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Exploratory Analysis of Similarities Between Social Choice Rules

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  • 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
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    References listed on IDEAS

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    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.
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    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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. SLINKO, Arkadii & WHITE, Shaun, 2006. "On the Manipulability of Proportional Representation," Cahiers de recherche 2006-20, Universite de Montreal, Departement de sciences economiques.
    6. SLINKO, Arkadii & WHITE, Shaun, 2006. "On the Manipulability of Proportional Representation," Cahiers de recherche 12-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    7. Arkadii Slinko & Shaun White, 2010. "Proportional Representation and Strategic Voters," Journal of Theoretical Politics, , vol. 22(3), pages 301-332, July.
    8. 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.
    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.

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