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Strategy-proof aggregation rules and single peakedness in bounded distributive lattices

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  • Ernesto Savaglio

    (University of Pescara
    University of Siena)

  • Stefano Vannucci

    (University of Siena)

Abstract

It is shown that, under a very comprehensive notion of single peakedness, an aggregation rule on a bounded distributive lattice is strategy-proof on any rich domain of single peaked total preorders if and only if it admits one of three distinct and mutually equivalent representations by lattice-polynomials, namely whenever it can be represented as a generalized weak consensus rule, a generalized weak sponsorship rule , or an iterated medianrule. The equivalence of individual and coalitional strategy-proofness that is known to hold for single peaked domains in bounded linearly ordered sets and in finite trees typically fails in such an extended setting. A related impossibility result concerning non-trivial anonymous and coalitionally strategy-proof aggregation rules is also obtained.

Suggested Citation

  • Ernesto Savaglio & Stefano Vannucci, 2019. "Strategy-proof aggregation rules and single peakedness in bounded distributive lattices," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(2), pages 295-327, February.
    • Handle: RePEc:spr:sochwe:v:52:y:2019:i:2:d:10.1007_s00355-018-1148-y
    DOI: 10.1007/s00355-018-1148-y
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    Cited by:

    1. Stefano Vannucci, 2022. "Agenda manipulation-proofness, stalemates, and redundant elicitation in preference aggregation. Exposing the bright side of Arrow's theorem," Papers 2210.03200, arXiv.org.
    2. Ernesto Savaglio & Stefano Vannucci, 2021. "Strategy-Proof Aggregation Rules in Median Semilattices with Applications to Preference Aggregation," Department of Economics University of Siena 867, Department of Economics, University of Siena.
    3. Vito Peragine & Maria G. Pittau & Ernesto Savaglio & Stefano Vannucci, 2021. "On multidimensional poverty rankings of binary attributes," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(2), pages 248-274, April.
    4. Ping Zhan, 2019. "A simple construction of complete single-peaked domains by recursive tiling," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(3), pages 477-488, December.
    5. Ernesto Savaglio & Stefano Vannucci, 2022. "Strategy-proof aggregation rules in median semilattices with applications to preference aggregation," Papers 2208.12732, arXiv.org.
    6. Arlegi, Ricardo & Teschl, Miriam, 2022. "Pareto rationalizability by two single-peaked preferences," Mathematical Social Sciences, Elsevier, vol. 118(C), pages 1-11.

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