IDEAS home Printed from https://ideas.repec.org/a/spr/grdene/v15y2006i1d10.1007_s10726-005-9007-5.html
   My bibliography  Save this article

Exploratory Analysis of Similarities Between Social Choice Rules

Author

Listed:
  • John C. McCabe-Dansted

    (University of Auckland)

  • Arkadii Slinko

    (University of Auckland)

Abstract

Nurmi (1987) investigated the relationship between voting rules by determining the frequency that two rules pick the same winner. We use statistical techniques such as hierarchical clustering and multidimensional scaling to further understand the relationships between rules. We use the urn model with a parameter representing contagion to model the presence of social homogeneity within the group of agents and investigate how the classification tree of the rules changes when the homogeneity of the voting population is increased. We discovered that the topology of the classification tree changes quite substantially when the parameter of homogeneity is increased from 0 to 1. We describe the most interesting changes and explain some of them. Most common social choice rules are included, 26 in total.

Suggested Citation

  • John C. McCabe-Dansted & Arkadii Slinko, 2006. "Exploratory Analysis of Similarities Between Social Choice Rules," Group Decision and Negotiation, Springer, vol. 15(1), pages 77-107, January.
  • Handle: RePEc:spr:grdene:v:15:y:2006:i:1:d:10.1007_s10726-005-9007-5
    DOI: 10.1007/s10726-005-9007-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10726-005-9007-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10726-005-9007-5?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. Sven Berg, 1985. "Paradox of voting under an urn model: The effect of homogeneity," Public Choice, Springer, vol. 47(2), pages 377-387, January.
    2. 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.
    3. Bilge Yilmaz & Murat R. Sertel, 1999. "The majoritarian compromise is majoritarian-optimal and subgame-perfect implementable," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 615-627.
    4. Glenn Milligan, 1980. "An examination of the effect of six types of error perturbation on fifteen clustering algorithms," Psychometrika, Springer;The Psychometric Society, vol. 45(3), pages 325-342, September.
    5. Bordley, Robert F., 1983. "A Pragmatic Method for Evaluating Election Schemes through Simulation," American Political Science Review, Cambridge University Press, vol. 77(1), pages 123-141, March.
    6. Merlin, V. & Tataru, M. & Valognes, F., 2000. "On the probability that all decision rules select the same winner," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 183-207, March.
    7. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    8. Gehrlein, William V. & Lepelley, Dominique, 2000. "The probability that all weighted scoring rules elect the same winner," Economics Letters, Elsevier, vol. 66(2), pages 191-197, February.
    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. SLINKO, Arkadii & WHITE, Shaun, 2006. "On the Manipulability of Proportional Representation," Cahiers de recherche 2006-20, Universite de Montreal, Departement de sciences economiques.
    2. SLINKO, Arkadii & WHITE, Shaun, 2006. "On the Manipulability of Proportional Representation," Cahiers de recherche 12-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. Arkadii Slinko & Shaun White, 2010. "Proportional Representation and Strategic Voters," Journal of Theoretical Politics, , vol. 22(3), pages 301-332, July.
    4. Niclas Boehmer & Robert Bredereck & Piotr Faliszewski & Rolf Niedermeier & Stanis{l}aw Szufa, 2021. "Putting a Compass on the Map of Elections," Papers 2105.07815, arXiv.org.
    5. Alexander V. Karpov, 2018. "An Informational Basis for Voting Rules," HSE Working papers WP BRP 188/EC/2018, National Research University Higher School of Economics.
    6. John McCabe-Dansted & Geoffrey Pritchard & Arkadii Slinko, 2008. "Approximability of Dodgson’s rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 311-330, August.
    7. Piotr Faliszewski & Arkadii Slinko & Kolja Stahl & Nimrod Talmon, 2018. "Achieving fully proportional representation by clustering voters," Journal of Heuristics, Springer, vol. 24(5), pages 725-756, October.
    8. Semih Koray & Arkadii Slinko, 2008. "Self-selective social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 129-149, June.
    9. Marie-Louise Lackner & Martin Lackner, 2017. "On the likelihood of single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 717-745, April.

    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. James Green-Armytage & T. Tideman & Rafael Cosman, 2016. "Statistical evaluation of voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 183-212, January.
    2. Brian Kogelmann, 2017. "Aggregating out of indeterminacy," Politics, Philosophy & Economics, , vol. 16(2), pages 210-232, May.
    3. William V. Gehrlein & Hemant V. Kher, 2004. "Decision Rules for the Academy Awards Versus Those for Elections," Interfaces, INFORMS, vol. 34(3), pages 226-234, June.
    4. Steven J. Brams & D. Marc Kilgour, 2001. "Fallback Bargaining," Group Decision and Negotiation, Springer, vol. 10(4), pages 287-316, July.
    5. Saari, Donald G. & Valognes, Fabrice, 1999. "The geometry of Black's single peakedness and related conditions," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 429-456, December.
    6. Marie-Louise Lackner & Martin Lackner, 2017. "On the likelihood of single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 717-745, April.
    7. Truchon, Michel, 2004. "Aggregation of Rankings in Figure Skating," Cahiers de recherche 0402, Université Laval - Département d'économique.
    8. Yuliya Veselova, 2016. "The difference between manipulability indices in the IC and IANC models," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 609-638, March.
    9. Felix Brandt & Patrick Lederer & René Romen, 2024. "Relaxed notions of Condorcet-consistency and efficiency for strategyproof social decision schemes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(1), pages 19-55, August.
    10. Murat R. Sertel & M. Remzi Sanver, 2004. "Strong equilibrium outcomes of voting games ¶are the generalized Condorcet winners," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(2), pages 331-347, April.
    11. Lirong Xia, 2020. "How Likely Are Large Elections Tied?," Papers 2011.03791, arXiv.org, revised Jul 2021.
    12. Barbera, S. & Bossert, W. & Pattanaik, P.K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    13. 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.
    14. Mizukami, Hideki & Saijo, Tatsuyoshi & Wakayama, Takuma, 2003. "Strategy-Proof Sharing," Working Papers 1170, California Institute of Technology, Division of the Humanities and Social Sciences.
    15. Bruno Frey, 2011. "Tullock challenges: happiness, revolutions, and democracy," Public Choice, Springer, vol. 148(3), pages 269-281, September.
    16. Takamiya, Koji, 2001. "Coalition strategy-proofness and monotonicity in Shapley-Scarf housing markets," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 201-213, March.
    17. Alcalde-Unzu, Jorge & Gallo, Oihane & Vorsatz, Marc, 2024. "Strategy-proofness with single-peaked and single-dipped preferences," Games and Economic Behavior, Elsevier, vol. 147(C), pages 107-127.
    18. Burak Can & Peter Csoka & Emre Ergin, 2017. "How to choose a non-manipulable delegation?," CERS-IE WORKING PAPERS 1713, Institute of Economics, Centre for Economic and Regional Studies.
    19. Roy, Souvik & Storcken, Ton, 2019. "A characterization of possibility domains in strategic voting," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 46-55.
    20. Berghammer, Rudolf & Schnoor, Henning, 2015. "Control of Condorcet voting: Complexity and a Relation-Algebraic approach," European Journal of Operational Research, Elsevier, vol. 246(2), pages 505-516.

    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:spr:grdene:v:15:y:2006:i:1:d:10.1007_s10726-005-9007-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.