukhan, S.
  • Storcken, A.J.A.

    (Quantitative Economics)

Abstract

We show that every strategy-proof and unanimous probabilistic rule on a binary restricted domain has binary support, and is a probabilistic mixture of strategy-proof and unanimous deterministic rules. Examples of binary restricted domains include several types of single-dipped domains, the single-peaked domain where peaks are restricted to two adjacent alternatives, and the single-crossing domain with two tops. We also provide some extensions to infinitely many alternatives.

Suggested Citation

  • Peters, H.J.M. & Roy, S. & Sadhukhan, S. & Storcken, A.J.A., 2016. "An extreme point characterization of strategy-proof and unanimous probabilistic rules over binary restricted domains," Research Memorandum 012, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2016012
    DOI: 10.26481/umagsb.2016012
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    Cited by:

    1. is not listed on IDEAS
    2. Sarvesh Bandhu & Abhinaba Lahiri & Anup Pramanik, 2024. "Stochastic same-sidedness in the random voting model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 62(1), pages 167-196, February.
    3. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "A unified characterization of the randomized strategy-proof rules," Journal of Economic Theory, Elsevier, vol. 197(C).
    4. 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.
    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. Gogulapati Sreedurga & Soumyarup Sadhukhan & Souvik Roy & Yadati Narahari, 2022. "Characterization of Group-Fair Social Choice Rules under Single-Peaked Preferences," Papers 2207.07984, arXiv.org.
    7. 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).
    8. Felix Brand & Patrick Lederer & Sascha Tausch, 2023. "Strategyproof Social Decision Schemes on Super Condorcet Domains," Papers 2302.12140, arXiv.org.

    More about this item

    JEL classification:

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

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