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A Comparison of Some Distance-Based Choice Rules in Ranking Environments

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  • Hannu Nurmi

Abstract

We discuss the relationships between positional rules (such as plurality and approval voting as well as the Borda count), Dodgson’s, Kemeny’s and Litvak’s methods of reaching consensus. The discrepancies between methods are seen as results of different intuitive conceptions of consensus goal states and ways of measuring distances therefrom. Saari’s geometric methodology is resorted to in the analysis of the consensus reaching methods. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Hannu Nurmi, 2004. "A Comparison of Some Distance-Based Choice Rules in Ranking Environments," Theory and Decision, Springer, vol. 57(1), pages 5-24, August.
    • Handle: RePEc:kap:theord:v:57:y:2004:i:1:p:5-24
    DOI: 10.1007/s11238-004-3671-9
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    References listed on IDEAS

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    1. Christian Klamler, 2004. "The Dodgson ranking and its relation to Kemeny’s method and Slater’s rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(1), pages 91-102, August.
    2. Christian Klamler, 2005. "On the Closeness Aspect of Three Voting Rules: Borda – Copeland – Maximin," Group Decision and Negotiation, Springer, vol. 14(3), pages 233-240, May.
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    Cited by:

    1. I. Contreras, 2012. "Ordered Weighted Disagreement Functions," Group Decision and Negotiation, Springer, vol. 21(3), pages 345-361, May.
    2. Muhammad Mahajne & Shmuel Nitzan & Oscar Volij, 2015. "Level $$r$$ r consensus and stable social choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 805-817, December.
    3. Eckert, Daniel & Klamler, Christian, 2010. "An equity-efficiency trade-off in a geometric approach to committee selection," European Journal of Political Economy, Elsevier, vol. 26(3), pages 386-391, September.
    4. Muhammad Mahajne & Shmuel Nitzan & Oscar Volij, 2013. "LEVEL r CONSENSUS AND STABLE SOCIAL CHOICE," Working Papers 1305, Ben-Gurion University of the Negev, Department of Economics.
    5. Ignacio Contreras, 2010. "A Distance-Based Consensus Model with Flexible Choice of Rank-Position Weights," Group Decision and Negotiation, Springer, vol. 19(5), pages 441-456, September.
    6. Kamwa, Eric, 2017. "On stable rules for selecting committees," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 36-44.
    7. Eric Kamwa, 2023. "On two voting systems that combine approval and preferences: fallback voting and preference approval voting," Public Choice, Springer, vol. 196(1), pages 169-205, July.
    8. Hannu Nurmi & Hannu Salonen, 2008. "More Borda Count Variations for Project Assesment," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(2), pages 109-122, September.

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