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Economic Theory

, Volume 56, Issue 1, pp 83–108 | Cite as

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

  • Murat Öztürk
  • Hans Peters
  • Ton Storcken
Research Article

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 \(x\) of the polytope is called single-best if there is a point \(y\) of the polytope such that \(x\) is the unique point of the polytope at maximal distance from \(y\). 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.

Keywords

Single-dipped preferences Pareto optimality Strategy-proofness Committee voting 

JEL Classification

D71 

References

  1. Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis, a Hitchhiker’s Guide. Springer, Berlin (2006)Google Scholar
  2. Barbera, S., Berga, D., Moreno, B.: Domains, ranges and strategy-proofness: the case of single-dipped preferences. Soc. Choice Welf. 39, 335–352 (2012)CrossRefGoogle Scholar
  3. Berliant, M., Peng, S.-K., Wang, P.: Taxing pollution: agglomeration and welfare consequences. Econ. Theory (2013). doi: 10.1007/s00199-013-0768-9
  4. Besfamille, M., Lozachmeur, J.M.: NIMBY and mechanism design under different constitutional constraints. Int. Tax Public Financ. 17, 114–132 (2010)CrossRefGoogle Scholar
  5. Black, D.: On the rationale of group decision-making. J. Political Econ. 56, 23–34 (1948)CrossRefGoogle Scholar
  6. Border, K.C., Jordan, J.S.: Straightforward elections, unanimity and phantom voters. Rev. Econ. Stud. 50, 153–170 (1983)CrossRefGoogle Scholar
  7. Ehlers, L.: Probabilistic allocation rules and single-dipped preferences. Soc. Choice Welf. 19, 325–348 (2002)CrossRefGoogle Scholar
  8. Gibbard, A.: Manipulation of voting schemes: a general result. Econometrica 41, 587–602 (1973)CrossRefGoogle Scholar
  9. Hansson, B.: The existence of group preference functions. Public Choice 38, 89–98 (1976)CrossRefGoogle Scholar
  10. Inada, K.: A note on the simple majority rule. Econometrica 31, 525–531 (1964)CrossRefGoogle Scholar
  11. Kirman, A., Sondermann, D.: Arrow’s theorem, many agents, and invisible dictators. J. Econ. Theory 3, 267–277 (1972)CrossRefGoogle Scholar
  12. Klaus, B.: Coalitional strategy-proofness in economies with single-dipped preferences and the assignment of an individual object. Games Econ. Behav. 34, 64–82 (2001)CrossRefGoogle Scholar
  13. Klaus, B., Peters, H., Storcken, T.: Strategy-proof division of a private good when preferences are single-dipped. Econ. Lett. 55, 339–346 (1997)CrossRefGoogle Scholar
  14. Kunreuther, H., Kleindorfer, P.R.: A sealed-bid auction mechanism for siting noxious facilities. Am. Econ. Rev. (Pap. Proc.) 76, 295–299 (1986)Google Scholar
  15. Lescop, D.: Optimal mechanisms for siting noxious facilities. Rev. Econ. Des. 10, 273–284 (2007)Google Scholar
  16. Manjunath, V: Efficient and strategy-proof social choice when preferences are single-dipped. Int. J. Game Theory (2013). doi: 10.1007/s00182-013-0396-4
  17. Moulin, H.: On strategy-proofness and single peakedness. Public Choice 35, 437–455 (1980)CrossRefGoogle Scholar
  18. Öztürk, M., Peters, H., Storcken, T.: Strategy-proof location of a public bad on a disc. Econ. Lett. 119, 14–16 (2013)CrossRefGoogle Scholar
  19. Peremans, W., Storcken, T.: Strategy-proofness on single-dipped preference domains. In: de Swart, H.M.C. (ed.) Logic, Game Theory and Social Choice. Tilburg University Press, The Netherlands (1999)Google Scholar
  20. Sakai, T.: Fair waste pricing: an axiomatic analysis to the NIMBY problem. Econ. Theory 50, 499–521 (2012)CrossRefGoogle Scholar
  21. Satterthwaite, M.A.: Strategy-proofness and Arrow’s conditions: existence and correspondence theorem for voting procedures and social choice functions. J. Econ. Theory 10, 187–217 (1975)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Quantitative EconomicsMaastricht UniversityMaastrichtThe Netherlands

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