A Note on the Probability of Having a Strong Condorcet Winner

In an election, a strong Condorcet winner is a candidate who is top-ranked by more than 50% of the voters. The purpose of this note is to provide some algebraic representations for the probability of having a strong Condorcet winner in three-candidate elections. Three alternative procedures for generating voting situations are considered: the Impartial Culture condition, the Impartial Anonymous Culture condition and the Maximal Culture condition. It turns out that the conclusions we obtain strongly depend on the way for generating voting situations.     

Condorcet meets Bentham

We show that if the statistical distribution of utility functions in a population satisfies a certain condition, then a Condorcet winner will not only exist, but will also maximize the utilitarian social welfare function. We also show that, if people’s utility functions are generated according to certain plausible random processes, then in a large population, this condition will be satisfied with very high probability. Thus, in a large population, the utilitarian outcome will be selected by any Condorcet consistent voting rule.     

Condorcet efficiency of two stage constant scoring rules

Previous research has developed a representation for the Condorcet efficiency of plurality and negative plurality rules on three candidates for large electorates under the impartial culture condition. This study considers the two stage voting rules on three candidates, plurality elimination and negative plurality elimination. A representation is obtained for the Condorcet efficiency of each for large electorates under impartial culture. The Condorcet efficiencies of both rules are equal and are shown to be substantially greater than the Condorcet efficiency of plurality and negative plurality.     

Production in incomplete markets: Expectations matter for political stability

In the present paper we study voting-based corporate control in a general equilibrium model with incomplete financial markets. Since voting takes place in a multi-dimensional setting, super-majority rules are needed to ensure existence of equilibrium. In a linear–quadratic setup we show that the endogenization of voting weights (given by portfolio holdings) can give rise to – through self-fulfilling expectations – dramatical political instability, i.e. Condorcet cycles of length two even for very high majority rules.     

Maximin choice of voting rules for committees

In the context of a probabilistic voting model with dichotomous choice, we investigate the consequences of choosing among voting rules according to the maximin criterion. A voting rule is the minimum number of voters who vote favorably on a change from the status quo required for it to be adopted. We characterize the voting rules that satisfy the maximin criterion as a function of the distribution of voters’ probabilities to favor change from the status quo. We prove that there are at most two maximin voting rules, at least one is Pareto efficient and is often different to the simple majority rule. If a committee is formed only by “conservative voters” (i.e. voters who are more likely to prefer the status quo to change) then the maximin criterion recommends voting rules that require no more voters supporting change than the simple majority rule. If there are only “radical voters”, then this criterion recommends voting rules that require no less than half of the total number of votes.Received: June 2003, Accepted: September 2004, JEL Classification: D71Salvador Barberá, Carmen Beviá, Mirko Cardinale, Wioletta Dziuda, Joan Esteban, Mahmut Erdem, Bernard Grofman, Matthew Jackson, Kai Konrad, Raul Lopez, Jordi Massó, Hugh Mullan, Shmuel Nitzan, Ana Pires do Prado, Elisabeth Schulte, Arnold Urken and two anonymous referees provided helpful comments. Finally, I also acknowledge financial support from Capes, Brazilian Ministry of Education and Spanish Ministry of Science and Technology (Project BEC2002-02130).     

The asymptotic strategyproofness of scoring and Condorcet consistent rules

We calculate the proportion of preference profiles where “small” coalitions of agents may successfully manipulate any given scoring rule and show that it decreases to zero at a rate proportional to with the number of agents. If agents have to incur a small cost in order to decide how to manipulate the voting rule, our results imply that scoring rules are robust to such manipulation in large groups of agents. We present examples of asymptotically strategyproof and non strategyproof Condorcet consistent rules. We thank Eric Maskin and Shmuel Nitzan for useful discussions. We also thank seminar participants at Harvard, Haifa, and Technion universities for their comments. Neeman is grateful for the generous financial support of the NSF under grant SBR-9806832.     

On intermediate utility functions

Intermediate utility functions have been recently introduced by Persson and Tabellini (2000, Political Economics: Explaining Economics Policy, MIT Press, Cambridge) and ensure the existence of a majority voting equilibrium at multi-dimensional voting. Here, we show that monotone transforms of these utility functions also are sufficient for the existence of a Condorcet winner.     

A comparative analysis of measures of social homogeneity

Social homogeneity refers to the degree to which the preferences of individuals in a society tend to be alike. A number of studies have been conducted to determine whether or not a relationship exists between various measures of social homogeneity and the probability that a Condorcet winner exists. In this study, it is shown that a strong general relationship of this type does not exist for measures of social homogeneity which account only for the proportions of individuals with various preference rankings. That is, for measures which account for these proportions but not for the preference rankings to which they are assigned. Profile specific measures of homogeneity do account for the preference rankings to which the proportions of voters are assigned. A much stronger relationship exists between profile specific measures of homogeneity and the probability that a Condorcet winner exists than for non-profile specific measures. In particular, Kendall's Coefficient of Condordance is shown to dominate twenty other measures of social homogeneity in terms of the strength of its relationship to the probability that a Condorcet winner exists.     

Measuring voting power in an international institution: the United States and the inter-American development bank

This paper applies a measure of relative voting power to the weighted voting system of the Inter-American Development Bank (IADB). Almost all assessments of internal governance of the IADB and other international financial institutions make reference to members' votes as a proxy for relative influence. But as this paper demonstrates, voting weights are misleading. The number of votes a country has in a weighted voting system does not necessarily denote its ability to affect outcomes. The conventional wisdom holds that the United States is omnipotent in the IADB because it has a large number (over 30 percent) of all the votes. This paper reveals that the U.S. obtains much more control over outcomes than originally intended by the institutions' designers. Received: September 2000 / Accepted: October 2001     

Targeting and political support for welfare spending

This paper investigates the political support for social assistance policies in a model in which incomes are stochastic (so that welfare policies have an insurance benefit) and unequal ex ante (so that welfare policies have a redistributive effect). With self-interested voting, narrow targeting may so reduce the probability of receiving benefits for the majority that the majority prefers to eliminate benefits altogether, even though the cost of narrowly targeted benefits is close to zero. In contrast, a majority of self-interested voters always supports positive welfare benefits when the policy is targeted sufficiently broadly. If voters are somewhat altruistic, the impact of targeting on political support for welfare spending diminishes but does not disappear. Received: July 1999 / Accepted: May 30, 2000     

累积投票制强制执行能否保护中小股东利益？——基于断点回归的实证检验

以2008—2020年A股上市公司为样本,运用精确断点回归方法检验累积投票制强制执行对控股股东利益侵占的影响,并进一步考察股权自由现金流水平在其中发挥的调节效应。研究发现：累积投票制强制执行政策能够显著抑制控股股东利益侵占,该政策能够促使上市公司累积投票制的实施,并通过制衡机制、抵御机制及预防机制改善公司治理,保护中小股东利益。进一步研究表明,在股权自由现金流水平越高的企业,累积投票制强制执行越有效。因此,累积投票制强制执行政策具有一定的合理性,应予以坚持并进一步推行。     

On stable rules for selecting committees

A voting rule is said to be stable if it always elects a fixed-size subset of candidates such that there is no outside candidate who is majority preferred to any candidate in this set whenever such a set exists. Such a set is called a Weak Condorcet Committee (WCC). Four stable rules have been proposed in the literature. In this paper, we propose two new stable rules. Since nothing is known about the properties of the stable rules, we evaluate all the identified stable rules on the basis of some appealing properties of voting rules. We show that they all satisfy the Pareto criterion and they are not monotonic. More, we show that every stable rule fails the reinforcement requirement.     

Local monotonicity of power: Axiom or just a property?

This paper discusses whether Local Monotonicity (LM) should be regarded as a property of the power distribution of a specific voting game under consideration, indicated by a power measure, or as a characteristic of power per se. The latter would require reasonable power measures to satisfy a corresponding LM axiom. The former suggests that measures which do not allow for a violation of LM fail to account for dimensions of power which can cause nonmonotonicity in voting weight. Only if a measure is able to indicate nonmonotonicity, it can help design voting games for which power turns out to be monotonic. The argument is discussed in the light of recent extensions of traditional power indices.     

基于张量投票的图像超分辨率算法

张量投票算法在提取图像主观轮廓上具有良好的效果。文章提出了一种基于张量投票的图像超分辨率算法。首先,用二维张量矩阵存储低分辨率图像各像素点所处的位置特征信息,并利用稀疏张量投票将特征信息进行加强,再使用稠密张量投票产生高分辨率图像对应的二维张量矩阵,此张量矩阵包含了视觉特性强的边缘信息,最后利用该边缘信息指导高分辨率图像的重构。实验结果表明,该方法得到的高分辨率图像信噪比高、视觉效果好。     

Epistemic democracy with correlated voters

We develop a general theory of epistemic democracy in large societies, which subsumes the classical Condorcet Jury Theorem, the Wisdom of Crowds, and other similar results. We show that a suitably chosen voting rule will converge to the correct answer in the large-population limit, even if there is significant correlation amongst voters, as long as the average covariance between voters becomes small as the population becomes large. Finally, we show that these hypotheses are consistent with models where voters are correlated via a social network, or through the DeGroot model of deliberation.     

Randomized decision rules in voting games: a model for strict proportional power

The concept of strict proportional power is introduced, as a means of formalizing a desire to avoid discrepancy between the seat distribution in a voting body and the actual voting power in that body, as measured by power indices in common use. Proportionality is obtained through use of a randomized decision rule (majority rule). Some technical problems which arise are discussed in terms of simplex geometry. Practical implications and problems in connection with randomized decision rules are indicated.     

Voting on welfare reform Stemming migration, assisting the needy, or promoting economic growth?

This paper examines the influences on voting by members of the House of Representatives on the Carter Administration's welfare reform legislation. The analysis finds some support for the hypothesis that voting by national legislators responded to the potential mobility of welfare recipients from low to high benefit states. Defining the public interest as promoting economic growth and the special interest as increasing redistribution, the results also provide evidence in support of the Stigler hypothesis that politically secure legislators are better able to vote the public, as opposed to the special, interest. Received: July 15, 1998 / Accepted: August 6, 1999     

Weighted representative democracy

We propose a new system of democratic representation. Any voter can choose any legislator as her representative; thus, different legislators can represent different numbers of voters. Decisions in the legislature are made by weighted majority voting, where the weight of each legislator is determined by the number of voters she represents. We show that, if the size of the electorate is very large, then with very high probability, the decisions obtained in the legislature agree with those which would have been reached by a popular referendum decided by simple majority vote.     

Election forecasts: Cracking the Danish case

Election forecasting models based on voting theories and estimated via regression analysis are routinely available for virtually all advanced industrial democracies. Denmark, however, offers an exception, for no such prediction equations have been published on the Danish case. This absence has sometimes been attributed to the puzzling nature of economic voting there, along with the complexity of its multi-party system, which renders formulation of the dependent variable problematic. We attempt to overcome these obstacles, offering a “synthetic” forecasting model for Danish national election outcomes, 1964–2015. The regression model, based on the variables of economic growth and vote intention, performs well, by various tests. Finally, we apply it, ex ante fashion, to the 2019 contest, where the prediction favored the Social Democratic led coalition, an outcome that came to pass.     

On the performance of voting systems in spatial voting simulations

We study the performance of voting systems in terms of minimizing the overall social disutility of making a collective choice in an univariate voting space with ideological voting and perfect information. In order to obtain a distribution of the performance indicator for each of the 12 systems chosen for this study—Baldwin’s Method, Black’s Method, The Borda Count, Bucklin’s Grand Junction System, Coombs’ Method, Dodgson’s System, Instant Run-Off Voting, Plurality, Simpson’s MinMax, Tideman’s Ranked Pairs, Schulze’s Beatpath Method, and Two-Round Majority—we simulate elections using an Agent-Based Computational approach under several different distributions for voters and candidates positioning, with up to 15 available candidates. At each iteration, voters generate complete and strict ordinal utility functions over the set of available candidates, based on which each voting system computes a winner. We define the performance of a system in terms of its capability of choosing among the available candidates the one that minimizes aggregate voter disutility. As expected, the results show an overall dominance of Condorcet completion methods over the traditional and more widely used voting systems, regardless of the distributions of voter and candidate positions.