Matemática Aplicada às Escolhas Sociais: um protótipo para decisões justas

Democratic political systems have as basic condition to use the majority opinion to force it society. Several mathematical models have become indispensable to the Social Sciences. One of the most important and present today is the study of the fair vote, a coherent means of making democratic decisions, reflecting the will of a majority. Suffrage, the right to vote and to be voted, has always been one of the deepest universal problems, but the process of fairness of choices has taken a long time to obtain mathematical treatment with consistent theorems and propositions about how to make a full election, from initial conditions rigorous. We will give an analysis of the history of the vote and the ideas developed by two Frenchmen who have researched hard and honestly what would be the most honest way to choose their representatives in the so-called majority elections today. In the second part of the investigation, we will show studies by famous Americans on how to make a proportional election coherent, in what concerns the division of vacancies, where trial and error is the scientific method used in most cases. In the end, we will give an exposition of the models adopted in the Brazilian elections and, intuitively, we will draw a parallel with all the work and how the processes listed are correct or misleading, regarding the application of the best means of social choices