Voting Weight Research Articles

Weighted committee games

Many binary collective choice situations can be described as weighted simple voting games. We introduce weighted committee games to model decisions on an arbitrary number of alternatives in analogous fashion. We compare the effect of different voting weights (shareholdings, party seats, etc.) under plurality, Borda, Copeland, and antiplurality rule. The number and geometry of weight equivalence classes differ widely across the rules. Decisions can be much more sensitive to weights in Borda committees than (anti-)plurality or Copeland ones.

A Comparison of Partisan-Gerrymandering Measures

We compare and contrast 14 measures that have been proposed for the purpose of quantifying partisan gerrymandering. We consider measures that, rather than examining the shapes of districts, utilize only the partisan vote distribution among districts. The measures considered are two versions of partisan bias, the efficiency gap and several of its variants, the mean-median difference and the equal vote weight standard, the declination and one variant, and the lopsided-means test. Our primary means of evaluating these measures is a suite of hypothetical elections we classify from the start as fair or unfair. We conclude that the declination is the most successful measure in terms of avoiding false positives and false negatives on the elections considered. We include in a supplementary appendix the most extreme outliers for each measure among historical congressional and state legislative elections.

Machine Learning Models in Type 2 Diabetes Risk Prediction: Results from a Cross-sectional Retrospective Study in Chinese Adults

Type 2 diabetes mellitus (T2DM) has become a prevalent health problem in China, especially in urban areas. Early prevention strategies are needed to reduce the associated mortality and morbidity. We applied the combination of rules and different machine learning techniques to assess the risk of development of T2DM in an urban Chinese adult population. A retrospective analysis was performed on 8000 people with non-diabetes and 3845 people with T2DM in Nanjing. Multilayer Perceptron (MLP), AdaBoost (AD), Trees Random Forest (TRF), Support Vector Machine (SVM), and Gradient Tree Boosting (GTB) machine learning techniques with 10 cross validation methods were used with the proposed model for the prediction of the risk of development of T2DM. The performance of these models was evaluated with accuracy, precision, sensitivity, specificity, and area under receiver operating characteristic (ROC) curve (AUC). After comparison, the prediction accuracy of the different five machine models was 0.87, 0.86, 0.86, 0.86 and 0.86 respectively. The combination model using the same voting weight of each component was built on T2DM, which was performed better than individual models. The findings indicate that, combining machine learning models could provide an accurate assessment model for T2DM risk prediction.

Systematic approach to binary classification of images in video streams using shifting time windows

Multiple algorithms classifying frames in video sequences consider them only as separate images. After pointing out the properties of real-life recordings and classifications of their frames, we propose a new shifting time window approach for improving binary classifications. It proceeds in two steps: First, well-known classification algorithms are used separately for each frame to acquire preliminary classifications. Secondly, the results of the previous step are analyzed in relatively short sequences of consecutive images (the shifting time window). Taking into account the continuous nature of analyzed real-life videos, the preliminary binary classification sequences can be corrected. In consequence, the classification quality is improved. Furthermore, we offer a systematic approach where all parameters of the proposed algorithm (such as the window length or vote weight distribution in the window) are considered and their optimal values are determined. Experiments on representative examples confirm the advantages of the proposed approach.

Enriching the random subspace method with margin theory – a solution for the high-dimensional classification task

ABSTRACTThe random subspace method (RSM) has proved its excellence in numbers of pattern recognition tasks. However, the standard RSM is limited owing to the randomness in its feature selection procedure that is likely to lead to feature subset having poor class separability. In this paper, a proposal for a margin-based criterion has been presented for the evaluation of the true significance of the features, together with the true classification ability of base classifiers, so that both the training phase and integration phase of standard RSM could be enhanced. In the training phase, the random feature selection procedure is enhanced using a weighted random feature selection procedure, in order to improve the classification ability of the base classifier. In the integration phase, the simple majority voting strategy is enhanced using a weighted majority voting strategy for the purpose of assigning the base classifiers with poor classification ability to the lower voting weights. Experimental results on 30 benchmark datasets, together with 6 high-dimensional datasets prove that the recommended approach is capable of better providing classification ability to the usual classification task, in addition to the high-dimensional classification task.

Can Gerrymanders Be Detected? An Examination of Wisconsin’s State Assembly

In October 2017, the Supreme Court heard an appeal of a November 2016 ruling striking down Wisconsin’s State Assembly districts as a Republican gerrymander that illegally dilutes the weight of Democratic votes. We take the opportunity to revisit this litigation to evaluate three proposed methods of detecting gerrymanders: the “efficiency gap,” a count of Assembly districts carried by statewide candidates, and the difference between the district-level partisan median and mean. The first two measures figure either centrally or peripherally in the plaintiffs’ case in Wisconsin, while the third is the approach we favor. We expand on the analysis offered at trial by evaluating how these measures fare across a variety of elections in Wisconsin and with the aid of 10,000 alternative Assembly maps drawn by computer. The alternative maps provide the appropriate baseline with which to gauge the level of vote dilution in Wisconsin and distinguish between the effect of residential geography and the Legislature’s actions. The results show that Wisconsin’s Assembly map is a substantial gerrymander according the median–mean comparison across all elections, while the two tests relied upon by the plaintiffs provide mixed results. We examine the measurement qualities of each test and show that the efficiency gap and districts-carried count both capture elements beyond partisan bias. We find no similar ambiguity with the median–mean comparison and conclude that the plaintiffs’ claim that Wisconsin’s Assembly map systematically dilutes the weight of Democratic votes is correct.

The probability of majority inversion in a two-stage voting system with three states

Abstract Two-stage voting is prone to majority inversions, a situation in which the outcome of an election is not backed by a majority of popular votes. We study the probability of majority inversion in a model with two candidates, three states and uniformly distributed fractions of supporters for each candidate. The model encompasses equal or distinct population sizes, with equal, population-based or arbitrary voting weights in the second stage. We prove that, when no state can dictate the outcome of the election by commanding a voting weight in excess of one half, the probability of majority inversion increases with the size disparity among the states.

A novel spontaneous facial expression recognition using dynamically weighted majority voting based ensemble classifier

Facial Expression Recognition (FER) is inherently data driven. Spontaneous expressions are substantially different from posed expressions. Spontaneous facial expressions are more challenging and more difficult to recognize. Any facial expression can be represented in many different patterns of muscles movements. Moreover, the facial expressions show discrepancies in different cultures and ethnicities. Therefore, a FER system has to learn a huge problem/feature space. A base classifier trained on a sub-region of feature space, cannot perform equally well in other areas of feature space. Therefore, a base classifier should be assigned higher voting weight in the regions near to its training space and a lower voting weight in the regions far from its training space. In order to maintain high accuracy and robustness of a FER system in space and time, a Dynamic Weight Majority Voting (DWMV) mechanism for base classifiers is introduced. An ensemble system for FER is proposed that has the aptitude of incrementally learning and thus, can learn all possible patterns of expressions that may be generated in feature or in various cultures and ethnicities. Speeded-Up Robust Features (SURF) are used to represent the feature space. Since no work in literature is found on “which similarity measure is more appropriate in SURF descriptor domain for facial expression recognition”, therefore, different similarity measures are used and the results are compared. A vast range of experimentation is performed on posed and spontaneous databases that demonstrates promising results.

Approximating Power by Weights

Determining the power distribution of the members of a shareholder meeting or a legislative committee is a well-known problem for many applications. In some cases it turns out that power is nearly proportional to relative voting weights, which is very beneficial for both theoretical considerations and practical computations with many members. We present quantitative approximation results with precise error bounds for several power indices as well as impossibility results for such approximations between power and weights.

A fast learn++.NSE classification algorithm based on weighted moving average

Current researches of incremental classification learning algorithms mainly focus on learning from data in a stationary environment. The incremental learning in a non-stationary environment (NSE), where the underlying data probability distribution changes over time, however, has received much less attentions despite the abundant real applications have generated the long-term and cumulative big data in NSE. Thus, the incremental learning in NSE has gradually received extensive attentions. Nevertheless, the popular incremental classification learning algorithms currently for NSE such as SEA and DWM generally place strict restrictions on the changes. These algorithms can only deal with gradual drift and noncyclical and no new category situations. Therefore, it is highly necessary to develop a novel efficient incremental classification learning algorithm for the gradually cumulative big data in complex NSE. The recently proposed Learn++.NSE algorithm is an important research achievement in this field. However, the vote weight of each base-classifier of the Learn++.NSE depends on its whole error rates in the environments experienced. Therefore, the classification learning efficiency of the Learn++.NSE should be further improved. A novel fast Learn++.NSE algorithm based on weighted moving average (WMA-Learn++.NSE) is presented in this paper, which computes the weighted average of error rates using the sliding window technology to optimize the weight calculation. By only using the recent classification error rates of each base-classifier inside the sliding window to calculate the vote weight, the WMA-Learn++.NSE accelerates the compute of vote weight and improves the efficiency of classification learning. The verification experiments and performance analyses on both synthetic and real data set are presented in this paper. The experimental results show that the WMA-Learn++.NSE can achieve a higher execution efficiency compared to the Learn++.NSE in getting the equivalent classification correct rate.

Hough Forest With Optimized Leaves for Global Hand Pose Estimation With Arbitrary Postures.

Vision-based hand pose estimation is important in human-computer interaction. While many recent works focus on full degree-of-freedom hand pose estimation, robust estimation of global hand pose remains a challenging problem. This paper presents a novel algorithm to optimize the leaf weights in a Hough forest to assist global hand pose estimation with a single depth camera. Different from traditional Hough forest, we propose to learn the vote weights stored at the leaf nodes of a forest in a principled way to minimize average pose prediction error, so that ambiguous votes are largely suppressed during prediction fusion. Experiments show that the proposed method largely improves pose estimation accuracy with optimized leaf weights on both synthesis and real datasets and performs favorably compared to state-of-the-art convolutional neural network-based methods. On real-world depth videos, the proposed method demonstrates improved robustness compared to several other recent hand tracking systems from both industry and academy. Moreover, we utilize the proposed method to build virtual/augmented reality applications to allow users to manipulate and examine virtual objects with bare hands.

Boosting landmark retrieval baseline with burstiness detection

In image retrieval, the bag-of-visual-words model-based approaches combined withthe spatial verification (SP) post-processing step have achieved considerableprogress. However, in practice, especially for retrieving landmark images, theauthors have observed that this baseline suffers from the problem of burst matches.This issue is caused by repetitive visual patterns that appear frequently amongimages. Local features derived from these burst patterns can redundantly matchothers, resulting in many invalid matches that vote over-estimated similarity scoresfor irrelevant images. Essentially, this problem can be mainly attributed to tworeasons, (i) the non-exclusive matching leads to one-to-many matches, (ii) the SPfails to filter burst matches that are closely located. To tackle this problem, aburstiness detection approach using geometric and visual word information of localfeatures is proposed. Firstly, a geometric filtering strategy is employed to removematches that are not consistent with global scale variation. Then, the one-to-onematching strategy is applied to detect and eliminate one-to-many matches. Finally,a down-weighting burstiness strategy is adopted to penalise the voting weight ofburst matches. Experimental results on three public datasets demonstrate that theproposed approach can achieve a comparable or even better accuracy over otherpopular approaches.

Considering the Prospects for Establishing a Packing Gerrymandering Standard

Abstract Courts have found it difficult to evaluate whether redistricting authorities have engaged in constitutionally impermissible partisan gerrymandering. The knotty problem is that no proposed standard has found acceptance as a convincing means for identifying whether a districting plan is a partisan gerrymander with knowable unconstitutional effects. We review five proposed standards for curbing gerrymandering. We take as our perspective how easily manageable and effective each would be to apply at the time a redistricting authority decides where to draw the lines or, post hoc, when a court is asked to decide whether an unconstitutional gerrymander has been enacted. We conclude that, among the five proposals, an equal vote weight standard offers the best prospects for identifying the form of unconstitutional gerrymanders that all but ensure one party is relegated to perpetual minority status.

Simple vs. Sophisticated Rules for the Allocation of Voting Weights

Representatives from differently sized constituencies form an assembly which takes political decisions by a weighted voting rule and adopts the ideal point of the weighted median amongst them. Preferences of each representative are supposed to coincide with the constituency’s median voter. Analytic results by Kurz et al. (J Polit Econ, 2017) for infinite chains of assemblies suggest that individual voters’ a priori influence on the collective decision can be equalized by allocating voting weight proportional to the square root of constituency sizes. This paper investigates numerically the performance of this simple square root rule and sophisticated variations, based on the Shapley value or the Penrose–Banzhaf power measure, when the number of constituencies is still “small”. Monte Carlo simulations indicate that power index-based rules are superior to simple rules.

Meaningful learning in weighted voting games: an experiment

By employing binary committee choice problems, this paper investigates how varying or eliminating feedback about payoffs affects: (1) subjects’ learning about the underlying relationship between their nominal voting weights and their expected payoffs in weighted voting games; (2) the transfer of acquired learning from one committee choice problem to a similar but different problem. In the experiment, subjects choose to join one of two committees (weighted voting games) and obtain a payoff stochastically determined by a voting theory. We found that: (i) subjects learned to choose the committee that generates a higher expected payoff even without feedback about the payoffs they received; (ii) there was statistically significant evidence of “meaningful learning” (transfer of learning) only for the treatment with no payoff-related feedback. This finding calls for re-thinking existing models of learning to incorporate some type of introspection.

Alliance-Building to Influence the EU: Measuring the Geography of Mutual Support

We assess a country’s influence on decision-making in the EU Council of Ministers not merely on the basis of the number of its votes, but based on a more refined measure that takes into account the voting behavior of other countries. A country that is likely to receive support from other countries will be more influential than a country with more votes, but which tends to be isolated in its policy preferences. We set out a novel quantitative methodology, which integrates the voting weight and the degree of support enjoyed by each country in one single measure, and we apply the methodology to a data set that is richer than existing data sets. We further use this measure (i) to assess whether the changes in voting weights from the Nice to the Lisbon Treaty have an influence on the odds whether countries get what they want when decisions are taken in the Council; and (ii) to study how these odds are affected by actor alignment in the Council.

Random subspace method with class separability weighting

AbstractThe random subspace method (RSM) is one of the ensemble learning algorithms widely used in pattern classification applications. RSM has the advantages of small error rate and improved noise insensitivity due to ensemble construction of the base‐learners. However, randomness may cause a reduction of the final ensemble decision performance because of contributions of classifiers trained by subsets with low class separability. In this study, we present a new and improved version of the RSM by introducing a weighting factor into the combination phase. One of the class separability criteria, J3, is used as a weighting factor to improve the classification performance and eliminate the drawbacks of the standard RSM algorithm. The randomly selected subsets are quantified by computing their J3 measure to determine voting weights in the model combination phase, assigning lower voting weight to classifiers trained by subsets with poor class separability. Two models are presented including J3‐weighted RSM and optimized J3 weighted RSM. In J3 weighted RSM, computed weighting values are directly multiplied by class assignment posteriors, whereas in optimized J3 weighted RSM, computed weighting values are optimized by a pattern search algorithm before multiplying by posteriors. Both models are shown to provide better error rates at lower subset dimensionality.

Computing the Power Distribution in the IMF

The International Monetary Fund is one of the largest international organizations using a weighted voting system. The weights of its 188 members are determined by a fixed amount of basic votes plus some extra votes for so-called Special Drawing Rights (SDR). On January 26, 2016, the conditions for the SDRs were increased at the 14th General Quota Review, which drastically changed the corresponding voting weights. However, since the share of voting weights in general is not equal to the influence, of a committee member on the committees overall decision, so-called power indices were introduced. So far the power distribution of the IMF was only computed by either approximation procedures or smaller games than then entire Board of Governors consisting of 188 members. We improve existing algorithms, based on dynamic programming, for the computation of power indices and provide the exact results for the IMF Board of Governors before and after the increase of voting weights. Tuned low-level details of the algorithms allow the repeated routine with sparse computational resources and can of course be applied to other large voting bodies. It turned out that the Banzhaf power shares are rather sensitive to changes of the quota.

A structural similarity-based label-smoothing algorithm for the post-processing of land-cover classification

ABSTRACTPost-processing is able to achieve a satisfactory classification performance with a low cost and simple assumption, making it widely used in the refinement of classification maps. In this study, a novel structural similarity-based label-smoothing algorithm is developed for the post-processing of land-cover classification. Inspired by the non-local (NL) means algorithm, the proposed algorithm assigns different voting weights to the neighbouring pixels for the identification of the central pixel. Here, the voting weight of a specific neighbouring pixel depends on its structural similarity to the central pixel. In this paper, two measurements are proposed to evaluate the similarity between pixels: (1) a consistency criterion; and (2) a histogram similarity criterion. The proposed algorithm was tested on three remote-sensing images. The experimental results confirm that the proposed algorithm reduces the classification noise and preserves the detail and structural information at the same time. Compared to the traditional post-processing approaches (e.g., majority voting), the proposed algorithm exhibits a more satisfactory performance.

Can electors combat corruption? Institutional arrangements and citizen behaviour

AbstractStudies interested in the cross‐national levels of corruption have concluded that specific institutional characteristics drive the aggregate variation. In countries with high institutional clarity and plurality electoral systems, corruption tends to be lower since increased voter monitoring and clarity of responsibility incentivise politicians to deliver virtuous policies. However, the underlying accountability mechanism has never been tested at the individual level. It is still unclear whether (1) voters do place voting weights on corruption, and (2) whether these weights vary in response to aggregate institutional characteristics. In this article, survey data from 23 democracies is used to put the accountability micro‐mechanism to this test. While there is some evidence that voters do vote on the basis of corruption, the moderating effect of institutional characteristics is not as strong as previously thought.