One of the main goals of social choice theory is the study of voting methods. Voting allows for the aggregation of several individual points of view in order to obtain a result that represents the general interest. Thus votes play a vital role in any society. Indeed, to elect a president of a republic, or deputies, we go through votes. Unfortunately, the transformation of individual preferences into a collective preference often leads to voter frustration and, above all, can lead to conflict. Thus, in the literature on social choice theory, many studies have been conducted in order to find methods that make it possible to converge towards the general interest and that generate less conflict. But it seems that there is no totally satisfactory method. It is within this framework that, in this article, we are inspired by the method of Voting based on Arithmetic Mean and Voting by Assent (VMAVA) and a preference distance allowing to evaluate the candidates with respect to the ideal candidate (i.e., preferred by all voters) to propose a voting method that best reflects the voters preferences.

voting methods, arithmetic mean, assent voting, preference distance.

Received: November 23, 2022; Revised: January 8, 2023; Accepted: January 11, 2023; Published: January 19, 2023

How to cite this article: Zoïnabo Savadogo, Stéphane Aimé Metchebon Takougang and Frédéric Nikiema, Voting method based on a distance assessment of preferences in relation to the ideal candidate, Universal Journal of Mathematics and Mathematical Sciences 18(1) (2023), 99-119. http://dx.doi.org/10.17654/2277141723007

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] M. Balinski and R. Laraki, Majority Judgment: Measuring, Ranking, and Electing, MIT Press, Cambridge-Massachusetts, USA, 2010.
[2] M. Balinski and R. Laraki, Jugement majoritaire et vote majoritaire, Ecole Polytechnique, Paris, 2012, p. 24.
[3] N. Barrot, Sur les aspects computationnels du vote par approbation, Thèse de Doctorat, Université Paris-Dauphine, Paris, 2016, p. 201.
[4] P. Blanchenay, Parodoxes de vote et modes de scrutin en France, Mmoire de Master, Ecole des hautes tudes commerciales Majeure conomie, Paris, 2004, p. 82.
[5] A. Baujard, R. Blanch, S. Bouveret, H. Igersheim, A. Laruelle, J.-F. Laslier and I. Lebon, Compte-rendu de l’exprimentation Voter Autrement lors du premier tour de l’lection prsidentielle franaise le 23 avril 2017 Allevard-les-Bains, Crolles, Grenoble, Hrouville-Saint-Clair, Strasbourg et sur internet, Working papers, Université de Lyon, Groupe d’Analyse et de Thorie Economique Lyon St-tienne (GATE Lyon St-tienne), 2017, p. 48.
[6] S. Duand, Sur quelques paradoxes en thorie du choix social et en Aide la decision, Thèse de Doctorat, Université Joseph-Fourier, Grenoble, 2000, p. 148.
[7] F. Durand, Vers des modes de scrutin moins manipulables, Thèse de Doctorat, Université Pierre et Marie Curie, Paris, 2015.
[8] H. Igersheim and A. Baujard, La question du vote, Expriementations en laboratoire et in situ, L’actualit Economique, Revue d’analyse Conomique 92 (2016), 1-2, 151-189.
[9] A. Z. Manzoor, A new framework for lections, Ph.D. Thesis, University of Tilburg, Tilburg, 2012, p. 126.
[10] V. Merlin, La thorie des choix collectifs porte de tous! Commentaires sur quatre livres de vulgarisation de Donald Saari, Mathématiques et Sciences Humaines 163 (2003), 147-160.
[11] R.-B. M. Ngoie, Z. Savadogo and B. E.-L. Ulungu, Median and average as tools for measuring, electing and ranking: new prospects, Fundamental Journal of Mathematics and Mathematical Sciences 1(1) (2014), 9-30.
[12] Z. Savadogo and B. Some, Voting method based on approval voting and arithmetic mean, International Journal of Applied Mathematical Research 9(1) (2020), 1-8.
[13] O. Sicard, Thorie du choix social, Episode 3, Une version cardinale de la Thorie, Working paper, Institut de Recherche sur l’enseignement des Mathématiques de la Reunion, 2016, p. 19.
[14] H. Smaoui and D. Lepelley, Le système de vote par note à trois niveaux: étude d’un nouveau mode de scrutin, Revue d’économie Politique 123(6) (2013), 827-850.
[15] J. G. Suitt, A. Guyon, T. Hennion, R. Laraki, X. Starkloff, S. Thibault and B. Favreau, Vers un systme de vote plus juste? Ecole Polytechnique, Paris, 2014, p. 65.
[16] N. Des Rosiers, B. Colas and J. R. Wood, Un vote qui compte: la rforme lectorale au Canadale, Commission du droit du Canada, 2016.
[17] Z. Savadogo, A. Compaor and P. O. F. Ouedraogo, Voting method based on an average gap assessment, Eur. J. Pure Appl. Math. 12(3) (2019), 1176-1186.