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.

The Risk Factors of Obesity Among Elderly in Sintang, Indonesia

Body Mass Index problem is becoming a double burden in Indonesia, including among older people. Nowadays, the elderly face a high index of BMI due to some risk factors and it is leading to other non-communicable diseases. This research aimed to examine the correlation between some determinants and obesity among older people in Sintang Regency, West Kalimantan. 358 elderly aged 46 to 65 years participated in this study selected by the total sampling method. The independent variables in this study were knowledge, activity, food intake, sex, attitude, age, the history of obesity, and obesity breeds, type contraception, and the duration of sleep. The multivariate analysis was found that knowledge, activity, food intake, age, and duration of sleep were significantly associated with obesity among the elderly. The preventive and promotive approach is needed to treat the obesity prevalence.

On the Complexity of the Inverse Semivalue Problem for Weighted Voting Games

Weighted voting games are a family of cooperative games, typically used to model voting situations where a number of agents (players) vote against or for a proposal. In such games, a proposal is accepted if an appropriately weighted sum of the votes exceeds a prespecified threshold. As the influence of a player over the voting outcome is not in general proportional to her assigned weight, various power indices have been proposed to measure each player’s influence. The inverse power index problem is the problem of designing a weighted voting game that achieves a set of target influences according to a predefined power index. In this work, we study the computational complexity of the inverse problem when the power index belongs to the class of semivalues. We prove that the inverse problem is computationally intractable for a broad family of semivalues, including all regular semivalues. As a special case of our general result, we establish computational hardness of the inverse problem for the Banzhaf indices and the Shapley values, arguably the most popular power indices.

An Integrated QFD-TOPSIS Approach for Supplier Selection Under Fuzzy Environment

This article describes how supplier selection is a multi-index problem which affects the efficiency of the whole supply chain in both manufacturing and service industries. Considering the importance of selecting effective suppliers, this article aims to integrate two well-known techniques, Quality Function Deployment (QFD) and The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) in order to evaluate suppliers and rank them based on their merits. In order to handle the inherent uncertainty in the process of experts' judgments, fuzzy logic is involved in the methodology applied in this study. The validity of the utilized integrated approach is demonstrated through conducting a case study in the detergent manufacturing industry in Iran.