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Strategic requirements with indifference: single-peaked versus single-plateaued preferences

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  • Dolors Berga

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  • Bernardo Moreno

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Abstract

We concentrate on the problem of the provision of one pure public good whenever agents that form the society have either single-plateaued preferences or single-peaked preferences over the set of alternatives. We are interested in comparing the relationships between different nonmanipulability notions under these two domains. On the single-peaked domain, under strategy-proofness, non-bossiness is equivalent to convexity of the range. Thus, minmax rules are the only strategy-proof non-bossy rules. On the single-plateaued domain, only constant rules are non-bossy or Maskin monotonic; but strategy-proofness and weak non-bossiness are equivalent to weak Maskin monotonicity. Moreover, strategy-proofness and plateau-invariance guarantee convexity of the range.
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  • Dolors Berga & Bernardo Moreno, 2009. "Strategic requirements with indifference: single-peaked versus single-plateaued preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 275-298, February.
  • Handle: RePEc:spr:sochwe:v:32:y:2009:i:2:p:275-298
    DOI: 10.1007/s00355-008-0323-y
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    Citations

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    Cited by:

    1. John Weymark, 2011. "A unified approach to strategy-proofness for single-peaked preferences," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 529-550, December.
    2. William Thomson, 2016. "Non-bossiness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 665-696, October.
    3. Bossert, Walter & Peters, Hans, 2014. "Single-basined choice," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 162-168.
    4. Katsuhiko Nishizaki, 2013. "An impossibility theorem for secure implementation in discrete public good economies," Economics Bulletin, AccessEcon, vol. 33(1), pages 300-308.
    5. Dolors Berga & Bernardo Moreno, 2009. "Strategic requirements with indifference: single-peaked versus single-plateaued preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 275-298, February.
    6. Doghmi, Ahmed & Ziad, Abderrahmane, 2015. "Nash implementation in private good economies with single-plateaued preferences and in matching problems," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 32-39.
    7. Katsuhiko Nishizaki, 2014. "An equivalence of secure implementability and full implementability in truthful strategies in pure exchange economies with Leontief utility functions," Review of Economic Design, Springer;Society for Economic Design, vol. 18(1), pages 73-82, March.
    8. Ahmed Doghmi & Abderrahmane Ziad, 2013. "Nash Implementation in Private Good Economies with Single-Plateaued Preferences," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201311, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    9. repec:spr:sochwe:v:49:y:2017:i:3:d:10.1007_s00355-017-1065-5 is not listed on IDEAS
    10. Richard Lee Brady & Christopher P. Chambers, 2017. "A spatial analogue of May’s Theorem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(3), pages 657-669, December.
    11. Bossert, Walter & Peters, Hans, 2013. "Single-plateaued choice," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 134-139.
    12. Bettina Klaus & Olivier Bochet, 2013. "The relation between monotonicity and strategy-proofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 41-63, January.
    13. Adachi, Tsuyoshi, 2014. "Robust and secure implementation: equivalence theorems," Games and Economic Behavior, Elsevier, vol. 86(C), pages 96-101.
    14. Doghmi Ahmed, 2014. "Nash Implementation in Rationing Problems with Single-Crossing Preferences," Mathematical Economics Letters, De Gruyter, vol. 1(2-4), pages 1-6, July.

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    JEL classification:

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

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