Mean-median compromise method as an innovating voting rule in social choice theory

  • Authors

    • Ruffin-Benoit Ngoie Institut Supérieur Pédagogique de Mbanza-Ngungu (Teaching College of Mbanza-Ngungu)
    • Berthold Ulungu E-L Institut Supérieur des Techniques Appliquées
    2015-02-20
    https://doi.org/10.14419/ijamr.v4i1.4139
  • Aggregation, Approval Voting, Borda Majority Count, Majority Judgment, Social Choice Function.
  • This paper aims at presenting a new voting function which is obtained in Balinski-Laraki's framework and benefits mean and median advantages. The so-called Mean-Median Comprise Method (MMCM) has fulfilled criteria such as unanimity, neutrality, anonymity, monotonicity, and Arrow's independence of irrelevant alternatives. It also generalizes approval voting system.

  • References

    1. [1] Nicolas Jean. Environnement politique et élections : Une étude des déterminants du vote appliquée aux élections municipales françaises. PhD thesis, Université des Sciences et Technologies de Lille, 2012.

      [2] Kenneth J. Arrow. Social choice and individual values, Yale University Press, 1951.

      [3] Kenneth J. Arrow. Social choice and individual values, Yale University Press, 1963.

      [4] Michel Balinski and Rida Laraki. A theory of measuring, electing and ranking. Proceedings of the National Academy of Sciences of the United States of America, pages 8720-8725, 2007.

      [5] Michel Balinski and Rida Laraki. Majority Judgment: measuring, ranking and electing. MIT Press, 2010.

      [6] Michel Balinski and Rida Laraki. Jugement majoritaire vs vote majoritaire. Cahier 2012-37, CNRS, 2012.

      [7] José Carlos R. Alcantud and Annick Laruelle. Dis& approval voting: a characterization. Social Choice and Welfare, 43(1):1-10, 2014. http://dx.doi.org/10.1007/s00355-013-0766-7.

      [8] Manzoor Ahmed Zahid. A new framework for elections. PhD thesis, Tilburg University, 2012.

      [9] Ruffin-Benoît M. Ngoie, Zoïnabo Savadogo, and Berthold E.-L. Ulungu. Median and average as tools for measuring, electing and ranking: new prospects. Fundamental Journal of Mathematics and Mathematical Sciences, 1(1):9-30, 2014.

      [10] Ruffin-Benoit M. Ngoie, Zoïnabo Savadogo, and Berthold E.-L. Ulungu. New Prospects in Social Choice Theory: Median and average as tools for measuring, electing and ranking. Adv. Stud. Contemp. Math., 25(1): 19-38, 2015.

      [11] Edurne Falco and José Luis Garcia-Lapresta. A distance-based extension of the majority judgement voting system. In Acta Universitatis Belii, Mathematics 18, pages 17-27, 2011.

      [12] Edurne Falco, José Luis Garcia-Lapresta, and Llorenç Rosello. Allowing voters to be imprecise: à proposal using multiple linguistic terms. Information Sciences, 2013.

      [13] Edurne Falco, José Luis Garcia-Lapresta, and Llorenç Rosello. Aggregating imprecise linguistic expressions. In P. Guo and W. Pedrycz, editors, Human-Centric Decision Making Models for Social Sciences. 2014. http://dx.doi.org/10.1007/978-3-642-39307-5_5.

      [14] Gilbert W. Basset and Joseph Persky. Robust voting. Public Choice, 99:299-310, 1999. http://dx.doi.org/10.1023/A:1018324807861.

      [15] Sylvain Durand. Sur quelques paradoxes en Théorie du Choix Social et en décision multicritère. PhD thesis, Université Joseph Fourier-Grenoble 1, 2000.

      [16] Dan S. Felsenthal. Electoral Systems. Paradoxes, Assumptions, and Procedures, chapter 3: Review of Paradoxes Afflicting Procedures for Electing a Single Candidate. Springer-Verlag, Berlin Heidelberg, 2012.

      [17] Jean-François Laslier. Electoral Systems, chapter 13: And the loser is... Plurality Voting. Springer-Verlag, Berlin Heilderberg, 2012.

      [18] Warren D. Smith. Range voting. http://rangevoting.org/RangeVoting.html, 2012.

      [19] Antoinette Baujard and Herrade Igersheim. Expérimentation du vote par note et du vote par approbation le 22 avril 2007. Premiers résultats. Revue économique, 60(1):189-201, 2009.

      [20] Antoinette Baujard, Frédéric Gavrel, Herrade Igersheim, Jean-François Laslier, and Isabelle Lebon. Who's favored by evaluative voting ? an experiment conducted during the 2012 french presidentiel election. Cahier 2013-05, CNRS, 2013.

      [21] Jean-François Laslier and Karine Van der Straeten. Une expérience de vote par assentiment. Revue française de science politique, 54(1):99-130, 2004. http://dx.doi.org/10.3917/rfsp.541.0099.

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  • How to Cite

    Ngoie, R.-B., & Ulungu E-L, B. (2015). Mean-median compromise method as an innovating voting rule in social choice theory. International Journal of Applied Mathematical Research, 4(1), 177-182. https://doi.org/10.14419/ijamr.v4i1.4139