O Problema do Poder Efetivo na Câmara dos Deputados

Proportionality in political representation is an essential theme for representative democracy. In Brazil, this debate appears in the context of non-proportionality between a federative unit’s population size and its number of representatives in the Chamber of Deputies. In other words, the number of deputies in a state is not proportional to its number of inhabitants, which violates the "one man, one vote" principle. Discussions around this disproportionality have motivated scholars to develop empirical research that aims to identify the causes and consequences of the phenomenon and to analyze the impact that the rule introduces in the political process. This article seeks to contribute to this debate by measuring the effective power of each Brazilian federation’s entity and proposing alternatives of distribution for the Brazilian Chamber of Deputies. To this end, we use a mathematical concept from game theory, called Power Index, which allows quantifying the existing representational discrepancies. After evaluating several distributions, we solved the Inverse Power Index Problem (IPIP) to obtain a distribution of chairs that reduces such disparities. To solve the IPIP, which is computationally hard, we use an evolutionary heuristic. As an objective function to minimize the discrepancy, we use the linear Shapley rule, in which the power index of each state is proportional to its population.