### Implementation of the VMAVA Method in Order to Make Applications with a Large Number of Candidates and Voters

Received: Jun. 29, 2023    Accepted: Aug. 01, 2023    Published: Aug. 31, 2023

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Abstract

Nowadays, we see everywhere in the world and particularly in Africa, revolts following elections. It is therefore important to find a voting method that represents consensus. It should also be noted that despite the votes, there are candidates who do not agree to recognize the results after their defeat. Faced with this situation, the ideal would be to find a good method that can result in less contrast. This is how the VMAVA method was developed. We notice that it is a good method because it fulfills good properties. However in the VMAVA method, we notice that the numerical applications have been made on voting situations where there are four candidates and five voters, sometimes four candidates and four voters, at most five candidates and seven voters. In our work, we are therefore interested in the implementation of the VMAVA method to facilitate calculations in voting situations where there are for example ten, fifteen candidates and ten thousand, twenty thousand voters. To do this, we have built two main functions, one which is responsible for choosing the elected candidate (s) on the basis of the total number of approvals and the other which makes it possible to decide between possible ties using the arithmetic averages of the candidates. Despite some difficulties encountered in this task, we have achieved quite interesting and concordant results.

 DOI 10.11648/j.pamj.20231203.12 Published in Pure and Applied Mathematics Journal ( Volume 12, Issue 3, June 2023 ) Page(s) 49-58 Creative Commons This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. Copyright Copyright © The Author(s), 2024. Published by Science Publishing Group
Keywords

Vote, Voter, Candidate, Approval, Arithmetic Mean, Implementation

References
 [1] Zoïnabo Savadogo and Blaise Somé. Voting method based on approval voting and arithmetic mean; International Journal of Applied Mathematical Research, 9 (1) (2020) 1-8. [2] Antoinette Baujard, Herrade Igersheim, Experimentation of vote by note and vote by approval during the French presidential election of April 22; HAL Id: halshs-00337290, https://shs.hal.science/halshs-00337290 Submitted on 23 Sep 2010. [3] Michel BALINSKI, Rida LARAKI, Jugement Majoritaire Vs. Vote Majoritaire (via les Présidentielles 2011-2012). [4] Adama COULIBALY, Group decision, Facilitation assistance: Adjustment of voting procedures depending on the context, doctoral thesis at the university of sciences, techniques and technologies of BAMAKO (USTTB). [5] Nathanaël Barrot; On the computational aspects of voting by approval, Thesis defended on March 31, 2016 at Paris-Dauphine University. [6] The MathWorks, Inc 24 Prime Park Way; Mail: http://www.mathworks.com Natick, MA 01760-1500. [7] F. Delebecque and J. C. Pesquet, MATLAB: Getting the software hand, https://www.math.u-bordeaux.fr/~ayger/MATLABSignal/Tutorials Quentin. [8] Glorieux, Mathematical tools and use of Matlab Course 2013-2014, Pierre and Marie Curie University - Paris VI. [9] D. Bouyssou (CNRS); Th. Marchant (Universiteit Gent); P. Perny (LIP6); Social choice theory and multi-criteria decision support, May 2002 – revised October 13, 2005. [10] François Durand, Towards less manipulable voting methods, Thesis defended on September 24, 2015, PIERRE AND MARIE CURIE UNIVERSITY; HAL Id: tel-03654945 https://hal.inria.fr/tel-03654945 Submitted on 29 Apr 2022. [11] Robert J. Weber; Approval Voting, The journal of economics perspectives, Vol. 9, No 1 (Winter, 1995), 39. [12] Patrick BLANCHENAY, Paradoxes de vote et modes de scrutin en France. [13] MAURICE SALLES, la théorie du choix social: une introduction a quelques résultats fondamentaux. [14] Nathanaël BARROT, Sur les aspects computationnels du vote par approbation, Université Paris-Dauphine. [15] Catherine Petillon, Si on votait autrement 25. 04. 2017.
• APA Style

Koumbèbarè Kambiré, Zoïnabo Savadogo, Frédéric Nikiéma. (2023). Implementation of the VMAVA Method in Order to Make Applications with a Large Number of Candidates and Voters. Pure and Applied Mathematics Journal, 12(3), 49-58. https://doi.org/10.11648/j.pamj.20231203.12

ACS Style

Koumbèbarè Kambiré; Zoïnabo Savadogo; Frédéric Nikiéma. Implementation of the VMAVA Method in Order to Make Applications with a Large Number of Candidates and Voters. Pure Appl. Math. J. 2023, 12(3), 49-58. doi: 10.11648/j.pamj.20231203.12

AMA Style

Koumbèbarè Kambiré, Zoïnabo Savadogo, Frédéric Nikiéma. Implementation of the VMAVA Method in Order to Make Applications with a Large Number of Candidates and Voters. Pure Appl Math J. 2023;12(3):49-58. doi: 10.11648/j.pamj.20231203.12

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author = {Koumbèbarè Kambiré and Zoïnabo Savadogo and Frédéric Nikiéma},
title = {Implementation of the VMAVA Method in Order to Make Applications with a Large Number of Candidates and Voters},
journal = {Pure and Applied Mathematics Journal},
volume = {12},
number = {3},
pages = {49-58},
doi = {10.11648/j.pamj.20231203.12},
url = {https://doi.org/10.11648/j.pamj.20231203.12},
abstract = {Nowadays, we see everywhere in the world and particularly in Africa, revolts following elections. It is therefore important to find a voting method that represents consensus. It should also be noted that despite the votes, there are candidates who do not agree to recognize the results after their defeat. Faced with this situation, the ideal would be to find a good method that can result in less contrast. This is how the VMAVA method was developed. We notice that it is a good method because it fulfills good properties. However in the VMAVA method, we notice that the numerical applications have been made on voting situations where there are four candidates and five voters, sometimes four candidates and four voters, at most five candidates and seven voters. In our work, we are therefore interested in the implementation of the VMAVA method to facilitate calculations in voting situations where there are for example ten, fifteen candidates and ten thousand, twenty thousand voters. To do this, we have built two main functions, one which is responsible for choosing the elected candidate (s) on the basis of the total number of approvals and the other which makes it possible to decide between possible ties using the arithmetic averages of the candidates. Despite some difficulties encountered in this task, we have achieved quite interesting and concordant results.},
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AB  - Nowadays, we see everywhere in the world and particularly in Africa, revolts following elections. It is therefore important to find a voting method that represents consensus. It should also be noted that despite the votes, there are candidates who do not agree to recognize the results after their defeat. Faced with this situation, the ideal would be to find a good method that can result in less contrast. This is how the VMAVA method was developed. We notice that it is a good method because it fulfills good properties. However in the VMAVA method, we notice that the numerical applications have been made on voting situations where there are four candidates and five voters, sometimes four candidates and four voters, at most five candidates and seven voters. In our work, we are therefore interested in the implementation of the VMAVA method to facilitate calculations in voting situations where there are for example ten, fifteen candidates and ten thousand, twenty thousand voters. To do this, we have built two main functions, one which is responsible for choosing the elected candidate (s) on the basis of the total number of approvals and the other which makes it possible to decide between possible ties using the arithmetic averages of the candidates. Despite some difficulties encountered in this task, we have achieved quite interesting and concordant results.
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Author Information
• Department of Mathematics, Laboratory of Numerical Analysis, Computer Science and Biomathematics, Joseph Ki-Zerbo University, Ouagadougou, Burkina Faso

• Department of Mathematics, Laboratory of Numerical Analysis, Computer Science and Biomathematics, Joseph Ki-Zerbo University, Ouagadougou, Burkina Faso

• Department of Mathematics, Laboratory of Numerical Analysis, Computer Science and Biomathematics, Joseph Ki-Zerbo University, Ouagadougou, Burkina Faso

• Section