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A Borda count for partially ordered ballots

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  • John Cullinan
  • Samuel Hsiao
  • David Polett

Abstract

The application of the theory of partially ordered sets to voting systems is an important development in the mathematical theory of elections. Many of the results in this area are on the comparative properties between traditional elections with linearly ordered ballots and those with partially ordered ballots. In this paper we present a scoring procedure, called the partial Borda count, that extends the classic Borda count to allow for arbitrary partially ordered preference rankings. We characterize the partial Borda count in the context of weighting procedures and in the context of social choice functions. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • John Cullinan & Samuel Hsiao & David Polett, 2014. "A Borda count for partially ordered ballots," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 913-926, April.
    • Handle: RePEc:spr:sochwe:v:42:y:2014:i:4:p:913-926
    DOI: 10.1007/s00355-013-0751-1
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    4. Niemi, Richard G., 1984. "The Problem of Strategic Behavior under Approval Voting," American Political Science Review, Cambridge University Press, vol. 78(4), pages 952-958, December.
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    6. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
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    Cited by:

    1. Nehring, Klaus & Puppe, Clemens, 2019. "Resource allocation by frugal majority rule," Working Paper Series in Economics 131, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    2. Terzopoulou, Zoi & Endriss, Ulle, 2021. "The Borda class," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 31-40.
    3. Nehring, Klaus & Puppe, Clemens, 2022. "Condorcet solutions in frugal models of budget allocation," Working Paper Series in Economics 156, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    4. Ivanov, Asen, 2022. "The Borda count with weak preferences," Economics Letters, Elsevier, vol. 210(C).
    5. Wen Li & Yicheng Ye & Nanyan Hu & Xianhua Wang & Qihu Wang, 2019. "Real-Time Warning and Risk Assessment of Tailings Dam Disaster Status Based on Dynamic Hierarchy-Grey Relation Analysis," Complexity, Hindawi, vol. 2019, pages 1-14, April.
    6. Haris Aziz, 2016. "A generalization of the AL method for fair allocation of indivisible objects," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 307-324, October.
    7. D. Marc Kilgour & Jean-Charles Grégoire & Angèle M. Foley, 2022. "Weighted scoring elections: is Borda best?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 365-391, February.

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