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Ensemble classifiers have been investigated by many in the artificial intelligence and machine learning community. Majority voting and weighted majority voting are two commonly used combination schemes in ensemble learning. However, understanding of them is incomplete at best, with some properties even misunderstood. In this paper, we present a group of properties of these two schemes formally under a geometric framework. Two key factors, every component base classifier’s performance and dissimilarity between each pair of component classifiers are evaluated by the same metric—the Euclidean distance. Consequently, ensembling becomes a deterministic problem and the performance of an ensemble can be calculated directly by a formula. We prove several theorems of interest and explain their implications for ensembles. In particular, we compare and contrast the effect of the number of component classifiers on these two types of ensemble schemes. Some important properties of both combination schemes are discussed. And a method to calculate the optimal weights for the weighted majority voting is presented. Empirical investigation is conducted to verify the theoretical results. We believe that the results from this paper are very useful for us to understand the fundamental properties of these two combination schemes and the principles of ensemble classifiers in general. The results are also helpful for us to investigate some issues in ensemble classifiers, such as ensemble performance prediction, diversity, ensemble pruning, and others.

Brain tumor is a crucial health problem that affects people’s lives and their life quality. The treatment of this disease varies according to the size, type, location, and condition of the tumor detected. Therefore, the treatment of this disease may vary from person to person. Early diagnosis of brain tumor in individuals is very important as it can change the course of treatment. The aim of this study is to provide a hybrid learning solution for early detection of brain tumors on Magnetic Resonance Imaging (MRI) and X-Ray scans. In this study, two separate datasets involving a total of 7600 MRI and X-Ray scans, available to users from Kaggle, were used. In the experimental part of this study, the 7600 MRI and X-Ray scans were trained and tested using a number of well-known learning models which are; XGBoost, Convolutional Neural Networks (CNN), ResNet50, DenseNet121 and AlexNet. After the experimental studies, the accuracy, sensitivity, specificity, precision, recall and F1-Score metrics of each of these models were obtained and compared. In addition, taking into account the results obtained from these models, a fusion approach named \"Majority Voting\" has been applied and the performance value of the system has been successfully increased. In summary, the performance results obtained from the used model are 98.98% for XGBoost, 99.75% for CNN, 99.65% for DenseNet121, 97.21% for ResNet50 and 99.84% for AlexNet. The accuracy after the “Majority Voting” approach applied is 100.00%. The results of the experimental studies demonstrate the promise of the proposed hybrid learning system with the Majority Voting approach and emphasizing its feasibility, effectiveness, and efficiency in processing both MRI and X-Ray tumor scanning techniques. Additionally, comparison with the state-of-the-art demonstrates that the proposed model outperforms the existing models for brain tumor detection.

This paper considers the political economy of financial development in an overlapping generations model that incorporates credit market imperfections, and shows that income inequality is a determinant of financial and economic development. Individuals have an opportunity to start an investment project at a fixed cost, but their income to finance the cost is unequal. The government proposes a policy financed by taxation that mitigates credit market imperfections, the implementation of which is determined through majority voting. The policy benefits middle-income individuals who can start the investment only after the implementation of the policy. The policy is, however, against the interest of the rich who wish to block such new entry, and that of the poor who wish to avoid the tax burden. Whether the policy obtains majority support depends on income inequality. High income inequality makes the policy hard to implement, which causes financial and economic underdevelopment.

This paper investigates the effects of members' exits from a currency union on the credibility of the common currency. In our currency union model, the inflation rate of the common currency is determined by majority voting among N member countries that are heterogeneous with respect to their output shocks. Once an inflation rate of the common currency has been selected, each member decides whether to remain in the currency union or not. If a member decides to exit, it has to pay a fixed social cost and individually chooses the inflation rate of its currency. Unlike previous research on this topic, we focus on the possibility of achieving an optimal outcome, which generates no inflation bias, when more than one member is expected to leave the currency union. We show that the optimal outcome can only be achieved if no members leave the currency union.

Land use land cover analysis aided by remote sensing provides the civic authorities a broader picture of the geographic area. This work aims to get the land cover map of the Bangalore Urban region using multispectral remotely sensed images. Three individual classifiers, namely random forest classifier, support vector machine classifier and the k-nearest neighbour, have been used. For the study area under consideration, the spectral signatures (which is the basis for classification) of water, vegetation and soil are not very distinct, which may cause misclassification. Also, the study area has imbalanced classes, because of which the individual classifiers may not give optimal results. The novelty of this work lies in the handling of these two shortcomings. A random unweighted hard MV (Overall accuracy = 82.75), priority-based unweighted hard MV (Overall accuracy = 86.06) and weighted hard MV (Overall accuracy = 86.92) classifiers are implemented here, and it is shown that they provide a better overall accuracy compared to the individual classifiers.

The mean majority deficit in a two-tier voting system is a function of the partition of the population. We derive a new square-root rule: For odd-numbered population sizes and equipopulous units the mean majority deficit is maximal when the member size of the units in the partition is close to the square root of the population size. Furthermore, within the partitions into roughly equipopulous units, partitions with small even numbers of units or small even-sized units yield high mean majority deficits. We discuss the implications for the winner-takes-all system in the US Electoral College.

A major challenge in instrumental variable (IV) analysis is to find instruments that are valid, or have no direct effect on the outcome and are ignorable. Typically one is unsure whether all of the putative IVs are in fact valid. We propose a general inference procedure in the presence of invalid IVs, called two-stage hard thresholding with voting. The procedure uses two hard thresholding steps to select strong instruments and to generate candidate sets of valid IVs. Voting takes the candidate sets and uses majority and plurality rules to determine the true set of valid IVs. In low dimensions with invalid instruments, our proposal correctly selects valid IVs, consistently estimates the causal effect, produces valid confidence intervals for the causal effect and has oracle optimal width, even if the so-called 50% rule or the majority rule is violated. In high dimensions, we establish nearly identical results without oracle optimality. In simulations, our proposal outperforms traditional and recent methods in the invalid IV literature. We also apply our method to reanalyse the causal effect of education on earnings.

This article strengthens existing analysis concerning the effectiveness of majority rule. It demonstrates a one-to-one equivalence between the basic issue of social choice theory (the problem of selection of a well-functioning social choice rule [SCR]) and the problems that majority rule faces (it fails decisiveness in certain preference profiles). It is shown that whenever an SCR works well, majority rule works well, and in these circumstances, the SCR yields the same outcome as majority rule. So whenever majority rule works we can never do better by choosing an alternative SCR. When majority rule does not work well, then any other SCR will face a serious problem, too. The article defines the conditions underlying the concept of an SCR working well that enables these results to be established.

Using data of contested decisions in the Council of the European Union, combined with data on the position of member states on the left-right and support for European integration dimensions, this paper provides an overview of winning coalitions formed in the council in the 1998 to 2004 time span. It shows distance between the combined policy positions of winning coalitions to individual EU states within these coalitions and demonstrates that most winning coalitions in the Council have a large combined voting weight, minimal winning coalitions are rare, and ideological connectedness plays a much smaller role than expected.