Weighted Voting Rule Research Articles

Voting Power of Citizens in a Democracy

Shapley and Shubik in 1954 proposed an index to measure the relative voting power of members of a decision-making body, given their weights in the said body. In this article, we have tried to investigate whether one can ensure equal voting power for all the citizens in a democracy through their respective representatives in the state legislature. The article shows that if the citizens realise their voting power through legislators and the number of constituencies in a democracy are at most four, then there does not exist any weighted voting rule such that the citizens enjoy equal voting power. JEL: C71, D71, D72

Ensemble classification for predicting the malignancy level of pulmonary nodules on chest computed tomography images.

Early identification and classification of pulmonary nodules are essential for improving the survival rates of individuals with lung cancer and are considered to be key requirements for computer-assisted diagnosis. To address this topic, the present study proposed a method for predicting the malignant phenotype of pulmonary nodules based on weighted voting rules. This method used the pulmonary nodule regions of interest as the input data and extracted the features of the pulmonary nodules using the Denoising Auto Encoder, ResNet-18. Moreover, the software also modifies texture and shape features to assess the malignant phenotype of the pulmonary nodules. Based on their classification accuracy (Acc), the different classifiers were assigned to different weights. Finally, an integrated classifier was obtained to score the malignant phenotype of the pulmonary nodules. The present study included training and testing experiments conducted by extracting the corresponding lung nodule image data from the Lung Image Database Consortium-Image Database Resource Initiative. The results of the present study indicated a final classification Acc of 93.10±2.4%, demonstrating the feasibility and effectiveness of the proposed method. This method includes the powerful feature extraction ability of deep learning combined with the ability to use traditional features in image representation.

Power, Control, and the Logic of Substitution in Institutional Design: The Case of International Climate Finance

AbstractHow do powerful states control international organizations (IOs)? In contrast to the conventional wisdom that treats weighted voting rules as the primary means that powerful states use to codify their asymmetric control in institutional design, we propose that funding rules are equally important. Our framework develops a logic of substitution whereby permissive earmark rules—that allow donors to stipulate how their contributions to an IO are used—are a design substitute for weighted voting from wealthy states’ perspective. Whether asymmetric control is incorporated in design through voting or funding rules depends on whether egalitarian norms emphasizing political and legal equality, or shareholder norms emphasizing influence commensurate with financial power, govern voting and representation rights at the IO. Focusing on the domain of climate finance, we demonstrate that weighted voting rules are used at international climate finance institutions (ICFIs) associated with multilateral development banks, but that wealthy states pursued permissive earmark rules at ICFIs within the United Nations system where egalitarian norms are strong. In this way, powerful donors can exert control over resource allocation even when developing states appear to hold equal influence on governing bodies. In addition to providing a reassessment of how power translates into control at IOs, our framework offers insight into forum-shopping behavior and sheds light on substitution dynamics that involve other dimensions of design across a range of issue areas.

Weighted random forests for fault classification in industrial processes with hierarchical clustering model selection

In this paper, a hierarchical clustering selection based weighted random forests scheme is proposed for fault classification in complex industrial processes. Model diversity and the strength of each model are deemed to be two key issues for the performance of ensemble learning method. To improve the diversity between classification trees and the performance of individual classification trees in random forests, the hierarchical clustering method is applied for offline model selection in random forests, which can simultaneously reduce the online fault classification complexity. Meanwhile, the weighted voting rule is used in random forests instead of majority voting, in order to boost the good performance models and weaken the bad ones. Detailed comparative studies between proposed method and conventional methods have been carried out through the Tennessee Eastman (TE) benchmark process.

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.

A note on the direct democracy deficit in two-tier voting

A large population of voters with single-peaked preferences are partitioned into disjoint constituencies. Collective decisions are taken by their representatives, one from each constituency, according to a weighted voting rule. It is assumed that each representative’s ideal point perfectly matches that of the respective constituency median and that top-tier decisions are in the voting game’s core. The resulting representative-democratic voting outcomes generally differ from those of a direct-democratic, single-tier system. The expected discrepancy varies with the voting weight allocation. It is minimized by weights proportional to constituency population sizes only if citizens differ sufficiently more between than within constituencies. Weights proportional to the square root of population sizes perform better if all citizens have independent and identically distributed ideal points.

Strategy-proofness and weighted voting

A strict social welfare function (SSWF) that always yields an asymmetric binary relation with a single maximal alternative induces a social choice rule on its domain. It is known that if the induced rule is strategy-proof then it can also be generated by a SSWF satisfying non-reversal. This paper proves that a SSWF satisfying anonymity and IIA satisfies non-reversal if and only if it is a weighted voting rule. If there are less than six voters then a SSWF satisfying neutrality and IIA satisfies non-reversal if and only if it is a weighted voting rule, but this equivalence does not hold for more than five voters.

The Role of the World Bank in Poverty Alleviation and Human Development in the Twenty-First Century: An Introduction

This month, October 2007, more than 140 journals worldwide are participating in an effort to raise awareness and stimulate research on a global theme of poverty and human development. In this spirit, Global Governance presents this special issue on the World Bank, the preeminent international aid agency whose core mission is the alleviation of poverty and the promotion of human and economic growth. Established on 1 July 1944, in Bretton Woods, New Hampshire, by the victors of World War II, the World Bank (hereafter the Bank) was designed to provide needed capital and technical assistance to rebuild postwar Europe. Since then, the Bank has transformed into a much larger and more broadly defined institution, self-characterized by the banner hanging in its Washington, DC, lobby: Our Dream Is a World Free of Poverty. The World Bank Group's (1) mandates and activities reflect an understanding of development that has dramatically expanded over the past sixty years. Today the Bank provides loans, grants, technical assistance, and highly influential research and data on issues as varied as infrastructure, gender, sustainable development, AIDS prevention and treatment, anticorruption, and postconflict reconstruction. Yet the years have taken a toll on the Bank. There is little, if any, consensus on whether the Bank has been successful in its endeavors. On the one hand, Bank proponents laud statistics demonstrating the dramatic reduction in absolute poverty and other indicators of economic growth and human development. On the other hand, Bank critics--an ever growing group--dispute these claims, providing their own interpretation of the evidence to argue that the Bank has not been effective in fostering equitable, sustained growth or human development, and in some instances has contributed to the perpetuation of poverty in many areas of the developing world. Whether you agree with the former or the latter statement, it is difficult to dispute that the tremendous growth of antiglobalization protest movements in the 1990s has made the World Bank a very popular target for metaphorical--and sometimes quite literal--tomato throwing. It is widely perceived by those inside and outside the institution that the Bank is in crisis. The first aspect of this crisis concerns the Bank's legitimacy. Critics lambaste the Bank for its ideological rigidity, pervasive corruption within aid programs, and weaknesses in bureaucratic transparency and accountability mechanisms. The Bank's legitimacy is further damaged by the perceived lack of democracy in its organizational governance, epitomized by the weighted voting rules of the executive board and the gentlemen's agreement underlying the selection process of the Bank presidency. This has led many critics to see the Bank as the handmaiden of its most powerful member state, the United States. At the same time, unchecked mission creep, persistent gaps between policy mandates and performance, and a checkered history of loan results have given rise to criticism of the Bank's effectiveness. And the abundance of private capital and the observable decline in demand for Bank lending from major middle-income countries give critics from both extremes of the political spectrum cause to question the very raison d'etre of the Bank. Since the Bank's fiftieth anniversary, in 1994, the debate on whether to demolish, reinvent, or rescue the Bank has been a favorite topic of nongovernmental organizations (NGOs), academics, and DC Beltway think tanks. (2) All of these criticisms have been compounded by the recent controversial departure of the Bank's president, Paul Wolfowitz, as a result of his involvement in the promotion and pay raise of his former girlfriend, Bank staffer Shaha Ali Riza. European executive directors opposed Wolfowitz's intention to remain in the top job amid an unprecedented staff revolt and media circus over the hypocrisy of the self-depicted anticorruption champion. …

First and Second Best Voting Rules in Committees

A group of people with identical preferences but different abilities in identifying the best alternative (e.g., a jury) takes a vote to decide between two alternatives. The first best voting rule is a weighted voting rule that takes into account the different individual competences, and is therefore not anonymous (i.e., the voters' identities matter). Under this rule, it is rational for group members to vote according to their true opinions, or informatively. This is not true for an anonymous voting rule, under which some group members may have an incentive to vote non-informatively. Sophisticated, strategic voters may therefore vary their voting strategies according to the voting rule used, rather than simply voting informatively. However, this paper shows that the best anonymous and monotone voting rule does not depend on whether the voters, or some of them, actually do so. A single, second best, rule gives the highest expected utility for any number of strategic voters.

First and second best voting rules in committees

A committee of people with common preferences but different abilities in identifying the best alternative (e.g., a jury) votes in order to decide between two alternatives. The first best voting rule is a weighted voting rule that takes the different individual competences into account, and is therefore not anonymous, i.e., the voters’ identities matter. Under this rule, it is rational for the committee members to vote according to their true opinions, or informatively. This is not necessarily true for an anonymous voting rule, under which members may have an incentive to vote non-informatively. Thus, strategic, sophisticated voters may vary their voting strategies according to the voting rule rather than naively voting informatively. This paper shows that the identity of the best anonymous and monotone (i.e., quota) voting rule does not depend on whether the committee members are strategic or naive or whether some are strategic and some are naive. One such rule, called the second best rule, affords the highest expected utility in all cases. “Wasn’t he sweet?” said Yossarian. “Maybe they should give him three votes.” Joseph Heller,

Voting in fuzzy rule-based systems for pattern classification problems

In this paper, we examine two kinds of voting schemes in fuzzy rule-based systems for pattern classification problems. One is the voting by multiple fuzzy if-then rules in a single fuzzy rule-based classification system. The other is the voting by multiple fuzzy rule-based classification systems. First, we discuss the voting by multiple fuzzy if-then rules, which is used as a fuzzy reasoning method for classifying input patterns in a single fuzzy rule-based classification system. The performance of the voting by multiple fuzzy if-then rules is examined by computer simulations on the iris data. Next, we discuss the voting by multiple fuzzy rule-based classification systems. Three voting methods (i.e., a perfect unison rule, a majority rule, and a weighted voting rule) are used for combining classification results by multiple fuzzy rule-based classification systems. Finally, we compare the performance of fuzzy rule-based classification systems with that of other classification methods such as neural networks and statistical techniques by computer simulations on some well-known test problems.

The weighted voting rule in the EU's Council of Ministers, 1958–1995: Intentions and outcomes

We consider the qualified majority voting rule in the Council of Ministers (CM) of the European Union (EU). Using the Banzhaf index—which, we argue, is the most appropriate for measuring the a priori voting power of members in the CM—we analyse the distribution of voting power of CM members in the various phases of expansion of the EU. We compare this distribution to the distribution of voting weights in the CM and the distribution of population in the EU. Finally, we assess the responsiveness (or volatility) of the voting rule in question.

On the Possibility of Faithfully Representative Committees

By faithful representation we mean the delegation of decision making to a relatively small committee that, using a weighted voting rule, will for each pair of alternatives make sincere choices identical to those that would be made by the society as a whole, and with the same vote margins. We show that for any society, no matter how large, faithful representation is possible by a committee with no more than m(m − 1)/2 members, where m is the number of alternatives. We also show that for any society, no matter how nonideological the bulk of its electorate, social preferences can be faithfully represented by a committee whose members all have singlepeaked or single-troughed preferences. Thus, all societies can be faithfully represented by a committee whose members see the world in unidimensional terms—that is, representatives can share a coherent ideological perspective even though the electorates they represent lack such a perspective. We further show that the usual mechanisms of proportional representation and the modified form of proportional representation recently proposed by Chamberlin and Courant (1983) do not guarantee faithful representation, and we discuss mechanisms that may provide faithful representation, even in a context in which new alternatives can arise.

Optimizing group judgmental accuracy in the presence of interdependencies

Consider a group of people confronted with a dichotomous choice (for example, a yes or no decision). Assume that we can characterize each person by a probability, pi, of making the 'better' of the two choices open to the group, such that we define 'better' in terms of some linear ordering of the alternatives. If individual choices are independent, and if the a priori likelihood that either of the two choices is correct is one half, we show that the group decision procedure that maximizes the likelihood that the group will make the better of the two choices open to it is a weighted voting rule that assigns weights, wi, such that

The accuracy of group majority decisions in groups with added members

Analytic results indicate that many heads often can be better than one even when none of the added heads is as individually competent as the first. We define individual competence (accuracy) in a dichotomous choice situation as the probability Pi of making the 'correct' or 'better' choice.~ Condorcet (1785) shows that if each person has equal competence, and if that competence, pi, is greater than chance (.5), then the accuracy of majority choice increases monotonically towards infallibility with increasing numbers of voters. Owen, Grofman and Feld (1981) generalize the Condorcet Theorem to verify that as long as the average competence of a group is greater than chance, then the competence of the group majority increases towards one as the group becomes larger. However, the practical problem in collective decision making often is to ascertain whether adding a particular set of persons to the decision-making group will add or detract from the competence of the decisions made. Shapley and Grofman (1981) and Nitzan and Paroush (1980, 1982) show that we can obtain the maximum competence with a weighted voting rule, with the weights monotonically related to the individual competences (according to a simple function that they specify). However, the competence of particular persons often is unknown; and in any case, weighting according to competence often is impractical. Consequently, we follow Grofman (1975, 1978); Margolis (1976); Owen, Grofman and Feld (1981); and Grofman, Owen and Feld