New Innovative Method in the Field of Social Choice Theory

: Social choice theory includes the study of voting methods. In the literature on social choice theory many methods exist, the main objective of all these methods is the determination of a good method. However, many of these methods give controversial results which often lead to disputes. It should also be noted that sometimes, regardless of the method used, there are people who are not ready to accept the results given by the ballot box. The ideal would be to find a method with good properties, because it seems that there are no completely satisfactory methods. Since the goal of a voting method is to reconcile several points of view into a general interest, one should focus on the properties. The geometric mean does not lead to a compensation of weak criteria by stronger ones as it is the case with the arithmetic mean. Indeed, by using the geometric mean, even if only one criterion is very weak and the others are very strong, a candidate may not be well ranked; moreover, assent voting is very well appreciated in the literature by many authors and also generates huge opportunities. This justifies our choice in this work to combine geometric mean and assent voting to develop a method with good properties.