O Problema do Poder Efetivo na Câmara dos Deputados
Proportionality in political representation is an essential theme forrepresentative democracy. In Brazil, this debate appears in the contextof non-proportionality between a federative unit’s populationsize and its number of representatives in the Chamber of Deputies.In other words, the number of deputies in a state is not proportionalto its number of inhabitants, which violates the "one man, one vote"principle.Discussions around this disproportionality have motivated scholarsto develop empirical research that aims to identify the causesand consequences of the phenomenon and to analyze the impactthat the rule introduces in the political process. This article seeksto contribute to this debate by measuring the effective power ofeach Brazilian federation’s entity and proposing alternatives ofdistribution 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 representationaldiscrepancies. After evaluating several distributions, wesolved the Inverse Power Index Problem (IPIP) to obtain a distributionof chairs that reduces such disparities. To solve the IPIP, whichis computationally hard, we use an evolutionary heuristic. As anobjective function to minimize the discrepancy, we use the linearShapley rule, in which the power index of each state is proportionalto its population.