长程选举模型的平均场极限

本文研究长程选举模型的平均场极限，利用对偶关系和特征函数方法证得长程选举模型的平均场极限满足下列微分方程：     

公平性与数学化：（I）选举理论

作在这一系列章中，将用不多的数学知识讨论由公平性问题派生出来的三个社会学课题；即选举理论，权力系数与公平分配。数学家的研究可以归结为这么一个结论：社会选择，一个难圆的梦。本篇讨论各种常用选举方法的利弊，并由此讨论选举理论中的一个重要的结果-Arrow定理，完全公平的选举系统不可能存在。     

公平性与数学化(Ⅰ)选举理论

作者在这一系列文章中,将用不多的数学知识讨论由公平性问题派生出来的三个社会学课题：即选举理论,权力指数与公平分配。数学家的研究可以归结为这么一个结论：社会选择,一个难圆的梦。本篇讨论各种常用选举方法的利弊,并由此讨论选举理论中的一个重要的结果——Ａｒｒｏｗ定理：完全公平的选举系统不可能存在     

一种安全高效的匿名电子选举方案

随着网络的迅速发展,电子选举已经成为了电子政务的一个重要应用方面,与传统选举方式相比,电子选举提供了更大的灵活性和更高的效率.基于格上的难题小整数解问题(SIS)和非齐次小整数解问题(ISIS),提出了一种安全高效的匿名电子选举方案,除了满足电子选举应满足的合法性、匿名性、可验证性、无收据性等性能之外,与以前方案相比,方案可以保证在后量子时代依然安全.     

随机环境中选举模型的Hydrodynamic极限

本文研究随机环境中选举模型的Hydrodynamic极限。首先，我们通过图表示构造出随机环境中的选举模型，然后利用对偶关系得到了该粒子模型的宏观偏微分方程。     

等价类空间中离散时间选举-排它混合模型的遍历性

利用李雅谱诺夫函数首先证明了等价类空间中离散时间非紧邻选举模型是正常返的,且首次击中D0时刻的阶为15/14,其次给出了等价类空间中离散时间非紧邻选举模型与排它过程的混合模型遍历性的一个判别准则,从而推广和改进了紧邻情形的相应结果.     

基于连通度的多跳传输路由算法

针对由各种功能不同的传感器构成的无线传感器网络,提出了一种基于连通度的多跳传输的路由协议(MHTA),该算法根据网络中节点能量分布的不同,引入权重因子作为调节参数进行簇头选举,选举过程中综合考虑了各节点消耗能量,与基站的邻近程度和周围邻节点的数目.为了减少在数据传输过程中消耗的能量,提出了一种簇内多跳和簇间多跳相结合进行数据传输的方法.模拟实验结果证明:该算法能够降低簇头能量消耗,均衡网络负载,从而延长网络生存时间.     

国内外学术活动简讯

1.中国数学会第四次全国代表大会于1983年10月22～27日在武汉举行.会议推选我国著名的老一辈数学家华罗庚、苏步青、江泽涵、柯召、吴大任为中国数学会名誉理事长;吴新谋、赵访熊、李国平为名誉理事.会议选举产生了中国数学会第四届理事会,并在会后以通讯选举的方式产生了理事会领导人选:     

等价类空间中离散时间选举一排它混合模型的遍历性

利用李雅谱诺夫函数首先证明了等价类空间中离散时间非紧邻选举模型是正常返的,且首次击中D0时刻的阶为15/14,其次给出了等价类空间中离散时间非紧邻选举模型与排它过程的混合模型遍历性的一个判别准则,从而推广和改进了紧邻情形的相应结果.     

中国数学会1990年学术会议概况

一、中国教学会计算数学学会第三届理事会第一次会议 1990年5月3日至5日在北京大学召开,50多名理事出席了这次会议。徐福臻秘书长做了第二届理事会的工作报告,与会理事讨论了学会工作,讨论修改并通过了新的会章。会议选举产生了常务理事会,选举周毓麟为理事长,李岳生、应隆安、孙继广为副理事长,李荫藩为秘书长。大会一致通过冯康为名誉理事长,徐利洽为名誉理事。     

Modeling social services performance: a four-stage DEA approach to evaluate fundraising efficiency,capacity building,service quality,and effectiveness in the nonprofit sector

The Swedish electoral system exhibits significant levels of proportionality compared with the systems used in other countries. However, it has several deficiencies that could be corrected. Therefore, this paper (a) evaluates the current Swedish electoral system by identifying the imbalances in the representation of political parties and the sizes of the electoral constituencies that can occur and (b) presents two proposals for improvement that seek to correct the previously identified deficiencies. The first proposal consists of a slight modification of the current system that applies when parties get more seats than they proportionally deserve according to their global number of votes, as occurred in the 2010 election. In this case, the proposal includes a criterion so that the overrepresented parties return their excess seats. The second proposal relies on the implementation of biproportional allotments and on the replacement of the electoral thresholds of 4 % of the total votes nationwide and 12 % of the votes in a given constituency by a new threshold based on a reduction in the number of votes of the parties. The application of any of these proposals to the Swedish election held in 2010 reveals that the deficiencies in the representation of political parties are eliminated. Furthermore, the second proposal also corrects the deficiencies in the sizes of the electoral constituencies for Sweden.     

Game theory and the french apparentements of 1951

The French apparentement electoral system is modeled as an-person cooperative game without side payments. The players are seat-maximizing political parties. Each electoral district constitutes an independent game. The Von-Neumann and Morgenstern solution is applied to generate theoretical postdictions for a cross section of observations from the 1951 French parliamentary elections. In statistical terms, this solution has a modest, but significant, degree of explanatory power.     

Error minimization methods in biproportional apportionment

One of the most active research lines in the area of electoral systems to date deals with the Biproportional Apportionment Problem, which arises in those proportional systems where seats must be allocated to parties within territorial constituencies. A matrix of the vote counts of the parties within the constituencies is given, and one has to convert the vote matrix into an integer matrix of seats ??as proportional as possible?? to it, subject to the constraints that each constituency be granted its pre-specified number of seats, each party be allotted the total number of seats it is entitled to on the basis of its national vote count, and a zero-vote zero-seat condition be satisfied. The matrix of seats must simultaneously meet the integrality and the proportionality requirement, and this not infrequently gives rise to self-contradictory procedures in the electoral laws of some countries. Here we discuss a class of methods for Biproportional Apportionment characterized by an ??error minimization?? approach. If the integrality requirement is relaxed, fractional seat allocations (target shares) can be obtained so as to achieve proportionality at least in theory. In order to restore integrality, one then looks for integral apportionments that are as close as possible to the ideal ones in a suitable metric. This leads to the formulation of constrained optimization problems called ??best approximation problems?? which are solvable in polynomial time through the use of network flow techniques. These error minimization methods can be viewed as an alternative to the classical axiomatic approach introduced by Balinski and Demange (in Math Oper Res 14:700?C719, 1989a; Math Program 45:193?C210, 1989b). We provide an empirical comparison between these two approaches with a real example from the Italian Elections and a theoretical discussion about the axioms that are not necessarily satisfied by the error minimization methods.     

Social utility functions for strategic decisions in probabilistic voting models

This paper studies societies which have probabilistic voting that is smooth, scalable and unbiased. Its results establish that, in such societies, the decisions of vote-seeking candidates who start at a common location (such as the status quo for the society's policies and/or the same allocation of campaign resources) contain implicit rationality properties. In particular, it shows that in every such society there exist social utility functions which simultaneously rationalize the directional Nash behavior of candidates, the stationary electoral equilibria, and the non-degenerate local electoral equilibria which can occur at these locations. This is shown to be true both for unconstrained and for constrained sets of possible candidate locations. An example of such a utility function (which occurs in every one of the societies under consideration) is also provided.     

Gerrymander-proof representative democracies

International Journal of Game Theory - This article is devoted to the analysis of electoral systems involving two step procedures. It appears that designers are able to manipulate the result of...     

Maximizing political efficiency via electoral cycles: An optimal control model

The exchange between an elected politician, such as a president, prime minister or a local governor and interest groups is analyzed as an optimization problem. The optimal control model shows the conditions required from regulatory policy and resource investment in order to maximize the politician's utility from the interest group's support. Given one interest group, such a policy includes two time intervals: Well in advance of the elections the politician in office should invest a constant level of resources, while for a certain period close to the elections the politician increases or decreases investment, depending on the electoral significance of that interest group. This proves that electoral cycles not only empirically exist, but also maximize the politician's utility from interest groups' support. Given several interest groups, at each point in time, the politician should invest in the group that contribute the most for his or her political interests.     

Simple and efficient classification scheme based on specific vocabulary

Assuming a binomial distribution for word occurrence, we propose computing a standardized Z score to define the specific vocabulary of a subset compared to that of the entire corpus. This approach is applied to weight terms (character n-gram, word, stem, lemma or sequence of them) which characterize a document. We then show how these Z score values can be used to derive a simple and efficient categorization scheme. To evaluate this proposition and demonstrate its effectiveness, we develop two experiments. First, the system must categorize speeches given by B. Obama as being either electoral or presidential speech. In a second experiment, sentences are extracted from these speeches and then categorized under the headings electoral or presidential. Based on these evaluations, the proposed classification scheme tends to perform better than a support vector machine model for both experiments, on the one hand, and on the other, shows a better performance level than a Na?ve Bayes classifier on the first test and a slightly lower performance on the second (10-fold cross validation).     

Bicolored graph partitioning, or: gerrymandering at its worst

This study is motivated by an electoral application where we look into the following question: how much biased can the assignment of parliament seats be in a majority system under the effect of vicious gerrymandering when the two competing parties have the same electoral strength? To give a first theoretical answer to this question, we introduce a stylized combinatorial model, where the territory is represented by a rectangular grid graph, the vote outcome by a “balanced” red/blue node bicoloring and a district map by a connected partition of the grid whose components all have the same size. We constructively prove the existence in cycles and grid graphs of a balanced bicoloring and of two antagonist “partisan” district maps such that the discrepancy between their number of “red” (or “blue”) districts for that bicoloring is extremely large, in fact as large as allowed by color balance.     

Bidimensional allocation of seats via zero-one matrices with given line sums

In some proportional electoral systems with more than one constituency the number of seats allotted to each constituency is pre-specified, as well as, the number of seats that each party has to receive at a national level. “Bidimensional allocation” of seats to parties within constituencies consists of converting the vote matrix V into an integer matrix of seats “as proportional as possible” to V, satisfying constituency and party totals and an additional “zero-vote zero-seat” condition. In the current Italian electoral law this Bidimensional Allocation Problem (or Biproportional Apportionment Problem—BAP) is ruled by an erroneous procedure that may produce an infeasible allocation, actually one that is not able to satisfy all the above conditions simultaneously. In this paper we focus on the feasibility aspect of BAP and, basing on the theory of (0,1)-matrices with given line sums, we formulate it for the first time as a “Matrix Feasibility Problem”. Starting from some previous results provided by Gale and Ryser in the 60’s, we consider the additional constraint that some cells of the output matrix must be equal to zero and extend the results by Gale and Ryser to this case. For specific configurations of zeros in the vote matrix we show that a modified version of the Ryser procedure works well, and we also state necessary and sufficient conditions for the existence of a feasible solution. Since our analysis concerns only special cases, its application to the electoral problem is still limited. In spite of this, in the paper we provide new results in the area of combinatorial matrix theory for (0,1)-matrices with fixed zeros which have also a practical application in some problems related to graphs.     

Local Nash Equilibrium in Multiparty Politics

We present a model of multi-party, spatial competition under proportional rule with both electoral and coalitional risk. Each party consists of a set of delegates with heterogeneous policy preferences. These delegates choose one delegate as leader or agent. This agent announces the policy declaration (or manifesto) to the electorate prior to the election. The choice of the agent by each party elite is assumed to be a local Nash equilibrium to a game form . This game form encapsulates beliefs of the party elite about the nature of both electoral risk and the post-election coalition bargaining game. It is demonstrated, under the assumption that is smooth, that, for almost all parameter values, a locally isolated, local Nash equilibrium exists.In the final section of the paper some empirical work is reviewed in order to obtain some insights into why parties do not simply converge to an electoral center in order to maximize expected vote shares.