IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v94y2015icp200-205.html
   My bibliography  Save this article

Spatial implementation

Author

Listed:
  • Brady, Richard L.
  • Chambers, Christopher P.

Abstract

In a spatial model with Euclidean preferences, we introduce a new rule, the geometric median, and characterize it as the smallest rule (with respect to set inclusion) satisfying a collection of axioms. The geometric median is independent of the choice of coordinates and is Nash implementable.

Suggested Citation

  • Brady, Richard L. & Chambers, Christopher P., 2015. "Spatial implementation," Games and Economic Behavior, Elsevier, vol. 94(C), pages 200-205.
    • Handle: RePEc:eee:gamebe:v:94:y:2015:i:c:p:200-205
    DOI: 10.1016/j.geb.2015.06.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825615000998
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2015.06.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Massó, Jordi & Moreno de Barreda, Inés, 2011. "On strategy-proofness and symmetric single-peakedness," Games and Economic Behavior, Elsevier, vol. 72(2), pages 467-484, June.
    2. Barbera, S. & Masso, J. & Serizawa, S., 1998. "Strategy-Proof Voting on Compact Ranges," Games and Economic Behavior, Elsevier, vol. 25(2), pages 272-291, November.
    3. Kim C. Border & J. S. Jordan, 1983. "Straightforward Elections, Unanimity and Phantom Voters," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(1), pages 153-170.
    4. Nina Baranchuk & Philip H. Dybvig, 2009. "Consensus in Diverse Corporate Boards," The Review of Financial Studies, Society for Financial Studies, vol. 22(2), pages 715-747, February.
    5. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    6. Michel Le Breton & Arunava Sen, 1999. "Separable Preferences, Strategyproofness, and Decomposability," Econometrica, Econometric Society, vol. 67(3), pages 605-628, May.
    7. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    8. Bordes, G. & Laffond, G. & Le Breton, Michel, 2012. "Euclidean Preferences, Option Sets and Strategy Proofness," TSE Working Papers 12-302, Toulouse School of Economics (TSE).
    9. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    10. Bordes, G. & Laffond, G. & Le Breton, Michel, 2012. "Euclidean Preferences, Option Sets and Strategy Proofness," IDEI Working Papers 717, Institut d'Économie Industrielle (IDEI), Toulouse.
    11. Kim, K.H. & Roush, F.W., 1984. "Nonmanipulability in two dimensions," Mathematical Social Sciences, Elsevier, vol. 8(1), pages 29-43, August.
    12. Bhaskar Dutta & Arunava Sen, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 121-128.
    13. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    14. Smith, John H, 1973. "Aggregation of Preferences with Variable Electorate," Econometrica, Econometric Society, vol. 41(6), pages 1027-1041, November.
    15. Le Breton, Michel & Weymark, John A., 1999. "Strategy-proof social choice with continuous separable preferences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 47-85, August.
    16. Young, H. P., 1974. "An axiomatization of Borda's rule," Journal of Economic Theory, Elsevier, vol. 9(1), pages 43-52, September.
    17. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-1099, September.
    18. Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993. "Generalized Median Voter Schemes and Committees," Journal of Economic Theory, Elsevier, vol. 61(2), pages 262-289, December.
    19. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    20. Cervone, Davide P. & Dai, Ronghua & Gnoutcheff, Daniel & Lanterman, Grant & Mackenzie, Andrew & Morse, Ari & Srivastava, Nikhil & Zwicker, William S., 2012. "Voting with rubber bands, weights, and strings," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 11-27.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Hun Chung & John Duggan, 2018. "Directional equilibria," Journal of Theoretical Politics, , vol. 30(3), pages 272-305, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lars-Gunnar Svensson & Pär Torstensson, 2008. "Strategy-proof allocation of multiple public goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 181-196, February.
    2. Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Oct 2022.
    3. Michel Breton & Vera Zaporozhets, 2009. "On the equivalence of coalitional and individual strategy-proofness properties," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 287-309, August.
    4. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2010. "Individual versus group strategy-proofness: When do they coincide?," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1648-1674, September.
    5. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2020. "Arrow on domain conditions: a fruitful road to travel," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 237-258, March.
    6. Chatterji, Shurojit & Zeng, Huaxia, 2018. "On random social choice functions with the tops-only property," Games and Economic Behavior, Elsevier, vol. 109(C), pages 413-435.
    7. Aziz, Haris & Chan, Hau & Lee, Barton E. & Parkes, David C., 2020. "The capacity constrained facility location problem," Games and Economic Behavior, Elsevier, vol. 124(C), pages 478-490.
    8. Chatterji, Shurojit & Zeng, Huaxia, 2023. "A taxonomy of non-dictatorial unidimensional domains," Games and Economic Behavior, Elsevier, vol. 137(C), pages 228-269.
    9. Shurojit Chatterji & Huaxia Zeng, 2023. "Decomposability and Strategy-proofness in Multidimensional Models," Papers 2303.10889, arXiv.org, revised Nov 2023.
    10. BOSSERT, Walter & WEYMARK, J.A., 2006. "Social Choice: Recent Developments," Cahiers de recherche 01-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    11. Sumit Goel & Wade Hann-Caruthers, 2023. "Optimality of the coordinate-wise median mechanism for strategyproof facility location in two dimensions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(1), pages 11-34, July.
    12. ,, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    13. Bordes, G. & Laffond, G. & Le Breton, Michel, 2012. "Euclidean Preferences, Option Sets and Strategy Proofness," TSE Working Papers 12-302, Toulouse School of Economics (TSE).
    14. Schummer, James & Vohra, Rakesh V., 2002. "Strategy-proof Location on a Network," Journal of Economic Theory, Elsevier, vol. 104(2), pages 405-428, June.
    15. , & ,, 2012. "Strategy-proof voting for multiple public goods," Theoretical Economics, Econometric Society, vol. 7(3), September.
    16. Alejandro Saporiti, 2006. "Strategic voting on single-crossing domains," Economics Discussion Paper Series 0617, Economics, The University of Manchester.
    17. Bordes, G. & Laffond, G. & Le Breton, Michel, 2012. "Euclidean Preferences, Option Sets and Strategy Proofness," IDEI Working Papers 717, Institut d'Économie Industrielle (IDEI), Toulouse.
    18. Margarita Kirneva & Matias Nunez, 2021. "Voting by Simultaneous Vetoes," Working Papers 2021-08, Center for Research in Economics and Statistics.
    19. Berga, Dolors & Serizawa, Shigehiro, 2000. "Maximal Domain for Strategy-Proof Rules with One Public Good," Journal of Economic Theory, Elsevier, vol. 90(1), pages 39-61, January.
    20. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.

    More about this item

    Keywords

    Geometric median; Euclidean preferences; Nash implementation; Maskin monotonicity;
    All these keywords.

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:94:y:2015:i:c:p:200-205. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.