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On the location of public bads: strategy-proofness under two-dimensional single-dipped preferences

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  • Murat Öztürk
  • Hans Peters
  • Ton Storcken

Abstract

In a model with finitely many agents who have single-dipped Euclidean preferences on a polytope in the Euclidean plane, a rule assigns to each profile of reported dips a point of the polytope. A point $$x$$ x of the polytope is called single-best if there is a point $$y$$ y of the polytope such that $$x$$ x is the unique point of the polytope at maximal distance from $$y$$ y . It is proved that if the polytope does not have either exactly two single-best points or exactly four single-best points which form the vertices of a rectangle, then any Pareto optimal and strategy-proof rule is dictatorial. If the polytope has exactly two single-best points, then there are non-dictatorial strategy-proof and Pareto optimal rules, which can be described by committee voting (simple games) between the two single-best points. This also holds if there are exactly four single-best points which form the vertices of a rectangle, but in that case, we limit ourselves to describing an example of such a rule. The framework under consideration models situations where public bads such as garbage dumping grounds or nuclear plants have to be located within a confined region. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Murat Öztürk & Hans Peters & Ton Storcken, 2014. "On the location of public bads: strategy-proofness under two-dimensional single-dipped preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 83-108, May.
  • Handle: RePEc:spr:joecth:v:56:y:2014:i:1:p:83-108
    DOI: 10.1007/s00199-013-0785-8
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    Cited by:

    1. Bossert, Walter & Peters, Hans, 2014. "Single-basined choice," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 162-168.
    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. Lahiri, Abhinaba & Peters, Hans & Storcken, Ton, 2017. "Strategy-proof location of public bads in a two-country model," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 150-159.
    4. Segal-Halevi, Erel & Nitzan, Shmuel & Hassidim, Avinatan & Aumann, Yonatan, 2017. "Fair and square: Cake-cutting in two dimensions," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 1-28.
    5. Souvik Roy & Soumyarup Sadhukhan, 2019. "A characterization of random min–max domains and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(4), pages 887-906, November.
    6. Roy, Souvik & Storcken, Ton, 2019. "A characterization of possibility domains in strategic voting," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 46-55.
    7. Yamamura, Hirofumi, 2016. "Coalitional stability in the location problem with single-dipped preferences: An application of the minimax theorem," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 48-57.
    8. Abhinaba Lahiri & Ton Storcken, 2019. "Strategy-proof location of public bads in an interval," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(1), pages 49-62, June.

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    More about this item

    Keywords

    Single-dipped preferences; Pareto optimality; Strategy-proofness; Committee voting; D71;
    All these keywords.

    JEL classification:

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

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